%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL802_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 : n009.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 07:52:59 AM UTC 2026
% Result : Theorem 132.06s 106.01s
% Output : Refutation 132.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 114
% Syntax : Number of formulae : 246 ( 87 unt; 0 typ; 0 def)
% Number of atoms : 2209 ( 215 equ; 0 cnn)
% Maximal formula atoms : 108 ( 8 avg)
% Number of connectives : 8760 ( 113 ~; 29 |; 56 &;8364 @)
% ( 14 <=>; 184 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 27 con; 0-5 aty)
% Number of variables : 688 ( 0 ^; 664 !; 24 ?; 688 :)
% 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(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TC @ fun ) @ ( TB @ ( TC @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_decl,type,
it: bool @ ( dB @ fun ) ).
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(lift_decl,type,
lift: dB > nat > dB ).
thf(subst_decl,type,
subst: 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(cons_decl,type,
cons:
!>[TA: $tType] : ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(listset_decl,type,
listset:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) @ list ) > ( bool @ ( TA @ list @ fun ) ) ) ).
thf(listsp_decl,type,
listsp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(set_Cons_decl,type,
set_Cons:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ list @ fun ) ) > ( bool @ ( TA @ list @ fun ) ) ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
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 ) ) > ( bool @ ( type @ fun ) @ ( dB @ 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(fEx_decl,type,
fEx:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(t2_decl,type,
t2: type ).
thf(t1_decl,type,
t1: type ).
thf(t_a_decl,type,
t_a: type ).
thf(t_decl,type,
t: type ).
thf(ts_decl,type,
ts: type @ list ).
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(n_decl,type,
n: nat ).
thf(rs_decl,type,
rs: dB @ list ).
thf(t3_decl,type,
t3: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(69,axiom,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ set_Cons ) ) )
= ( A @ ( TA @ list @ member @ ( bool @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ list @ ( bool @ ( bool @ combb ) ) @ ( TA @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ combc ) ) ) ) @ ( TA @ cons @ ( TA @ list @ fequal @ ( TA @ list @ ( bool @ ( TA @ list @ combb ) ) @ ( TA @ list @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ combb ) ) @ ( TA @ list @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ combc ) ) ) ) @ ( fconj @ ( TA @ list @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ aa ) ) ) @ ( TA @ list @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ list @ combs ) ) @ ( TA @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ fun ) @ aa ) ) ) @ ( TA @ list @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ combs ) ) @ ( TA @ list @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ combc ) ) ) ) @ ( TA @ list @ fEx @ ( TA @ ( bool @ ( bool @ ( TA @ list @ fun ) @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ list @ fun ) @ fun ) @ aa ) ) ) @ ( TA @ list @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ fEx @ ( TA @ list @ ( bool @ ( bool @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_set__Cons__def) ).
thf(347,plain,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ set_Cons ) ) )
= ( A @ ( TA @ list @ member @ ( bool @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ list @ ( bool @ ( bool @ combb ) ) @ ( TA @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ combc ) ) ) ) @ ( TA @ cons @ ( TA @ list @ fequal @ ( TA @ list @ ( bool @ ( TA @ list @ combb ) ) @ ( TA @ list @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ combb ) ) @ ( TA @ list @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ combc ) ) ) ) @ ( fconj @ ( TA @ list @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ aa ) ) ) @ ( TA @ list @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ list @ combs ) ) @ ( TA @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ fun ) @ aa ) ) ) @ ( TA @ list @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ combs ) ) @ ( TA @ list @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ combc ) ) ) ) @ ( TA @ list @ fEx @ ( TA @ ( bool @ ( bool @ ( TA @ list @ fun ) @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ list @ fun ) @ fun ) @ aa ) ) ) @ ( TA @ list @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ fEx @ ( TA @ list @ ( bool @ ( bool @ ( TA @ fun ) @ combb ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(78,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( G
= ( B @ ( A @ ( D @ ( type @ shift ) ) ) ) )
=> ( E @ ( A @ ( C @ ( F @ subst ) ) @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_subst__lemma) ).
