%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL785_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:52:53 AM UTC 2026
% Result : Theorem 40.36s 21.72s
% Output : Refutation 40.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 111
% Syntax : Number of formulae : 224 ( 99 unt; 0 typ; 0 def)
% Number of atoms : 2264 ( 342 equ; 0 cnn)
% Maximal formula atoms : 116 ( 10 avg)
% Number of connectives : 8263 ( 66 ~; 22 |; 97 &;7882 @)
% ( 28 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 23 con; 0-5 aty)
% Number of variables : 810 ( 0 ^; 782 !; 28 ?; 810 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(type_type,type,
type: $tType ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ fun ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ ( TC @ 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(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(app_decl,type,
app: dB @ ( dB @ fun ) @ ( 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(subst_decl,type,
subst: dB > dB > nat > dB ).
thf(append_decl,type,
append:
!>[TA: $tType] : ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) ) ).
thf(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(foldr_decl,type,
foldr:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TA @ fun ) @ ( TB @ fun ) ) > ( TB @ list ) > TA > TA ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA @ 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 ) ) > ( TA @ list ) > TB ) ).
thf(listsp_decl,type,
listsp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(maps_decl,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( TA @ list @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(rotate1_decl,type,
rotate1:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(shift_decl,type,
shift:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > nat > TA > ( TA @ ( nat @ fun ) ) ) ).
thf(fun1_decl,type,
fun1: type @ ( type @ fun ) @ ( type @ fun ) ).
thf(type_case_decl,type,
type_case:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( type @ fun ) @ ( type @ fun ) ) > type > TA ) ).
thf(typing_decl,type,
typing: ( type @ ( nat @ fun ) ) > dB > ( bool @ ( type @ fun ) ) ).
thf(typings_decl,type,
typings: ( type @ ( nat @ fun ) ) > ( dB @ list ) > ( bool @ ( type @ list @ fun ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(t_decl,type,
t: type ).
thf(t_a_decl,type,
t_a: type ).
thf(t1_decl,type,
t1: type ).
thf(a_decl,type,
a: dB ).
thf(as_decl,type,
as: dB @ list ).
thf(e_decl,type,
e: type @ ( nat @ fun ) ).
thf(ea_decl,type,
ea: type @ ( nat @ fun ) ).
thf(i_decl,type,
i: nat ).
thf(ia_decl,type,
ia: nat ).
thf(n_decl,type,
n: nat ).
thf(rs_decl,type,
rs: dB @ list ).
thf(t2_decl,type,
t2: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_64_splice_Osimps_I3_J) ).
thf(460,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)],[78]) ).
thf(26,axiom,
t_a @ ( rs @ ( n @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Var_I2_J) ).
thf(212,plain,
t_a @ ( rs @ ( n @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(57,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_subst__eq) ).
thf(343,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(65,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_self__append__conv2) ).
thf(386,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_list_Osimps_I4_J) ).
thf(138,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(84,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Nil__is__append__conv) ).
thf(481,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [E: TA,F: TA,G: TB] :
( ( F @ ( E @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( F @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_foldl__fun__comm) ).
thf(352,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [E: TA,F: TA,G: TB] :
( ( F @ ( E @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( F @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(107,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_dB_Osimps_I2_J) ).
thf(582,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(41,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Var__IT) ).
thf(276,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(5,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_splice_Osimps_I1_J) ).
thf(120,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(110,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
<=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_listsp__conj__eq) ).
thf(597,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) )
=> ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) ) )
& ( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(64,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ var @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_app__Var__IT) ).
thf(384,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ var @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_rev__exhaust2) ).
thf(340,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(45,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_append__eq__Cons__conv) ).
thf(288,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ 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 @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(52,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_True) ).
thf(320,plain,
n = i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(18,axiom,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_list__app__typeE) ).
thf(174,plain,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_list_Osimps_I5_J) ).
thf(404,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(21,axiom,
! [A: type,B: type @ list,C: type,D: dB @ list,E: dB @ list,F: nat,G: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( ( A @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ? [H: type @ list] :
( ( H @ ( D @ ( G @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
& ( A
= ( C @ ( H @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_var__app__types) ).
