%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL829_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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:53:08 AM UTC 2026
% Result : Theorem 79.12s 59.41s
% Output : Refutation 79.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 234 ( 139 unt; 0 typ; 0 def)
% Number of atoms : 2538 ( 265 equ; 0 cnn)
% Maximal formula atoms : 20 ( 10 avg)
% Number of connectives : 7565 ( 57 ~; 22 |; 55 &;7336 @)
% ( 17 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 60 usr; 17 con; 0-5 aty)
% Number of variables : 658 ( 0 ^; 626 !; 32 ?; 658 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) @ ( TB @ fun ) ) ) ).
thf(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ fun ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(n_lists_decl,type,
n_lists:
!>[TA: $tType] : ( nat > ( TA @ list ) > ( TA @ list @ list ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(equal_equal_decl,type,
equal_equal:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(var_decl,type,
var: nat > dB ).
thf(dB_case_decl,type,
dB_case:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( dB @ fun ) ) > dB > TA ) ).
thf(dB_rec_decl,type,
dB_rec:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( TA @ fun ) @ ( dB @ fun ) ) > dB > TA ) ).
thf(dB_size_decl,type,
dB_size: dB > nat ).
thf(lift_decl,type,
lift: dB @ ( nat @ fun ) @ ( dB @ fun ) ).
thf(liftn_decl,type,
liftn: nat > dB > nat > dB ).
thf(subst_decl,type,
subst: dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(substn_decl,type,
substn: dB > dB > nat > dB ).
thf(listMem_decl,type,
listMem:
!>[TA: $tType] : ( TA > ( TA @ list ) > $o ) ).
thf(concat_decl,type,
concat:
!>[TA: $tType] : ( ( TA @ list @ list ) > ( TA @ list ) ) ).
thf(filter_decl,type,
filter:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list @ ( TA @ list @ fun ) ) ) ).
thf(hd_decl,type,
hd:
!>[TA: $tType] : ( TA @ ( TA @ list @ fun ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TB @ ( TA @ list @ fun ) ) ) ).
thf(list_rec_decl,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_size_decl,type,
list_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ list ) > nat ) ).
thf(listsp_decl,type,
listsp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ fun ) ) ).
thf(maps_decl,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( TA @ list @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(member1_decl,type,
member1:
!>[TA: $tType] : ( ( TA @ list ) > TA > $o ) ).
thf(monoid_add_listsum_decl,type,
monoid_add_listsum:
!>[TA: $tType] : ( ( TA @ list ) > TA ) ).
thf(null_decl,type,
null:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(sublist_decl,type,
sublist:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( nat @ fun ) ) > ( TA @ list ) ) ).
thf(tl_decl,type,
tl:
!>[TA: $tType] : ( TA @ list @ ( TA @ list @ fun ) ) ).
thf(transpose_decl,type,
transpose:
!>[TA: $tType] : ( ( TA @ list @ list ) > ( TA @ list @ list ) ) ).
thf(transpose_rel_decl,type,
transpose_rel:
!>[TA: $tType] : ( bool @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ fun ) ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(accp_decl,type,
accp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) > TA > $o ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
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] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a_decl,type,
a: dB ).
thf(as_decl,type,
as: dB @ list ).
thf(i_decl,type,
i: nat ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Cons__eq__map__conv) ).
thf(533,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
=> ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_map_Osimps_I1_J) ).
thf(404,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(34,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(248,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
as @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( nat @ aa ) ) ) @ ( dB @ ( dB @ map ) @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( as @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( nat @ aa ) ) ) @ ( dB @ ( dB @ map ) @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
~ ( as @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( nat @ aa ) ) ) @ ( dB @ ( dB @ map ) @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_nat_Oinject) ).
thf(154,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_map_Osimps_I2_J) ).
thf(479,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(35,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( nat @ zero_zero @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_n__lists_Osimps_I1_J) ).
thf(249,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( nat @ zero_zero @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(97,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_filter__filter) ).
thf(468,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ( ( TA @ nil @ ( TA @ monoid_add_listsum ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_listsum__simps_I1_J) ).
thf(170,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ( ( TA @ nil @ ( TA @ monoid_add_listsum ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(42,axiom,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_dB_Osize_I4_J) ).
thf(276,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(22,axiom,
! [TA: $tType,A: TA @ list @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) @ ( B @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) @ ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_transpose_Opsimps_I3_J) ).
thf(202,plain,
! [TA: $tType,A: TA @ list @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) @ ( B @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) @ ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_member__rec_I2_J) ).