thf(392,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( G
= ( B @ ( A @ ( D @ ( type @ shift ) ) ) ) )
=> ( E @ ( A @ ( C @ ( F @ subst ) ) @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(58,axiom,
t_a @ ( rs @ ( n @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Var_I2_J) ).
thf(308,plain,
t_a @ ( rs @ ( n @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_zero__reorient) ).
thf(120,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)],[4]) ).
thf(39,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_73_Abs__App__neq__Var__apps) ).
thf(247,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)],[39]) ).
thf(9,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(142,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ list,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) @ ( 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_35_foldr_Osimps_I2_J) ).
thf(340,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ list,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) @ ( 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)],[66]) ).
thf(11,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_dB_Osimps_I3_J) ).
thf(153,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)],[11]) ).
thf(17,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_lift_Osimps_I2_J) ).
thf(174,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(22,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 @ fun ) @ ( dB @ aa ) ) ) @ ( 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 @ fun ) @ ( dB @ aa ) ) ) @ ( 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_45_var__app__types) ).
thf(185,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 @ fun ) @ ( dB @ aa ) ) ) @ ( 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 @ fun ) @ ( dB @ aa ) ) ) @ ( 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)],[22]) ).
thf(86,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_46_Var__apps__eq__Var__apps__conv) ).
thf(417,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)],[86]) ).
thf(42,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_95_apps__preserves__betas) ).
thf(257,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)],[42]) ).
thf(107,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Var__IT) ).
thf(504,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(26,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_81_beta) ).
thf(196,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)],[26]) ).
thf(96,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_19_type_Osimps_I2_J) ).
thf(460,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)],[96]) ).
thf(50,axiom,
t3 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(277,plain,
t3 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(13,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(166,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(167,plain,
~ ( fFalse @ pp ),
inference(polarity_switch,[status(thm)],[166]) ).
thf(557,plain,
( ( ( t3 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,167]) ).
thf(558,plain,
( ( t3 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[557]) ).
thf(559,plain,
( ( t3 @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[558]) ).
thf(62,axiom,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( A @ ( B @ var @ ( C @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_typing__elims_I1_J) ).
thf(325,plain,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( A @ ( B @ var @ ( C @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(61,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_list_Oinject) ).
thf(316,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(20,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_82_appR) ).
thf(179,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)],[20]) ).
thf(75,axiom,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( 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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_typing__elims_I3_J) ).
thf(376,plain,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( 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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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_55_list_Osimps_I5_J) ).
thf(211,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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)],[32]) ).
thf(54,axiom,
! [A: type,B: dB,C: type,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( nat @ zero_zero @ ( D @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( B @ abs @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Abs) ).
thf(293,plain,
! [A: type,B: dB,C: type,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( nat @ zero_zero @ ( D @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( B @ abs @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(93,axiom,
! [A: type @ list,B: dB @ list,C: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( B @ ( C @ typing @ ( type @ fEx @ ( dB @ ( bool @ ( bool @ ( type @ fun ) @ combb ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ fun ) @ ( bool @ ( bool @ ( type @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ listsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_lists__typings) ).
thf(453,plain,
! [A: type @ list,B: dB @ list,C: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( B @ ( C @ typing @ ( type @ fEx @ ( dB @ ( bool @ ( bool @ ( type @ fun ) @ combb ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ fun ) @ ( bool @ ( bool @ ( type @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ listsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(6,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_dB_Osimps_I7_J) ).
thf(132,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(79,axiom,
~ ! [A: type] :
( ( t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( A @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( n @ var @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( A @ ( a @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(396,plain,
~ ! [A: type] :
( ( t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( A @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( n @ var @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( A @ ( a @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1,conjecture,
as @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( type @ fEx @ ( dB @ ( bool @ ( bool @ ( type @ fun ) @ combb ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ fun ) @ ( bool @ ( bool @ ( type @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ listsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( as @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( type @ fEx @ ( dB @ ( bool @ ( bool @ ( type @ fun ) @ combb ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ fun ) @ ( bool @ ( bool @ ( type @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ listsp ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(116,plain,
~ ( as @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( type @ fEx @ ( dB @ ( bool @ ( bool @ ( type @ fun ) @ combb ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ fun ) @ ( bool @ ( bool @ ( type @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( dB @ fun ) @ ( bool @ ( type @ fun ) @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(243,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(92,axiom,
t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_headT) ).