thf(189,plain,
! [A: type,B: type @ list,C: type,D: dB @ list,E: dB @ list,F: nat,G: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( ( A @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ? [H: type @ list] :
( ( H @ ( D @ ( G @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
& ( A
= ( C @ ( H @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(51,axiom,
! [A: type,B: dB,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_typing__elims_I2_J) ).
thf(316,plain,
! [A: type,B: dB,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(37,axiom,
! [A: type @ list,B: dB,C: dB @ list,D: type @ ( nat @ fun )] :
( ( A @ ( dB @ nil @ ( B @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( C @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list,F: type] :
( ( A
= ( type @ nil @ ( F @ ( type @ cons @ ( type @ list @ ( type @ list @ fun ) @ ( type @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( E @ ( type @ append @ ( type @ list @ ( type @ list @ fun ) @ ( type @ list @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) ) )
=> ( ( E @ ( C @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ~ ( F @ ( B @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_types__snocE) ).
thf(261,plain,
! [A: type @ list,B: dB,C: dB @ list,D: type @ ( nat @ fun )] :
( ( A @ ( dB @ nil @ ( B @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( C @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list,F: type] :
( ( A
= ( type @ nil @ ( F @ ( type @ cons @ ( type @ list @ ( type @ list @ fun ) @ ( type @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( E @ ( type @ append @ ( type @ list @ ( type @ list @ fun ) @ ( type @ list @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) ) )
=> ( ( E @ ( C @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ~ ( F @ ( B @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(25,axiom,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_uIT) ).
thf(211,plain,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_apps__eq__tail__conv) ).
thf(253,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( C = A )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(111,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_append__is__Nil__conv) ).
thf(602,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ list,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_foldr_Osimps_I2_J) ).
thf(147,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ list,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(67,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_self__append__conv) ).
thf(397,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(8,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_listsp_ONil) ).
thf(133,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(48,axiom,
! [A: type,B: type,C: dB @ list,D: nat,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_var__app__type__eq) ).
thf(307,plain,
! [A: type,B: type,C: dB @ list,D: nat,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( TB @ nil @ ( B @ ( TA @ ( TB @ foldr ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_foldr_Osimps_I1_J) ).
thf(117,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( TB @ nil @ ( B @ ( TA @ ( TB @ foldr ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(39,axiom,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ? [E: type @ list] :
( ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
& ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_list__app__typeD) ).
thf(270,plain,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ? [E: type @ list] :
( ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
& ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(101,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_subst__Var__IT) ).
thf(546,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(23,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_same__append__eq) ).
thf(201,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',fact_44_neq__Nil__conv) ).
thf(220,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)],[28]) ).
thf(93,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ listsp ) ) )
<=> ( ( A @ ( C @ ( TA @ listsp ) ) )
& ( B @ ( C @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_append__in__listsp__conv) ).
thf(512,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ listsp ) ) )
& ( B @ ( C @ ( TA @ listsp ) ) ) )
=> ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ listsp ) ) ) )
& ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ listsp ) ) )
=> ( ( A @ ( C @ ( TA @ listsp ) ) )
& ( B @ ( C @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(75,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(439,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)],[75]) ).
thf(15,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( dB @ nil @ ( A @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( B @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_app__last) ).
thf(160,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( dB @ nil @ ( A @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( B @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(69,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_rev__cases) ).
thf(407,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(80,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(467,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)],[80]) ).
thf(74,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_dB_Osimps_I4_J) ).
thf(435,plain,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(54,axiom,
t @ ( rs @ ( n @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_nT) ).
thf(329,plain,
t @ ( rs @ ( n @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_foldl__Nil) ).
thf(493,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(103,axiom,
! [A: dB @ list,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( ( A
!= ( dB @ nil ) )
=> ? [E: dB @ list] :
( ( D
= ( E @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
& ( A
= ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ) ) )
& ( ( A
= ( dB @ nil ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_App__eq__foldl__conv) ).
thf(551,plain,
! [A: dB @ list,B: dB,C: dB,D: dB] :
( ( ( ( ( A
!= ( dB @ nil ) )
=> ? [E: dB @ list] :
( ( D
= ( E @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
& ( A
= ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ) ) )
& ( ( A
= ( dB @ nil ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= B ) ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( ( A
!= ( dB @ nil ) )
=> ? [E: dB @ list] :
( ( D
= ( E @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
& ( A
= ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ) ) )
& ( ( A
= ( dB @ nil ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(44,axiom,
! [TA: $tType,A: type,B: type,C: TA @ ( type @ fun ) @ ( type @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ ( TA @ type_case ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( TA @ ( type @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_type_Osimps_I6_J) ).
