%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL834_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:53:09 AM UTC 2026
% Result : Theorem 20.03s 9.65s
% Output : Refutation 20.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 110
% Syntax : Number of formulae : 222 ( 91 unt; 0 typ; 0 def)
% Number of atoms : 831 ( 239 equ; 0 cnn)
% Maximal formula atoms : 96 ( 3 avg)
% Number of connectives : 5090 ( 101 ~; 13 |; 55 &;4708 @)
% ( 17 <=>; 196 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 47 usr; 22 con; 0-5 aty)
% Number of variables : 726 ( 0 ^; 714 !; 12 ?; 726 :)
% 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_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ fun ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_decl,type,
it: dB > $o ).
thf(beta_decl,type,
beta: bool @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(abs_decl,type,
abs: dB > dB ).
thf(app_decl,type,
app: dB @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(var_decl,type,
var: nat > dB ).
thf(dB_size_decl,type,
dB_size: dB > nat ).
thf(liftn_decl,type,
liftn: nat > dB > nat > dB ).
thf(subst_decl,type,
subst: dB > dB > nat > dB ).
thf(substn_decl,type,
substn: dB > dB > nat > dB ).
thf(step1_decl,type,
step1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > ( TA @ list ) > $o ) ).
thf(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(foldr_decl,type,
foldr:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TA @ fun ) @ ( TB @ fun ) ) > ( TB @ list ) > TA > TA ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(sublist_decl,type,
sublist:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( nat @ fun ) ) > ( TA @ list ) ) ).
thf(shift_decl,type,
shift:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > nat > TA > ( TA @ ( nat @ fun ) ) ) ).
thf(fun1_decl,type,
fun1: type @ ( type @ fun ) @ ( type @ fun ) ).
thf(type_case_decl,type,
type_case:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( type @ fun ) @ ( type @ fun ) ) > type > TA ) ).
thf(typing_decl,type,
typing: ( type @ ( nat @ fun ) ) > dB > ( bool @ ( type @ fun ) ) ).
thf(typings_decl,type,
typings: ( type @ ( nat @ fun ) ) > ( dB @ list ) > ( bool @ ( type @ list @ fun ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(t1_decl,type,
t1: type ).
thf(t_a_decl,type,
t_a: type ).
thf(t_decl,type,
t: type ).
thf(a_decl,type,
a: dB ).
thf(as_decl,type,
as: dB @ list ).
thf(e_decl,type,
e: type @ ( nat @ fun ) ).
thf(ea_decl,type,
ea: type @ ( nat @ fun ) ).
thf(i_decl,type,
i: nat ).
thf(ia_decl,type,
ia: nat ).
thf(r_decl,type,
r: dB ).
thf(t2_decl,type,
t2: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(40,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_dB_Osimps_I7_J) ).
thf(260,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(97,axiom,
! [A: type @ list,B: type @ ( nat @ fun )] :
( ( A @ ( dB @ nil @ ( B @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
<=> ( A
= ( type @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_typings_Osimps_I1_J) ).
thf(486,plain,
! [A: type @ list,B: type @ ( nat @ fun )] :
( ( ( A
= ( type @ nil ) )
=> ( A @ ( dB @ nil @ ( B @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) )
& ( ( A @ ( dB @ nil @ ( B @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( A
= ( type @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(68,axiom,
! [A: type,B: type,C: dB @ list,D: nat,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_var__app__type__eq) ).
thf(365,plain,
! [A: type,B: type,C: dB @ list,D: nat,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(94,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(479,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(104,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_liftn_Osimps_I2_J) ).
thf(518,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(36,axiom,
a @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Beta_I3_J) ).
thf(234,plain,
a @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(72,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(379,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(101,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(511,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(33,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ it )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_subst__Var__IT) ).
thf(217,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ it )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(45,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_dB_Osimps_I6_J) ).
thf(276,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(48,axiom,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [D: type,E: type] :
( ( A
= ( E @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_typing__elims_I3_J) ).
thf(288,plain,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [D: type,E: type] :
( ( A
= ( E @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(51,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_appR) ).
thf(301,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(70,axiom,
! [TA: $tType,A: type,B: type,C: TA @ ( type @ fun ) @ ( type @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ ( TA @ type_case ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( TA @ ( type @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_type_Osimps_I6_J) ).