thf(184,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_sublist__singleton) ).
thf(344,plain,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(20,axiom,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_sublist__nil) ).
thf(196,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(83,axiom,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_uIT) ).
thf(421,plain,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(57,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_transpose_Opsimps_I2_J) ).
thf(325,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: TA @ list @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ maps ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_maps__simps_I2_J) ).
thf(164,plain,
! [TA: $tType,TB: $tType,A: TA @ list @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ maps ) ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_equal__Nil__null) ).
thf(321,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) ) )
& ( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(73,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ listsp ) ) )
<=> ( ? [C: TA,D: TA @ list] :
( ( D @ ( B @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( A
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_listsp_Osimps) ).
thf(376,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ( ? [C: TA,D: TA @ list] :
( ( D @ ( B @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( A
= ( TA @ nil ) ) )
=> ( A @ ( B @ ( TA @ listsp ) ) ) )
& ( ( A @ ( B @ ( TA @ listsp ) ) )
=> ( ? [C: TA,D: TA @ list] :
( ( D @ ( B @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( A
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(66,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_dB_Osize_I1_J) ).
thf(353,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(8,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_splice__Nil2) ).
thf(147,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_map__eq__Cons__conv) ).
thf(221,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(94,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ tl @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_tl_Osimps_I2_J) ).
thf(453,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ tl @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(81,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_equal__list__def) ).
thf(411,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ list @ equal_equal ) ) ) )
& ( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( B @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_maps__def) ).
thf(206,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( B @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_transpose_Opsimps_I1_J) ).
thf(527,plain,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(53,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 @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(312,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 @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(85,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 @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
<=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_listsp__conj__eq) ).
thf(424,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 @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) ) )
& ( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(79,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(407,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(86,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_listsp_ONil) ).
thf(429,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(101,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_list_Osimps_I3_J) ).
thf(484,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(36,axiom,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_liftn__lift) ).
thf(252,plain,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) @ ( TA @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) @ ( TA @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(59,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 ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_list_Osimps_I5_J) ).
thf(329,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 ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(112,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) )
= ( A @ ( TA @ nil @ ( TA @ list @ fequal @ ( bool @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( fNot @ ( TA @ list @ ( bool @ ( bool @ combb ) ) ) ) @ ( TA @ list @ filter ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ tl @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_transpose__aux__filter__tail) ).
thf(522,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) )
= ( A @ ( TA @ nil @ ( TA @ list @ fequal @ ( bool @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( fNot @ ( TA @ list @ ( bool @ ( bool @ combb ) ) ) ) @ ( TA @ list @ filter ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ tl @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) )
= ( A @ ( B @ ( TB @ ( TA @ maps ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_concat__map__maps) ).
thf(493,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) )
= ( A @ ( B @ ( TB @ ( TA @ maps ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(95,axiom,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_substn__subst__0) ).
thf(456,plain,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(45,axiom,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ listMem ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_elem) ).
thf(285,plain,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ listMem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(111,axiom,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_list_Osize_I1_J) ).
thf(519,plain,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(67,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_map__ident) ).
thf(356,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(106,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(499,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)],[106]) ).
thf(18,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_null__rec_I2_J) ).
thf(193,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ tl @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ tl @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_map__tl) ).
thf(212,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ tl @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ tl @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(58,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(328,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_map__eq__Cons__D) ).
thf(471,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ null ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_List_Onull__def) ).
thf(173,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) )
& ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,axiom,
! [TA: $tType,A: TA @ list,B: nat] :
( ( A @ ( B @ suc @ ( TA @ n_lists ) ) )
= ( A @ ( B @ ( TA @ n_lists ) ) @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ fun ) @ combb ) ) ) ) @ ( TA @ list @ list @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_n__lists_Osimps_I2_J) ).
thf(371,plain,
! [TA: $tType,A: TA @ list,B: nat] :
( ( A @ ( B @ suc @ ( TA @ n_lists ) ) )
= ( A @ ( B @ ( TA @ n_lists ) ) @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ fun ) @ combb ) ) ) ) @ ( TA @ list @ list @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(23,axiom,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
thf(205,plain,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(76,axiom,
! [TA: $tType,A: TA @ list @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ concat ) @ ( B @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_filter__concat) ).
thf(398,plain,
! [TA: $tType,A: TA @ list @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ concat ) @ ( B @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(115,axiom,
i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096IT_A_Ia_091u_Pi_093_J_096) ).