thf(452,plain,
t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(3,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_subst__lift) ).
thf(117,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(110,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
<=> ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_IT_Osimps) ).
thf(512,plain,
! [A: dB] :
( ( ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) )
=> ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
& ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(47,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_85_abs) ).
thf(270,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)],[47]) ).
thf(28,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_subst__Var__IT) ).
thf(201,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(76,axiom,
t1 @ ( as @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
thf(381,plain,
t1 @ ( as @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(111,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(534,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)],[111]) ).
thf(74,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA,E: bool @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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_97_Cons__step1__Cons) ).
thf(361,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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( E @ ( TA @ step1 ) ) ) ) )
& ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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)],[74]) ).
thf(95,axiom,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A )
=> ( A @ ( B @ var @ ( C @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_typing_OVar) ).
thf(456,plain,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A )
=> ( A @ ( B @ var @ ( C @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(81,axiom,
! [A: type @ list,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( 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_50_typings_Osimps_I2_J) ).
thf(403,plain,
! [A: type @ list,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( 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 @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( 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)],[81]) ).
thf(15,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_dB_Osize_I1_J) ).
thf(169,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(105,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ) @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ cons @ ( bool @ ( TA @ fun ) @ list @ ( bool @ ( TA @ fun ) @ list @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ list @ ( bool @ ( TA @ fun ) @ list @ aa ) ) ) @ ( TA @ listset ) )
= ( A @ ( TA @ listset ) @ ( B @ ( TA @ set_Cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_listset_Osimps_I2_J) ).
thf(499,plain,
! [TA: $tType,A: bool @ ( TA @ fun ) @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ cons @ ( bool @ ( TA @ fun ) @ list @ ( bool @ ( TA @ fun ) @ list @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ list @ ( bool @ ( TA @ fun ) @ list @ aa ) ) ) @ ( TA @ listset ) )
= ( A @ ( TA @ listset ) @ ( B @ ( TA @ set_Cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(328,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(24,axiom,
t @ ( u @ ( e @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_uT) ).
thf(193,plain,
t @ ( u @ ( e @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(112,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_52_subst__App) ).
thf(537,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)],[112]) ).
thf(30,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_lift__preserves__beta) ).
thf(205,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(109,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_typing__elims_I2_J) ).
thf(508,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(5,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_dB_Osimps_I6_J) ).
thf(128,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(67,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_86_subst__preserves__beta) ).
thf(343,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)],[67]) ).
thf(84,axiom,
t1 @ ( rs @ ( n @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_nT) ).
thf(412,plain,
t1 @ ( rs @ ( n @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(45,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 @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ ( C @ ( D @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( G @ ( A @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_MI1) ).
thf(264,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 @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ ( C @ ( D @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( G @ ( A @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(56,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: bool @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ step1 ) ) ) )
=> ( ! [E: TA] :
( ( C
= ( A @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ~ ( B @ ( E @ ( D @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ~ ! [E: TA @ list] :
( ( C
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ~ ( A @ ( E @ ( D @ ( TA @ step1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Cons__step1E) ).
thf(296,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: bool @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ step1 ) ) ) )
=> ( ! [E: TA] :
( ( C
= ( A @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ~ ( B @ ( E @ ( D @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ~ ! [E: TA @ list] :
( ( C
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ~ ( A @ ( E @ ( D @ ( TA @ step1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(53,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_83_appL) ).
thf(291,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)],[53]) ).
thf(52,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_54_dB_Osimps_I2_J) ).
thf(281,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)],[52]) ).
thf(115,axiom,
( t
= ( t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( t2 @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_T) ).
thf(545,plain,
( t
= ( t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( t2 @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(43,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_not__Cons__self2) ).
thf(259,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(85,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_68_dB_Osimps_I9_J) ).
thf(413,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)],[85]) ).
thf(77,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_65_Abs__apps__eq__Abs__apps__conv) ).