thf(372,plain,
! [TA: $tType,A: type,B: type,C: TA @ ( type @ fun ) @ ( type @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ ( TA @ type_case ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( TA @ ( type @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(504,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(26,axiom,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ? [E: type @ list] :
( ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
& ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_list__app__typeD) ).
thf(189,plain,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ? [E: type @ list] :
( ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
& ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(47,axiom,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_dB_Osimps_I9_J) ).
thf(284,plain,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_list_Oinject) ).
thf(152,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(87,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( B @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_apps__preserves__beta) ).
thf(448,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( B @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(58,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ it )
=> ( ( B @ it )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ it ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_IT_OBeta) ).
thf(321,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ it )
=> ( ( B @ it )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ it ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [E: TA,F: TA,G: TB] :
( ( F @ ( E @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( F @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_foldl__fun__comm) ).
thf(348,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [E: TA,F: TA,G: TB] :
( ( F @ ( E @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( F @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_foldl__Cons) ).
thf(480,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(77,axiom,
! [A: dB,B: type,C: dB,D: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_subject__reduction) ).
thf(397,plain,
! [A: dB,B: type,C: dB,D: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(46,axiom,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A )
=> ( A @ ( B @ var @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_typing_OVar) ).
thf(280,plain,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A )
=> ( A @ ( B @ var @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(49,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( a @ ( t @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ it )
=> ( ( t @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( a @ subst ) ) @ it ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_SI2) ).
thf(293,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( a @ ( t @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ it )
=> ( ( t @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( a @ subst ) ) @ it ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(76,axiom,
as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Beta_I1_J) ).
thf(396,plain,
as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(8,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_neq__Nil__conv) ).
thf(133,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_list_Osimps_I4_J) ).
thf(116,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(100,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Var__apps__neq__Abs__apps) ).
thf(507,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(107,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_dB_Osimps_I5_J) ).
thf(527,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(73,axiom,
! [A: type,B: type,C: type,D: type] :
( ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_type_Osimps_I2_J) ).
thf(381,plain,
! [A: type,B: type,C: type,D: type] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(109,axiom,
! [A: dB,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ! [D: dB] :
( ( A
= ( nat @ zero_zero @ ( B @ ( D @ subst ) ) ) )
=> ( C
!= ( D @ abs ) ) )
=> ( ! [D: dB] :
( ( A
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
=> ~ ! [D: dB] :
( ( A
= ( D @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_beta__cases_I3_J) ).
thf(534,plain,
! [A: dB,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ! [D: dB] :
( ( A
= ( nat @ zero_zero @ ( B @ ( D @ subst ) ) ) )
=> ( C
!= ( D @ abs ) ) )
=> ( ! [D: dB] :
( ( A
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
=> ~ ! [D: dB] :
( ( A
= ( D @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(35,axiom,
! [A: dB,B: dB @ list,C: nat] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ? [D: dB @ list] :
( ( A
= ( D @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
& ( D @ ( B @ ( beta @ ( dB @ step1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_head__Var__reduction) ).
thf(229,plain,
! [A: dB,B: dB @ list,C: nat] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ? [D: dB @ list] :
( ( A
= ( D @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
& ( D @ ( B @ ( beta @ ( dB @ step1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(67,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dB_Osimps_I8_J) ).
thf(361,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(61,axiom,
! [A: type,B: dB,C: type,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( nat @ zero_zero @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( B @ abs @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Abs) ).
thf(329,plain,
! [A: type,B: dB,C: type,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( nat @ zero_zero @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( B @ abs @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(90,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Abs__eq__apps__conv) ).
thf(461,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) )
=> ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(57,axiom,
! [TA: $tType,A: TA,B: TA @ ( nat @ fun ),C: nat,D: nat] :
( ( D = C )
=> ( ( C @ ( A @ ( D @ ( B @ ( TA @ shift ) ) ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_shift__eq) ).
thf(317,plain,
! [TA: $tType,A: TA,B: TA @ ( nat @ fun ),C: nat,D: nat] :
( ( D = C )
=> ( ( C @ ( A @ ( D @ ( B @ ( TA @ shift ) ) ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(18,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(169,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(91,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_appL) ).
thf(471,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(27,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_beta__cases_I2_J) ).
thf(193,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_sublist__singleton) ).
thf(547,plain,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(75,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subst__eq) ).
thf(393,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun ) @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( B @ ( TA @ step1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_not__step1__Nil) ).