thf(285,plain,
! [TA: $tType,A: type,B: type,C: TA @ ( type @ fun ) @ ( type @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ ( TA @ type_case ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( TA @ ( type @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(95,axiom,
! [A: dB @ list,B: type,C: type @ list,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( D @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_list__app__typeI) ).
thf(519,plain,
! [A: dB @ list,B: type,C: type @ list,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( D @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(20,axiom,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Var_I3_J) ).
thf(188,plain,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rotate1 ) )
= ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ fun ) @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_rotate1__def) ).
thf(141,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rotate1 ) )
= ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ fun ) @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_foldl__append) ).
thf(499,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(66,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_eq__Nil__appendI) ).
thf(393,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_40_not__Cons__self) ).
thf(457,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)],[77]) ).
thf(72,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(430,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(573,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)],[104]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',fact_33_list_Osimps_I2_J) ).
thf(579,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)],[106]) ).
thf(100,axiom,
t2 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(545,plain,
t2 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_49_splice_Osimps_I2_J) ).
thf(313,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)],[50]) ).
thf(112,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_append__self__conv) ).
thf(611,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
& ( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',fact_46_insert__Nil) ).
thf(144,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)],[12]) ).
thf(98,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_append__Nil2) ).
thf(540,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1,conjecture,
t @ ( as @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( t @ ( as @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ( t @ ( as @ ( a @ ( n @ var @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(40,axiom,
! [A: type,B: dB,C: type @ list,D: dB @ list,E: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( type @ nil @ ( A @ ( type @ cons @ ( type @ list @ ( type @ list @ fun ) @ ( type @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( C @ ( type @ append @ ( type @ list @ ( type @ list @ fun ) @ ( type @ list @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( dB @ nil @ ( B @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_types__snoc) ).
thf(274,plain,
! [A: type,B: dB,C: type @ list,D: dB @ list,E: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( type @ nil @ ( A @ ( type @ cons @ ( type @ list @ ( type @ list @ fun ) @ ( type @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( C @ ( type @ append @ ( type @ list @ ( type @ list @ fun ) @ ( type @ list @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( dB @ nil @ ( B @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_append1__eq__conv) ).
thf(230,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(509,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)],[92]) ).
thf(24,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_append__Nil) ).
thf(208,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(62,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_append__assoc) ).
thf(367,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(109,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_append__Cons) ).
thf(594,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(27,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
<=> ( B
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_append__self__conv2) ).
thf(213,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) )
& ( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
=> ( B
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(35,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(251,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)],[35]) ).
thf(55,axiom,
! [A: type,B: type,C: type,D: type] :
( ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_type_Osimps_I2_J) ).
thf(330,plain,
! [A: type,B: type,C: type,D: type] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(96,axiom,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Var__apps__eq__Var__apps__conv) ).
thf(521,plain,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(7,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(130,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_dB_Osimps_I5_J) ).
thf(278,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TA @ list @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ maps ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_maps__simps_I2_J) ).
thf(135,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)],[9]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(267,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)],[38]) ).
thf(90,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(505,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(17,axiom,
! [A: type,B: type @ list,C: dB,D: dB @ list,E: type @ ( nat @ fun )] :
( ( type @ nil @ ( A @ ( type @ cons @ ( type @ list @ ( type @ list @ fun ) @ ( type @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( B @ ( type @ append @ ( type @ list @ ( type @ list @ fun ) @ ( type @ list @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
<=> ( ( A @ ( C @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
& ( B @ ( D @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_types__snoc__eq) ).
thf(167,plain,
! [A: type,B: type @ list,C: dB,D: dB @ list,E: type @ ( nat @ fun )] :
( ( ( ( A @ ( C @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
& ( B @ ( D @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) )
=> ( type @ nil @ ( A @ ( type @ cons @ ( type @ list @ ( type @ list @ fun ) @ ( type @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( B @ ( type @ append @ ( type @ list @ ( type @ list @ fun ) @ ( type @ list @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) )
& ( ( type @ nil @ ( A @ ( type @ cons @ ( type @ list @ ( type @ list @ fun ) @ ( type @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( B @ ( type @ append @ ( type @ list @ ( type @ list @ fun ) @ ( type @ list @ aa ) ) ) @ ( type @ list @ ( type @ list @ aa ) ) ) @ ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
& ( B @ ( D @ ( E @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_34_list_Osimps_I3_J) ).