thf(530,plain,
i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(48,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(298,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)],[48]) ).
thf(39,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_list_Osimps_I2_J) ).
thf(264,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(43,axiom,
n != i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_False) ).
thf(279,plain,
n != i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(15,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Suc__n__not__n) ).
thf(180,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(91,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_list_Oexhaust) ).
thf(444,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(75,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_neq__Nil__conv) ).
thf(391,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TB @ nil @ ( B @ ( TB @ cons @ ( TA @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ combb ) ) ) ) @ ( TB @ list @ ( TB @ list @ ( TA @ combc ) ) ) @ ( TB @ list @ ( TA @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_concat__map__singleton) ).
thf(335,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TB @ nil @ ( B @ ( TB @ cons @ ( TA @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ combb ) ) ) ) @ ( TB @ list @ ( TB @ list @ ( TA @ combc ) ) ) @ ( TB @ list @ ( TA @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ hd @ ( TB @ ( TB @ list @ aa ) ) ) )
= ( B @ ( TA @ hd @ ( TA @ ( TA @ list @ aa ) ) ) @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_hd__map) ).
thf(350,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ hd @ ( TB @ ( TB @ list @ aa ) ) ) )
= ( B @ ( TA @ hd @ ( TA @ ( TA @ list @ aa ) ) ) @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(33,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(245,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)],[33]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ tl @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_tl_Osimps_I1_J) ).
thf(318,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ tl @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TA @ list @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TB @ transpose ) )
= ( A @ ( TA @ transpose ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_transpose__map__map) ).
thf(303,plain,
! [TA: $tType,TB: $tType,A: TA @ list @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TB @ transpose ) )
= ( A @ ( TA @ transpose ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Nil__is__map__conv) ).
thf(509,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A
= ( TA @ nil ) )
=> ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(88,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Suc__neq__Zero) ).
thf(434,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Suc__inject) ).
thf(130,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(306,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_dB_Osimps_I1_J) ).
thf(135,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)],[6]) ).
thf(40,axiom,
t @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(267,plain,
t @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) @ ( TA @ ( TB @ list @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_list_Osimps_I4_J) ).
thf(438,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) @ ( TA @ ( TB @ list @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(87,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_substn__subst__n) ).
thf(431,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_list_Orecs_I1_J) ).
thf(167,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(103,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_13_not__Cons__self2) ).
thf(490,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)],[103]) ).
thf(116,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_lift__IT) ).
thf(531,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(72,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ null ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_null__rec_I1_J) ).
thf(374,plain,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ monoid_add )
=> ! [A: TB @ list] :
( ( A @ ( TA @ zero_zero @ ( TB @ ( TA @ combk ) @ ( TA @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) @ ( TA @ monoid_add_listsum ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_listsum__0) ).
thf(255,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ monoid_add )
=> ! [A: TB @ list] :
( ( A @ ( TA @ zero_zero @ ( TB @ ( TA @ combk ) @ ( TA @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) @ ( TA @ monoid_add_listsum ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(110,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 @ fun ) @ ( TA @ aa ) ) ) @ ( 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(516,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 @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(63,axiom,
! [A: dB @ list] :
( ( A @ ( it @ ( dB @ listsp ) ) )
=> ( A @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( nat @ aa ) ) ) @ ( dB @ ( dB @ map ) @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_lifts__IT) ).
thf(342,plain,
! [A: dB @ list] :
( ( A @ ( it @ ( dB @ listsp ) ) )
=> ( A @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( nat @ aa ) ) ) @ ( dB @ ( dB @ map ) @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(7,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(145,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_transpose_Osimps_I1_J) ).
thf(209,plain,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(102,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_insert__Nil) ).
thf(487,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(113,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_subst__Var__IT) ).
thf(525,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(47,axiom,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_dB_Osimps_I10_J) ).
thf(295,plain,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(44,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_transpose_Osimps_I2_J) ).
thf(282,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(9,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_n__not__Suc__n) ).
thf(150,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(80,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(409,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( 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 ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_splice_Osimps_I3_J) ).
thf(199,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( 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 ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(90,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_splice_Osimps_I2_J) ).
thf(441,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(107,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(502,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_splice_Osimps_I1_J) ).
thf(127,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(62,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(338,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)],[62]) ).
thf(68,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Var__IT) ).
thf(359,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(93,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(450,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)],[93]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ listMem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_insert) ).
thf(482,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ listMem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(28,axiom,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_dB_Orecs_I1_J) ).