thf(129,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun ) @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( B @ ( TA @ step1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(81,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(412,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(102,axiom,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_beta__cases_I1_J) ).
thf(513,plain,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_not__Cons__self) ).
thf(166,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(264,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(14,axiom,
ua @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Beta_I6_J) ).
thf(161,plain,
ua @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_substn_Osimps_I2_J) ).
thf(180,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(85,axiom,
! [A: dB,B: type,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( D @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_App) ).
thf(444,plain,
! [A: dB,B: type,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( D @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(12,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_list_Oexhaust) ).
thf(149,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(71,axiom,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Abs__App__neq__Var__apps) ).
thf(375,plain,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun ) @ ( TA @ fun )] :
~ ( A @ ( TA @ nil @ ( B @ ( TA @ step1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_not__Nil__step1) ).
thf(176,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun ) @ ( TA @ fun )] :
~ ( A @ ( TA @ nil @ ( B @ ( TA @ step1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( A @ ( B @ var @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_typing__elims_I1_J) ).
thf(204,plain,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( A @ ( B @ var @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(74,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(391,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(55,axiom,
t1 @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_T) ).
thf(313,plain,
t1 @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(63,axiom,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Var__apps__eq__Var__apps__conv) ).
thf(335,plain,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(25,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ it )
=> ( ( t @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ subst ) ) @ it ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_SI1) ).
thf(187,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ it )
=> ( ( t @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ subst ) ) @ it ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,axiom,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_sublist__nil) ).
thf(172,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( TB @ nil @ ( B @ ( TA @ ( TB @ foldr ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_foldr_Osimps_I1_J) ).
thf(113,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( TB @ nil @ ( B @ ( TA @ ( TB @ foldr ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) )
<=> ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_apps__eq__Abs__conv) ).
thf(219,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) )
=> ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(89,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Abs__apps__eq__Abs__apps__conv) ).
thf(451,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ list,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ cons ) ) @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_foldr_Osimps_I2_J) ).
thf(303,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ list,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ cons ) ) @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(98,axiom,
! [A: dB @ list,B: dB,C: nat] :
( ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Var__eq__apps__conv) ).
thf(494,plain,
! [A: dB @ list,B: dB,C: nat] :
( ( ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) )
=> ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(64,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ it )
=> ( ( B @ ( E @ ( G @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ it )
=> ( ( G @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ it ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_MI1) ).
thf(345,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ it )
=> ( ( B @ ( E @ ( G @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ it )
=> ( ( G @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ it ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(323,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_list_Osimps_I3_J) ).
thf(140,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_list_Osimps_I5_J) ).
thf(483,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(28,axiom,
! [A: dB] :
( ( A @ it )
=> ( A @ abs @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Lambda) ).
thf(198,plain,
! [A: dB] :
( ( A @ it )
=> ( A @ abs @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(105,axiom,
! [A: type,B: dB,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_typing__elims_I2_J) ).
thf(521,plain,
! [A: type,B: dB,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(78,axiom,
! [A: dB,B: dB @ list,C: dB @ list] :
( ( B @ ( C @ ( beta @ ( dB @ step1 ) ) ) )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_apps__preserves__betas) ).
thf(399,plain,
! [A: dB,B: dB @ list,C: dB @ list] :
( ( B @ ( C @ ( beta @ ( dB @ step1 ) ) ) )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(53,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_dB_Osimps_I4_J) ).
thf(306,plain,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(42,axiom,
t_a @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Beta_I5_J) ).
thf(267,plain,
t_a @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(92,axiom,
t @ ( u @ ( e @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_uT) ).
thf(473,plain,
t @ ( u @ ( e @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1,conjecture,
as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(112,plain,
~ ( as @ ( nat @ zero_zero @ ( a @ ( r @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,axiom,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ subst ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_beta) ).
thf(516,plain,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ subst ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(111,axiom,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ var @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_app__Var__IT) ).
thf(553,plain,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ var @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(15,axiom,
u @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_uIT) ).
thf(162,plain,
u @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(108,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_subst__App) ).
thf(531,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(106,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( B @ abs @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_abs) ).