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 ) ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',fact_21_list_Oinject) ).
thf(531,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)],[97]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_45_list_Oexhaust) ).
thf(548,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)],[102]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rotate1__is__Nil__conv) ).
thf(123,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(60,axiom,
! [A: type @ list,B: type @ ( nat @ fun )] :
( ( A @ ( dB @ nil @ ( B @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
<=> ( A
= ( type @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_typings_Osimps_I1_J) ).
thf(355,plain,
! [A: type @ list,B: type @ ( nat @ fun )] :
( ( ( A
= ( type @ nil ) )
=> ( A @ ( dB @ nil @ ( B @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) )
& ( ( A @ ( dB @ nil @ ( B @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( A
= ( type @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(22,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_append__same__eq) ).
thf(194,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(282,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [A: dB @ list,B: dB,C: nat] :
( ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Var__eq__apps__conv) ).
thf(150,plain,
! [A: dB @ list,B: dB,C: nat] :
( ( ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) )
=> ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Cons__eq__append__conv) ).
thf(414,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ 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 @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_foldl__Cons) ).
thf(310,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(76,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_append__eq__append__conv2) ).
thf(441,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',fact_43_listsp_Osimps) ).
thf(370,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)],[63]) ).
thf(89,axiom,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( A @ ( B @ var @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_typing__elims_I1_J) ).
thf(502,plain,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( A @ ( B @ var @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(79,axiom,
! [A: nat,B: type,C: dB,D: type @ ( nat @ fun ),E: type,F: dB,G: type @ ( nat @ fun )] :
( ( E @ ( F @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( G
= ( B @ ( A @ ( D @ ( type @ shift ) ) ) ) )
=> ( E @ ( A @ ( C @ ( F @ subst ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_subst__lemma) ).
thf(463,plain,
! [A: nat,B: type,C: dB,D: type @ ( nat @ fun ),E: type,F: dB,G: type @ ( nat @ fun )] :
( ( E @ ( F @ ( G @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( G
= ( B @ ( A @ ( D @ ( type @ shift ) ) ) ) )
=> ( E @ ( A @ ( C @ ( F @ subst ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(81,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_append__eq__appendI) ).
thf(470,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_39_not__Cons__self2) ).
thf(576,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)],[105]) ).
thf(34,axiom,
t1 @ ( u @ ( e @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uT) ).
thf(250,plain,
t1 @ ( u @ ( e @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(61,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ list @ fun )] :
( ( TA @ nil @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_rev__induct) ).
thf(363,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ list @ fun )] :
( ( TA @ nil @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(94,axiom,
! [A: dB,B: type,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( D @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_App) ).
thf(517,plain,
! [A: dB,B: type,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( D @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(46,axiom,
t1 @ ( ua @ ( ea @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Var_I4_J) ).
thf(304,plain,
t1 @ ( ua @ ( ea @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(3,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_splice__Nil2) ).
thf(114,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A )
=> ( A @ ( B @ var @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_typing_OVar) ).
thf(246,plain,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A )
=> ( A @ ( B @ var @ ( C @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(83,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_dB_Osimps_I11_J) ).
thf(478,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(58,axiom,
! [A: type @ list,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing ) @ ( fconj @ ( type @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ aa ) ) ) @ ( type @ list @ ( bool @ ( bool @ combb ) ) @ ( type @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( type @ combc ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ list @ fun ) @ aa ) ) ) @ ( fFalse @ ( type @ ( bool @ list_case ) ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_typings_Osimps_I2_J) ).