thf(218,plain,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(38,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_filter_Osimps_I2_J) ).
thf(258,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(74,axiom,
as @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( nat @ aa ) ) ) @ ( dB @ ( dB @ map ) @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Cons_I3_J) ).
thf(390,plain,
as @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( nat @ aa ) ) ) @ ( dB @ ( dB @ map ) @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(17,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_eq__Nil__null) ).
thf(186,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(77,axiom,
! [TA: $tType,A: TA @ list @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) @ ( B @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) @ ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_transpose_Osimps_I3_J) ).
thf(401,plain,
! [TA: $tType,A: TA @ list @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) @ ( B @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) @ ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( 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_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_list_Orecs_I2_J) ).
thf(418,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( 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_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_zero__reorient) ).
thf(119,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)],[3]) ).
thf(46,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ member1 ) ) )
<=> ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_member__rec_I1_J) ).
thf(287,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ member1 ) ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ member1 ) ) )
=> ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(49,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 @ 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(300,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 @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(92,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_subst__eq) ).
thf(447,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ concat ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_concat_Osimps_I1_J) ).
thf(315,plain,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ concat ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(84,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(422,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)],[84]) ).
thf(19,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(195,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(31,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_subst__lift) ).
thf(239,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(32,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_filter_Osimps_I1_J) ).
thf(242,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ filter ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(108,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ hd @ ( TA @ ( TA @ list @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_hd_Osimps) ).
thf(506,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ hd @ ( TA @ ( TA @ list @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Cons__eq__map__D) ).
thf(268,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA @ list @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ concat ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TB @ concat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_map__concat) ).
thf(332,plain,
! [TA: $tType,TB: $tType,A: TA @ list @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ concat ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TB @ concat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(96,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_9_list_Oinject) ).
thf(459,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)],[96]) ).
thf(52,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) )
= ( A @ ( TA @ nil @ ( TA @ list @ fequal @ ( bool @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( fNot @ ( TA @ list @ ( bool @ ( bool @ combb ) ) ) ) @ ( TA @ list @ filter ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ hd @ ( TA @ ( TA @ list @ map ) @ ( TA @ list @ ( TA @ list @ list @ fun ) @ ( TA @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_transpose__aux__filter__head) ).
thf(309,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) )
= ( A @ ( TA @ nil @ ( TA @ list @ fequal @ ( bool @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( fNot @ ( TA @ list @ ( bool @ ( bool @ combb ) ) ) ) @ ( TA @ list @ filter ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ hd @ ( TA @ ( TA @ list @ map ) @ ( TA @ list @ ( TA @ list @ list @ fun ) @ ( TA @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(27,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_liftn__0) ).
thf(215,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(105,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_12_not__Cons__self) ).
thf(496,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)],[105]) ).
thf(70,axiom,
! [TA: $tType,A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_n__lists__Nil) ).
thf(364,plain,
! [TA: $tType,A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TB @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_map__is__Nil__conv) ).
thf(232,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TB @ nil ) ) )
& ( ( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TB @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(544,plain,
$false,
inference(e,[status(thm)],[533,404,248,118,154,479,249,468,170,276,202,184,344,196,421,325,164,321,376,353,147,221,453,411,206,527,312,424,407,429,484,252,361,329,522,493,456,285,519,356,499,193,212,328,471,173,371,205,398,530,298,264,279,180,444,391,335,350,245,318,303,509,434,130,306,135,267,438,431,167,490,531,374,255,516,342,145,209,487,525,295,282,150,409,199,441,502,127,338,359,450,482,218,258,390,186,401,418,119,287,300,447,315,422,195,239,242,506,268,332,459,309,215,496,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL829_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.42 % Computer : n006.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Fri Sep 25 23:39:40 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 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
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/0.93 % [INFO] Parsing done (208ms).
% 1.32/0.93 % [INFO] Running in sequential loop mode.
% 2.29/1.15 % [INFO] eprover registered as external prover.
% 2.29/1.16 % [INFO] Scanning for conjecture ...
% 2.84/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 115 axioms. Running axiom selection ...
% 3.72/1.51 % [INFO] Axiom selection finished. Selected 115 axioms (removed 0 axioms).
% 4.63/1.78 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.07/1.83 % [INFO] Type checking passed.
% 5.07/1.83 % [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 ...
% 79.12/59.41 % External prover 'e' found a proof!
% 79.12/59.41 % [INFO] Killing All external provers ...