thf(525,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( B @ abs @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(50,axiom,
! [A: type @ list,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( dB @ cons ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing ) @ ( fconj @ ( type @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ aa ) ) ) @ ( type @ list @ ( bool @ ( bool @ combb ) ) @ ( type @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( type @ combc ) ) ) ) @ ( fFalse @ ( type @ ( bool @ list_case ) ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_typings_Osimps_I2_J) ).
thf(295,plain,
! [A: type @ list,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing ) @ ( fconj @ ( type @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ aa ) ) ) @ ( type @ list @ ( bool @ ( bool @ combb ) ) @ ( type @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( type @ combc ) ) ) ) @ ( fFalse @ ( type @ ( bool @ list_case ) ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( dB @ cons ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( dB @ cons ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing ) @ ( fconj @ ( type @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ aa ) ) ) @ ( type @ list @ ( bool @ ( bool @ combb ) ) @ ( type @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( type @ combc ) ) ) ) @ ( fFalse @ ( type @ ( bool @ list_case ) ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(80,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_dB_Osize_I1_J) ).
thf(409,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(54,axiom,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [D: type,E: type] :
~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_abs__typeE) ).
thf(310,plain,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [D: type,E: type] :
~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(62,axiom,
! [A: nat,B: type,C: dB,D: type @ ( nat @ fun ),E: type,F: dB,G: type @ ( nat @ fun )] :
( ( E @ ( F @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( G
= ( B @ ( A @ ( D @ ( type @ shift ) ) ) ) )
=> ( E @ ( A @ ( C @ ( F @ subst ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_subst__lemma) ).
thf(331,plain,
! [A: nat,B: type,C: dB,D: type @ ( nat @ fun ),E: type,F: dB,G: type @ ( nat @ fun )] :
( ( E @ ( F @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( G
= ( B @ ( A @ ( D @ ( type @ shift ) ) ) ) )
=> ( E @ ( A @ ( C @ ( F @ subst ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(84,axiom,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ subst ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_substn__subst__0) ).
thf(441,plain,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ subst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(20,axiom,
t2 @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(175,plain,
t2 @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(56,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_liftn__0) ).
thf(314,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(86,axiom,
! [A: dB @ list,B: type,C: type @ list,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( D @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_list__app__typeI) ).
thf(446,plain,
! [A: dB @ list,B: type,C: type @ list,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( D @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_not__Cons__self2) ).
thf(143,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_apps__eq__tail__conv) ).
thf(250,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( C = A )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(88,axiom,
t @ ( ua @ ( ea @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Beta_I7_J) ).
thf(450,plain,
t @ ( ua @ ( ea @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(30,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(203,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(69,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(368,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(39,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(258,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(66,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_dB_Osimps_I3_J) ).
thf(351,plain,
! [A: dB,B: dB] :
( ( ( B = A )
=> ( ( B @ abs )
= ( A @ abs ) ) )
& ( ( ( B @ abs )
= ( A @ abs ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_zero__reorient) ).
thf(401,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_dB_Osimps_I1_J) ).
thf(119,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ var )
= ( A @ var ) ) )
& ( ( ( B @ var )
= ( A @ var ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA,E: bool @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( E @ ( TA @ step1 ) ) ) )
<=> ( ( ( A @ ( C @ ( E @ ( TA @ step1 ) ) ) )
& ( B = D ) )
| ( ( A = C )
& ( B @ ( D @ ( E @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Cons__step1__Cons) ).
thf(235,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA,E: bool @ ( TA @ fun ) @ ( TA @ fun )] :
( ( ( ( ( A @ ( C @ ( E @ ( TA @ step1 ) ) ) )
& ( B = D ) )
| ( ( A = C )
& ( B @ ( D @ ( E @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( E @ ( TA @ step1 ) ) ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( E @ ( TA @ step1 ) ) ) )
=> ( ( ( A @ ( C @ ( E @ ( TA @ step1 ) ) ) )
& ( B = D ) )
| ( ( A = C )
& ( B @ ( D @ ( E @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_dB_Osimps_I2_J) ).
thf(207,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(44,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ it )
=> ( ( B @ ( E @ ( F @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ it )
=> ( ( F @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ it ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_MI2) ).
thf(272,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ it )
=> ( ( B @ ( E @ ( F @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ it )
=> ( ( F @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ it ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(83,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: bool @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ step1 ) ) ) )
=> ( ! [E: TA] :
( ( C
= ( A @ ( E @ ( TA @ cons ) ) ) )
=> ~ ( B @ ( E @ ( D @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ~ ! [E: TA @ list] :
( ( C
= ( E @ ( B @ ( TA @ cons ) ) ) )
=> ~ ( A @ ( E @ ( D @ ( TA @ step1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Cons__step1E) ).