thf(346,plain,
! [A: type @ list,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing ) @ ( fconj @ ( type @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ aa ) ) ) @ ( type @ list @ ( bool @ ( bool @ combb ) ) @ ( type @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( type @ combc ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ list @ fun ) @ aa ) ) ) @ ( fFalse @ ( type @ ( bool @ list_case ) ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( D @ typings ) @ ( C @ ( D @ typing ) @ ( fconj @ ( type @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ fun ) @ aa ) ) ) @ ( type @ list @ ( bool @ ( bool @ combb ) ) @ ( type @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ fun ) @ ( type @ fun ) @ ( bool @ ( bool @ fun ) @ ( type @ fun ) @ aa ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( bool @ ( type @ list @ fun ) @ ( type @ combc ) ) ) @ ( bool @ ( type @ list @ fun ) @ ( type @ fun ) @ ( bool @ ( type @ list @ fun ) @ aa ) ) ) @ ( fFalse @ ( type @ ( bool @ list_case ) ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ list,C: TB @ list,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ append @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_foldr__append) ).
thf(432,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ list,C: TB @ list,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ append @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: TA @ ( nat @ fun ),C: nat,D: nat] :
( ( D = C )
=> ( ( C @ ( A @ ( D @ ( B @ ( TA @ shift ) ) ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_shift__eq) ).
thf(410,plain,
! [TA: $tType,A: TA,B: TA @ ( nat @ fun ),C: nat,D: nat] :
( ( D = C )
=> ( ( C @ ( A @ ( D @ ( B @ ( TA @ shift ) ) ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(47,axiom,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_IT_OVar) ).
thf(305,plain,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ maps ) ) ) @ ( B @ ( C @ ( TB @ list @ ( TA @ aa ) ) ) @ ( TB @ append @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_maps__simps_I1_J) ).
thf(506,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ maps ) ) ) @ ( B @ ( C @ ( TB @ list @ ( TA @ aa ) ) ) @ ( TB @ append @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(82,axiom,
! [A: type,B: dB @ list,C: nat,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ var @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_var__app__typesE) ).
thf(474,plain,
! [A: type,B: dB @ list,C: nat,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ var @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ~ ( E @ ( B @ ( D @ typings ) @ ( bool @ ( type @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_27_dB_Osimps_I10_J) ).
thf(239,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)],[31]) ).
thf(32,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t1
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( F @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( F @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_MI2) ).
thf(242,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t1
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( F @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( F @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Cons__eq__appendI) ).
thf(163,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_dB_Osimps_I1_J) ).
thf(178,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)],[19]) ).
thf(29,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_subst__App) ).
thf(227,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA] :
( ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ rotate1 ) )
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( TB @ nil @ ( TB @ rotate1 ) )
= ( TB @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rotate__simps) ).
thf(322,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA] :
( ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ rotate1 ) )
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( TB @ nil @ ( TB @ rotate1 ) )
= ( TB @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(99,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(543,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(108,axiom,
( rs
= ( as @ ( a @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Cons) ).
thf(592,plain,
( rs
= ( as @ ( a @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(87,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t1
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( G @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_MI1) ).
thf(496,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t1
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( G @ ( A @ ( D @ typing ) @ ( bool @ ( type @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( E @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(657,plain,
$false,
inference(e,[status(thm)],[460,212,343,386,138,481,352,582,276,120,597,384,340,288,320,174,404,189,316,261,211,253,602,147,397,133,307,117,270,546,201,220,512,439,160,407,467,435,329,493,551,285,519,188,141,499,393,457,430,573,579,545,313,611,144,540,113,274,230,509,208,367,594,213,251,330,521,130,278,135,267,505,167,490,531,548,123,355,194,282,150,414,310,441,370,502,463,470,576,250,363,517,304,114,246,478,346,432,410,305,506,474,239,242,163,178,227,322,543,592,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL785_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/0.40 % Computer : n016.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Fri Sep 25 23:38:29 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.91/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.90/1.38 % [INFO] Parsing done (379ms).
% 1.90/1.39 % [INFO] Running in sequential loop mode.
% 3.23/1.79 % [INFO] eprover registered as external prover.
% 3.43/1.80 % [INFO] Scanning for conjecture ...
% 3.63/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 110 axioms. Running axiom selection ...
% 4.43/2.14 % [INFO] Axiom selection finished. Selected 110 axioms (removed 0 axioms).
% 5.85/2.50 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.85/2.52 % [INFO] Type checking passed.
% 5.85/2.52 % [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 ...
% 7.04/2.83 % [INFO] [Domain constraints] Detected constraint on bool
% 7.04/2.83 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 40.36/21.71 % External prover 'e' found a proof!