% 79.12/59.41 % Time passed: 58898ms (effective reasoning time: 58471ms)
% 79.12/59.41 % 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)>
% 79.12/59.41 % Axioms used in derivation (115): fact_97_n__not__Suc__n, fact_89_map__tl, fact_94_hd__map, fact_9_list_Oinject, fact_95_Suc__inject, help_COMBS_1_1_U, fact_70_transpose_Osimps_I1_J, fact_26_listsum__0, fact_60_sublist__nil, fact_45_list_Osimps_I3_J, fact_66_equal__list__def, help_fconj_3_1_U, fact_49_null__rec_I2_J, fact_7_listsp__conj__eq, fact_64_concat_Osimps_I1_J, fact_87_liftn__lift, help_COMBI_1_1_U, fact_21_subst__lift, fact_27_zero__reorient, fact_54_splice_Osimps_I2_J, fact_16_Cons__eq__map__D, fact_19_Var__IT, fact_40_map_Osimps_I1_J, fact_75_mem__def, fact_48_splice__Nil2, fact_8_map__ident, fact_85_filter_Osimps_I1_J, fact_43_member__rec_I2_J, help_fNot_2_1_U, fact_10_Cons__eq__map__conv, fact_15_lifts__IT, help_fNot_1_1_U, fact_0__096IT_At_096, fact_65_map__concat, fact_68_concat__map__maps, fact_74_ext, fact_77_n__lists_Osimps_I1_J, fact_44_list_Osimps_I2_J, fact_29_dB_Osize_I4_J, fact_6_map_Osimps_I2_J, help_COMBB_1_1_U, fact_81_n__lists_Osimps_I2_J, fact_14_subst__Var__IT, fact_98_Suc__neq__Zero, fact_78_n__lists__Nil, fact_59_sublist__singleton, fact_61_equal__Nil__null, help_fconj_2_1_U, fact_92_nat_Oinject, fact_22_subst__eq, fact_25_list_Orecs_I2_J, fact_56_list_Oexhaust, fact_31_dB_Osimps_I10_J, fact_1_Var_I3_J, fact_17_map__eq__Cons__D, fact_51_eq__Nil__null, fact_46_list_Osimps_I4_J, fact_36_insert, help_fequal_1_1_T, fact_38_elem, fact_84_filter_Osimps_I2_J, arity_Nat_Onat___Groups_Ozero, fact_20_dB_Osimps_I1_J, help_COMBK_1_1_U, fact_12_not__Cons__self, fact_5_Cons_I3_J, fact_86_tl_Osimps_I1_J, fact_72_transpose__map__map, fact_58_insert__Nil, fact_73_maps__simps_I2_J, fact_63_list_Osize_I1_J, help_COMBC_1_1_U, fact_3_uIT, help_fequal_2_1_T, help_fconj_1_1_U, fact_28_dB_Osize_I1_J, fact_83_filter__filter, fact_18_lift__IT, fact_41_map__is__Nil__conv, fact_91_transpose__aux__filter__head, fact_52_list_Orecs_I1_J, fact_2_False, fact_57_neq__Nil__conv, fact_90_filter__concat, fact_88_tl_Osimps_I2_J, fact_67_transpose_Osimps_I3_J, fact_39_Nil__is__map__conv, fact_55_listsp_Osimps, fact_50_List_Onull__def, fact_37_member__rec_I1_J, fact_80_transpose_Opsimps_I2_J, fact_32_null__rec_I1_J, fact_33_dB_Orecs_I1_J, help_pp_1_1_U, fact_24_splice_Osimps_I3_J, fact_34_substn__subst__n, arity_Nat_Onat___Groups_Omonoid__add, fact_71_transpose_Osimps_I2_J, fact_96_Suc__n__not__n, fact_42_listsp_ONil, fact_35_listsum__simps_I1_J, fact_4__096IT_A_Ia_091u_Pi_093_J_096, fact_82_transpose__aux__filter__tail, fact_30_substn__subst__0, fact_47_splice_Osimps_I1_J, fact_23_list_Osimps_I5_J, fact_62_concat__map__singleton, help_pp_2_1_U, fact_76_transpose_Opsimps_I3_J, fact_69_maps__def, fact_93_hd_Osimps, fact_11_map__eq__Cons__conv, fact_79_transpose_Opsimps_I1_J, fact_53_liftn__0, fact_13_not__Cons__self2
% 79.12/59.41 % No. of inferences in proof: 234
% 79.12/59.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 58898 ms resp. 58471 ms w/o parsing
% 79.60/59.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 79.60/59.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------