thf(432,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: bool @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ step1 ) ) ) )
=> ( ! [E: TA] :
( ( C
= ( A @ ( E @ ( TA @ cons ) ) ) )
=> ~ ( B @ ( E @ ( D @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ~ ! [E: TA @ list] :
( ( C
= ( E @ ( B @ ( TA @ cons ) ) ) )
=> ~ ( A @ ( E @ ( D @ ( TA @ step1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_list_Osimps_I2_J) ).
thf(146,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_list__app__typeE) ).
thf(183,plain,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_foldl__Nil) ).
thf(326,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(43,axiom,
! [A: type,B: dB @ list,C: nat,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ var @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_var__app__typesE) ).
thf(268,plain,
! [A: type,B: dB @ list,C: nat,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ var @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(93,axiom,
! [A: type,B: type @ list,C: type,D: dB @ list,E: dB @ list,F: nat,G: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( ( A @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ? [H: type @ list] :
( ( H @ ( D @ ( G @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
& ( A
= ( C @ ( H @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_var__app__types) ).
thf(474,plain,
! [A: type,B: type @ list,C: type,D: dB @ list,E: dB @ list,F: nat,G: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( ( A @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ? [H: type @ list] :
( ( H @ ( D @ ( G @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
& ( A
= ( C @ ( H @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(82,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ! [D: dB] :
( ( D @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A
!= ( B @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
=> ( ! [D: dB @ list] :
( ( D @ ( B @ ( beta @ ( dB @ step1 ) ) ) )
=> ( A
!= ( D @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
=> ~ ! [D: dB] :
( ( C
= ( D @ abs ) )
=> ! [E: dB,F: dB @ list] :
( ( B
= ( F @ ( E @ ( dB @ cons ) ) ) )
=> ( A
!= ( F @ ( nat @ zero_zero @ ( E @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_apps__betasE) ).
thf(415,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ! [D: dB] :
( ( D @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A
!= ( B @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
=> ( ! [D: dB @ list] :
( ( D @ ( B @ ( beta @ ( dB @ step1 ) ) ) )
=> ( A
!= ( D @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
=> ~ ! [D: dB] :
( ( C
= ( D @ abs ) )
=> ! [E: dB,F: dB @ list] :
( ( B
= ( F @ ( E @ ( dB @ cons ) ) ) )
=> ( A
!= ( F @ ( nat @ zero_zero @ ( E @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(7,axiom,
! [A: nat] : ( A @ var @ it ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Var__IT) ).
thf(131,plain,
! [A: nat] : ( A @ var @ it ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_subst__preserves__beta) ).
thf(178,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_insert__Nil) ).
thf(163,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(29,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ subst ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_substn__subst__n) ).
thf(200,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ subst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(574,plain,
$false,
inference(e,[status(thm)],[260,486,365,479,518,234,379,511,217,276,288,301,372,504,189,284,152,448,321,348,480,397,280,293,396,133,116,507,527,381,534,229,361,329,461,317,169,471,193,547,393,129,412,513,166,264,161,180,444,149,375,176,204,391,313,335,187,172,113,219,451,303,494,345,323,140,483,198,521,399,306,267,473,112,516,553,162,531,525,295,409,310,331,441,175,314,446,143,250,450,203,368,258,351,401,119,235,207,272,432,146,183,326,268,474,415,131,178,163,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL834_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 23:43:36 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.78/1.32 % [INFO] Parsing done (321ms).
% 1.78/1.33 % [INFO] Running in sequential loop mode.
% 2.45/1.71 % [INFO] eprover registered as external prover.
% 2.45/1.72 % [INFO] Scanning for conjecture ...
% 2.82/1.91 % [INFO] Found a conjecture (or negated_conjecture) and 109 axioms. Running axiom selection ...
% 2.82/2.04 % [INFO] Axiom selection finished. Selected 109 axioms (removed 0 axioms).
% 3.85/2.29 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.17/2.32 % [INFO] Type checking passed.
% 4.17/2.33 % [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 ...
% 5.50/2.75 % [INFO] [Domain constraints] Detected constraint on bool
% 5.50/2.75 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 20.03/9.65 % External prover 'e' found a proof!