% 40.36/21.71 % [INFO] Killing All external provers ...
% 40.36/21.72 % Time passed: 21153ms (effective reasoning time: 20317ms)
% 40.36/21.72 % 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)>
% 40.36/21.72 % Axioms used in derivation (110): fact_17_Var_I4_J, fact_88_types__snocE, fact_28_App, fact_44_neq__Nil__conv, fact_85_list_Osimps_I5_J, help_COMBS_1_1_U, fact_43_listsp_Osimps, help_fconj_3_1_U, fact_11_Var_I3_J, fact_67_append__Nil, fact_1_True, fact_16_Var_I2_J, fact_31_listsp_ONil, fact_70_append__eq__append__conv2, fact_32_subst__App, fact_71_append__eq__appendI, fact_65_append1__eq__conv, fact_18_Var__IT, fact_77_rev__induct, fact_12_dB_Osimps_I1_J, fact_37_subst__Var__IT, fact_33_list_Osimps_I2_J, fact_13_dB_Osimps_I2_J, fact_60_append__self__conv, fact_0__096IT_At_096, fact_10_uIT, fact_90_list__app__typeI, fact_2_Cons, help_fFalse_1_1_T, fact_27_dB_Osimps_I10_J, fact_72_append__eq__Cons__conv, fact_57_self__append__conv, fact_52_append__assoc, fact_91_var__app__types, fact_96_list__app__typeE, fact_50_app__last, help_COMBB_1_1_U, fact_3_uT, fact_81_rotate1__is__Nil__conv, fact_7_typing__elims_I1_J, fact_49_splice_Osimps_I2_J, fact_82_rotate1__def, fact_86_list_Osimps_I4_J, fact_61_append__self__conv2, fact_38_subst__lemma, fact_98_maps__simps_I1_J, fact_48_foldl__fun__comm, help_fconj_2_1_U, fact_35_foldl__Nil, fact_76_splice_Osimps_I1_J, fact_55_append__Cons, fact_20_shift__eq, fact_21_list_Oinject, fact_83_types__snoc, fact_19_app__Var__IT, fact_47_type_Osimps_I6_J, fact_8_apps__eq__tail__conv, fact_40_not__Cons__self, fact_14_dB_Osimps_I4_J, fact_41_dB_Osimps_I11_J, fact_93_foldr_Osimps_I1_J, fact_53_same__append__eq, fact_23_MI2, fact_89_typings_Osimps_I2_J, fact_29_type_Osimps_I2_J, fact_6_typing_OVar, fact_92_foldr__append, fact_34_list_Osimps_I3_J, fact_63_append__in__listsp__conv, fact_22_foldl__Cons, help_COMBC_1_1_U, fact_99_maps__simps_I2_J, fact_9_var__app__type__eq, fact_69_eq__Nil__appendI, fact_45_list_Oexhaust, fact_58_self__append__conv2, fact_97_list__app__typeD, fact_68_append__Nil2, help_fconj_1_1_U, fact_95_var__app__typesE, fact_42_typing__elims_I2_J, fact_59_append__is__Nil__conv, fact_26_Var__eq__apps__conv, help_fFalse_1_1_U, fact_51_App__eq__foldl__conv, fact_87_types__snoc__eq, fact_39_not__Cons__self2, fact_56_Nil__is__append__conv, help_pp_1_1_U, fact_79_rev__exhaust2, fact_74_splice__Nil2, fact_46_insert__Nil, fact_15_dB_Osimps_I5_J, fact_75_ext, fact_24_MI1, fact_78_rev__cases, help_pp_2_1_U, fact_25_IT_OVar, fact_54_append__same__eq, fact_5_Var__apps__eq__Var__apps__conv, fact_30_listsp__conj__eq, fact_4_nT, fact_66_Cons__eq__appendI, fact_64_splice_Osimps_I3_J, fact_62_foldl__append, fact_36_subst__eq, fact_84_typings_Osimps_I1_J, fact_73_Cons__eq__append__conv, fact_80_rotate__simps, fact_94_foldr_Osimps_I2_J
% 40.36/21.72 % No. of inferences in proof: 224
% 40.36/21.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21153 ms resp. 20317 ms w/o parsing
% 40.83/21.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 40.83/21.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------