thf(382,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)],[77]) ).
thf(21,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_56_dB_Osimps_I4_J) ).
thf(181,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)],[21]) ).
thf(70,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_9_shift__eq) ).
thf(350,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)],[70]) ).
thf(113,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(540,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)],[113]) ).
thf(16,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(172,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(49,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(274,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)],[49]) ).
thf(89,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_94_type_Osimps_I6_J) ).
thf(434,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)],[89]) ).
thf(103,axiom,
ts @ ( as @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_argsT) ).
thf(494,plain,
ts @ ( as @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(68,axiom,
n = i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_True) ).
thf(345,plain,
n = i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(100,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_57_dB_Osimps_I5_J) ).
thf(483,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)],[100]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(198,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( t2 @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( n @ var @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_varT) ).
thf(240,plain,
t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( t2 @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( n @ var @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(40,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_72_Var__apps__neq__Abs__apps) ).
thf(251,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)],[40]) ).
thf(51,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_84_beta__cases_I1_J) ).
thf(278,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)],[51]) ).
thf(94,axiom,
i @ ( u @ ( a @ subst ) ) @ ( u @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
thf(455,plain,
i @ ( u @ ( a @ subst ) ) @ ( u @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(46,axiom,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_dB_Osize_I4_J) ).
thf(267,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(88,axiom,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [D: type,E: type] :
~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_abs__typeE) ).
thf(431,plain,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [D: type,E: type] :
~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(37,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_90_apps__preserves__beta) ).
thf(241,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)],[37]) ).
thf(98,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_96_head__Var__reduction) ).
thf(473,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)],[98]) ).
thf(41,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_list__app__typeI) ).
thf(255,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(101,axiom,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( 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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_list__app__typeD) ).
thf(487,plain,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( 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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(72,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 @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( F @ ( C @ ( D @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( F @ ( A @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_MI2) ).
thf(355,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 @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( F @ ( C @ ( D @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( F @ ( A @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(19,axiom,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_uIT) ).
thf(178,plain,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(551,plain,
( ( ( u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,167]) ).
thf(552,plain,
( ( u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[551]) ).
thf(553,plain,
( ( u @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[552]) ).
thf(25,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Lambda) ).
thf(194,plain,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(55,axiom,
t @ ( ua @ ( ea @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Var_I4_J) ).
thf(295,plain,
t @ ( ua @ ( ea @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(82,axiom,
t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( t2 @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( u @ ( e @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_uT_H) ).
thf(409,plain,
t1 @ ( ts @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( t2 @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( u @ ( e @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(18,axiom,
nat @ zero_zero @ ( i @ ( u @ ( a @ subst ) ) @ ( nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ lift ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
thf(177,plain,
nat @ zero_zero @ ( i @ ( u @ ( a @ subst ) ) @ ( nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ lift ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(106,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_lift__IT) ).
thf(502,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(97,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_not__Cons__self) ).
thf(470,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(73,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_App) ).
thf(359,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(60,axiom,
( rs
= ( as @ ( a @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Cons) ).
thf(314,plain,
( rs
= ( as @ ( a @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_dB_Osimps_I1_J) ).
thf(143,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)],[10]) ).
thf(91,axiom,
! [A: dB,B: type,C: dB,D: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_subject__reduction) ).
thf(450,plain,
! [A: dB,B: type,C: dB,D: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( beta @ ( bool @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(35,axiom,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Var_I3_J) ).
thf(239,plain,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(554,plain,
( ( ( ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[239,167]) ).
thf(555,plain,
( ( ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[554]) ).
thf(556,plain,
( ( ua @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[555]) ).
thf(29,axiom,
! [A: type,B: nat,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( D @ lift ) @ ( A @ ( B @ ( E @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_lift__type) ).
thf(203,plain,
! [A: type,B: nat,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( D @ lift ) @ ( A @ ( B @ ( E @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(104,axiom,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_list__app__typeE) ).
thf(495,plain,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(80,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(401,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)],[80]) ).
thf(8,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_subst__eq) ).