% 20.03/9.65 % [INFO] Killing All external provers ...
% 20.03/9.65 % Time passed: 9111ms (effective reasoning time: 8310ms)
% 20.03/9.65 % 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)>
% 20.03/9.65 % Axioms used in derivation (109): fact_68_typings_Osimps_I2_J, fact_48_not__Nil__step1, fact_29_Abs__eq__apps__conv, fact_56_Cons__step1__Cons, fact_89_dB_Osimps_I6_J, fact_12_dB_Osimps_I2_J, help_fconj_3_1_U, fact_31_MI1, fact_4_Abs__apps__eq__Abs__apps__conv, fact_58_list_Osimps_I5_J, fact_65_Cons__step1E, fact_78_var__app__types, fact_96_Abs__App__neq__Var__apps, fact_9_apps__eq__tail__conv, fact_91_Var__IT, fact_81_typing_OVar, fact_50_foldl__Nil, fact_28_substn_Osimps_I2_J, fact_19_IT_OBeta, fact_92_app__Var__IT, fact_75_mem__def, fact_88_dB_Osimps_I7_J, fact_72_list__app__typeD, fact_80_dB_Osimps_I1_J, fact_42_Beta_I5_J, fact_97_head__Var__reduction, fact_35_abs__typeE, fact_0__096IT_At_096, fact_3_beta, fact_93_subst__Var__IT, help_fFalse_1_1_T, fact_74_ext, fact_16_zero__reorient, fact_62_list_Osimps_I3_J, fact_57_foldl__Cons, help_COMBB_1_1_U, fact_5_abs, fact_63_neq__Nil__conv, fact_36_Beta_I7_J, fact_39_liftn_Osimps_I2_J, fact_11_dB_Osimps_I3_J, fact_22_beta__cases_I3_J, help_fconj_2_1_U, fact_37_type_Osimps_I2_J, fact_1_Beta_I3_J, fact_26_apps__eq__Abs__conv, fact_40_App, fact_44_shift__eq, fact_51_type_Osimps_I6_J, fact_84_Var__apps__eq__Var__apps__conv, fact_18_dB_Osimps_I9_J, fact_64_list_Oexhaust, fact_90_subst__eq, fact_24_apps__preserves__betas, fact_55_list_Oinject, fact_15_uIT, fact_41_Abs, fact_14_Beta_I6_J, fact_43_liftn__0, fact_61_list_Osimps_I2_J, fact_8_appR, fact_87_dB_Osimps_I5_J, arity_Nat_Onat___Groups_Ozero, fact_38_SI2, fact_30_MI2, fact_94_var__app__type__eq, fact_10_apps__preserves__beta, fact_95_Var__apps__neq__Abs__apps, fact_53_apps__betasE, fact_6_subst__App, fact_2_Beta_I1_J, fact_73_list__app__typeE, fact_59_not__Cons__self2, help_COMBC_1_1_U, fact_17_dB_Osimps_I8_J, fact_85_Var__eq__apps__conv, fact_32_subst__lemma, fact_46_typing__elims_I3_J, help_fconj_1_1_U, fact_71_list__app__typeI, fact_77_foldr_Osimps_I2_J, fact_7_appL, fact_52_foldl__fun__comm, fact_83_beta__cases_I1_J, fact_13_subst__preserves__beta, fact_98_dB_Osize_I1_J, help_fFalse_1_1_U, fact_33_SI1, fact_76_foldr_Osimps_I1_J, fact_67_sublist__singleton, fact_86_dB_Osimps_I4_J, help_pp_1_1_U, fact_70_typings_Osimps_I1_J, fact_20_beta__cases_I2_J, fact_45_subject__reduction, fact_21_Lambda, fact_34_substn__subst__n, fact_27_uT, fact_69_sublist__nil, fact_49_not__step1__Nil, help_pp_2_1_U, fact_54_list_Osimps_I4_J, fact_47_typing__elims_I2_J, fact_66_insert__Nil, fact_60_not__Cons__self, fact_79_var__app__typesE, fact_82_typing__elims_I1_J, fact_23_substn__subst__0, fact_25_T
% 20.03/9.65 % No. of inferences in proof: 222
% 20.03/9.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9111 ms resp. 8310 ms w/o parsing
% 20.66/9.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.66/9.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------