thf(139,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(118,plain,
! [C: dB,B: nat,A: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
inference(cnf,[status(esa)],[117]) ).
thf(119,plain,
! [C: dB,B: nat,A: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
inference(lifteq,[status(thm)],[118]) ).
thf(31,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_67_dB_Osimps_I8_J) ).
thf(207,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)],[31]) ).
thf(99,axiom,
~ ! [A: type @ list] :
( ( t1 @ ( A @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( A @ ( as @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(478,plain,
~ ! [A: type @ list] :
( ( t1 @ ( A @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( A @ ( as @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(48,axiom,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_IT_OVar) ).
thf(272,plain,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(346,plain,
n = i,
inference(lifteq,[status(thm)],[345]) ).
thf(14,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(168,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(547,plain,
( ( ( fTrue @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,167]) ).
thf(548,plain,
( ( fTrue @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[547]) ).
thf(549,plain,
fTrue != fFalse,
inference(simp,[status(thm)],[548]) ).
thf(33,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_49_apps__eq__tail__conv) ).
thf(214,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)],[33]) ).
thf(83,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Beta) ).
thf(410,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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_34_foldl__Cons) ).
thf(190,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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)],[23]) ).
thf(44,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(262,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)],[44]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(305,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(7,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(136,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(108,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ var @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_app__Var__IT) ).
thf(506,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ var @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(90,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_91_beta__cases_I3_J) ).
thf(437,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)],[90]) ).
thf(64,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_89_beta__cases_I2_J) ).
thf(332,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)],[64]) ).
thf(87,axiom,
! [A: type,B: dB @ list,C: nat,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ var @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_var__app__typesE) ).
thf(427,plain,
! [A: type,B: dB @ list,C: nat,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ var @ ( D @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(12,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(163,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(65,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_var__app__type__eq) ).
thf(337,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 @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(71,axiom,
t2 @ ( a @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_argT) ).
thf(354,plain,
t2 @ ( a @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing @ ( bool @ ( type @ fun ) @ ( dB @ aa ) ) ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(59,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ listsp ) ) )
<=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_listsp__conj__eq) ).
thf(309,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) )
=> ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ listsp ) ) ) )
& ( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ listsp ) ) )
=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(114,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ fEx @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
thf(543,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ fEx @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(102,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(491,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)],[102]) ).
thf(34,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 @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) )
=> ( A
!= ( F @ ( nat @ zero_zero @ ( E @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_apps__betasE) ).
thf(222,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 @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) )
=> ( A
!= ( F @ ( nat @ zero_zero @ ( E @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(560,plain,
$false,
inference(e,[status(thm)],[347,392,308,120,247,142,340,153,174,185,417,257,504,196,460,559,325,316,179,376,211,293,453,132,396,116,243,452,117,512,270,201,381,534,361,456,403,169,499,328,193,537,205,508,128,343,412,166,264,296,291,281,545,259,413,382,181,350,540,172,274,434,494,345,483,198,240,251,278,455,267,431,241,167,473,255,487,355,553,194,295,409,177,502,470,359,314,143,450,556,203,495,401,139,119,207,478,272,346,549,214,410,190,168,262,305,239,136,506,437,332,427,163,178,277,337,354,309,543,491,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL802_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
% 0.14/0.40 % Computer : n009.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 23:36:00 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.89/1.33 % [INFO] Parsing done (340ms).
% 1.89/1.35 % [INFO] Running in sequential loop mode.
% 3.05/1.74 % [INFO] eprover registered as external prover.
% 3.05/1.75 % [INFO] Scanning for conjecture ...
% 3.50/1.97 % [INFO] Found a conjecture (or negated_conjecture) and 113 axioms. Running axiom selection ...
% 3.91/2.12 % [INFO] Axiom selection finished. Selected 113 axioms (removed 0 axioms).
% 5.21/2.35 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.21/2.38 % [INFO] Type checking passed.
% 5.21/2.38 % [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 ...
% 6.14/2.59 % [INFO] [Domain constraints] Detected constraint on bool
% 6.14/2.59 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 132.06/106.00 % External prover 'e' found a proof!
% 132.06/106.00 % [INFO] Killing All external provers ...
% 132.06/106.00 % Time passed: 105458ms (effective reasoning time: 104651ms)
% 132.06/106.01 % 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)>
% 132.06/106.01 % Axioms used in derivation (113): fact_21_typing_OVar, fact_75_mem__def, fact_40_subst__lemma, fact_12_varT, fact_17_uIT, fact_41_IT_OVar, fact_98_Cons__step1E, help_COMBS_1_1_U, fact_38_list__app__typeI, help_fconj_3_1_U, fact_64_Lambda, fact_83_appL, fact_97_Cons__step1__Cons, fact_58_subst__eq, fact_86_subst__preserves__beta, fact_1_True, fact_16_nT, fact_85_abs, fact_73_Abs__App__neq__Var__apps, fact_90_apps__preserves__beta, fact_77_typing__elims_I3_J, fact_62_set__Cons__def, fact_70_dB_Osimps_I7_J, fact_44_var__app__typesE, fact_54_dB_Osimps_I2_J, fact_60_dB_Osize_I1_J, fact_55_list_Osimps_I5_J, fact_53_dB_Osimps_I1_J, fact_81_beta, fact_37_subst__Var__IT, fact_3_Var_I4_J, fact_63_dB_Osimps_I3_J, fact_13_MI1, fact_32_not__Cons__self, fact_71_zero__reorient, fact_0__096IT_At_096, fact_50_typings_Osimps_I2_J, help_fFalse_1_1_T, fact_74_ext, fact_94_type_Osimps_I6_J, fact_92_dB_Osize_I4_J, fact_23__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096, fact_24_headT, fact_52_subst__App, help_COMBB_1_1_U, fact_5_argT, fact_51_lift_Osimps_I2_J, fact_84_beta__cases_I1_J, fact_4_uT, fact_39_var__app__type__eq, fact_29__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_76_Collect__def, fact_35_foldr_Osimps_I2_J, fact_93_apps__betasE, help_fconj_2_1_U, fact_65_Abs__apps__eq__Abs__apps__conv, fact_47_list__app__typeD, fact_18_list_Oinject, fact_48_list__app__typeE, help_fequal_1_1_T, fact_28_uT_H, fact_20_typing__elims_I1_J, fact_78_abs__typeE, fact_27_Var_I2_J, fact_30__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, arity_Nat_Onat___Groups_Ozero, fact_82_appR, fact_68_dB_Osimps_I9_J, fact_59_subst__lift, fact_14_MI2, fact_49_apps__eq__tail__conv, fact_66_Abs, fact_33_not__Cons__self2, fact_36_app__Var__IT, fact_19_type_Osimps_I2_J, fact_43_typing__elims_I2_J, fact_80_IT_Osimps, fact_11_Cons, fact_87_lift__preserves__beta, fact_9_shift__eq, fact_7_lists__typings, help_COMBC_1_1_U, fact_69_dB_Osimps_I6_J, fact_31_Var__IT, fact_57_dB_Osimps_I5_J, fact_67_dB_Osimps_I8_J, help_fequal_2_1_T, fact_2_argsT, fact_79_listset_Osimps_I2_J, help_fconj_1_1_U, fact_56_dB_Osimps_I4_J, help_fFalse_1_1_U, fact_46_Var__apps__eq__Var__apps__conv, fact_96_head__Var__reduction, fact_6_listsp__conj__eq, fact_72_Var__apps__neq__Abs__apps, fact_61_Beta, help_pp_1_1_U, fact_15__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096, fact_34_foldl__Cons, fact_89_beta__cases_I2_J, fact_10_lift__type, fact_22_lift__IT, fact_91_beta__cases_I3_J, help_pp_2_1_U, fact_88_subject__reduction, help_fEx_1_1_U, fact_42__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096, fact_26_App, fact_95_apps__preserves__betas, fact_45_var__app__types, fact_25_T, fact_8_Var_I3_J
% 132.06/106.01 % No. of inferences in proof: 246
% 132.06/106.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 105458 ms resp. 104651 ms w/o parsing
% 132.61/106.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 132.61/106.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------