TSTP Solution File: SWW551_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW551_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:25:02 EDT 2023
% Result : Theorem 49.05s 34.20s
% Output : Refutation 49.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 169
% Syntax : Number of formulae : 288 ( 86 unt; 52 typ; 0 def)
% Number of atoms : 2796 ( 320 equ; 0 cnn)
% Maximal formula atoms : 46 ( 11 avg)
% Number of connectives : 9938 ( 86 ~; 36 |; 59 &;9537 @)
% ( 22 <=>; 198 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 19 con; 0-6 aty)
% Number of variables : 1001 ( 0 ^; 923 !; 31 ?;1001 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char_type,type,
char: $tType ).
thf(ty_type,type,
ty: $tType ).
thf(val_type,type,
val: $tType ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(hconf_type,type,
hconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > $o ) ).
thf(oconf_type,type,
oconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) > $o ) ).
thf(preallocated_type,type,
preallocated: ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > $o ).
thf(start_heap_type,type,
start_heap:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) ).
thf(new_type,type,
new:
!>[TA: $tType] : ( ( list @ char ) > ( exp @ TA ) ) ).
thf(fun_upd_type,type,
fun_upd:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA > ( fun @ TB @ TA ) ) ).
thf(map_comp_type,type,
map_comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( option @ TB ) ) > ( fun @ TA @ ( option @ TC ) ) > TA > ( option @ TB ) ) ).
thf(ran_type,type,
ran:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( option @ TA ) ) > ( fun @ TA @ bool ) ) ).
thf(hext_type,type,
hext: ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > $o ).
thf(init_fields_type,type,
init_fields: ( list @ ( product_prod @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ty ) ) > ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ).
thf(new_Addr_type,type,
new_Addr: ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( option @ nat ) ).
thf(bind_type,type,
bind:
!>[TA: $tType,TB: $tType] : ( fun @ ( option @ TB ) @ ( fun @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) ) ) ).
thf(is_none_type,type,
is_none:
!>[TA: $tType] : ( ( option @ TA ) > $o ) ).
thf(map_type,type,
map:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( fun @ ( option @ TB ) @ ( option @ TA ) ) ) ).
thf(none_type,type,
none:
!>[TA: $tType] : ( option @ TA ) ).
thf(some_type,type,
some:
!>[TA: $tType] : ( fun @ TA @ ( option @ TA ) ) ).
thf(option_case_type,type,
option_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) > ( fun @ ( option @ TA ) @ TB ) ) ).
thf(option_rec_type,type,
option_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) > ( option @ TA ) > TB ) ).
thf(set_type,type,
set:
!>[TA: $tType] : ( ( option @ TA ) > ( fun @ TA @ bool ) ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(quickcheck_orelse_type,type,
quickcheck_orelse:
!>[TA: $tType] : ( ( option @ TA ) > ( option @ TA ) > ( option @ TA ) ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(fields_type,type,
fields:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( list @ char ) > ( list @ ( product_prod @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ty ) ) > $o ) ).
thf(wTrt_type,type,
wTrt: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > ( exp @ ( list @ char ) ) > ty > $o ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(fimplies_type,type,
fimplies: fun @ bool @ ( fun @ bool @ bool ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(c_type,type,
c: list @ char ).
thf(e_type,type,
e: fun @ ( list @ char ) @ ( option @ ty ) ).
thf(fDTs_type,type,
fDTs: list @ ( product_prod @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ty ) ).
thf(p_type,type,
p: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ).
thf(t_type,type,
t: ty ).
thf(a_type,type,
a: nat ).
thf(h_a_type,type,
h_a: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ).
thf(ha_type,type,
ha: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(379,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ ( option @ TA ),B: TC] :
( ( map_comp @ TB @ TA @ TC @ A @ ( combk @ ( option @ TB ) @ TC @ ( none @ TB ) ) @ B )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_map__comp__empty_I1_J) ).
thf(231,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ ( option @ TA ),B: TC] :
( ( map_comp @ TB @ TA @ TC @ A @ ( combk @ ( option @ TB ) @ TC @ ( none @ TB ) ) @ B )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Pair__inject) ).
thf(138,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: TB,C: fun @ TB @ bool,D: option @ TA,E: fun @ TA @ bool,F: bool] :
( ( pp @ ( aa @ ( option @ TA ) @ bool @ ( option_case @ bool @ TA @ F @ E ) @ D ) )
=> ( ( ( pp @ F )
=> ( pp @ ( aa @ TB @ bool @ C @ B ) ) )
=> ( ! [G: TA] :
( ( pp @ ( aa @ TA @ bool @ E @ G ) )
=> ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ A @ G ) ) ) )
=> ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( option @ TA ) @ TB @ ( option_case @ TB @ TA @ B @ A ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_disjE__realizer2) ).
thf(234,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: TB,C: fun @ TB @ bool,D: option @ TA,E: fun @ TA @ bool,F: bool] :
( ( pp @ ( aa @ ( option @ TA ) @ bool @ ( option_case @ bool @ TA @ F @ E ) @ D ) )
=> ( ( ( pp @ F )
=> ( pp @ ( aa @ TB @ bool @ C @ B ) ) )
=> ( ! [G: TA] :
( ( pp @ ( aa @ TA @ bool @ E @ G ) )
=> ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ A @ G ) ) ) )
=> ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( option @ TA ) @ TB @ ( option_case @ TB @ TA @ B @ A ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( C = A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_insertCI) ).
thf(555,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( C = A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(102,axiom,
( h_a
= ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ha @ a @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ c @ ( init_fields @ fDTs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_RedNew_I3_J) ).
thf(472,plain,
( h_a
= ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ha @ a @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ c @ ( init_fields @ fDTs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(340,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(18,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_insert__absorb2) ).
thf(174,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] : ( hext @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_hext__refl) ).
thf(185,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] : ( hext @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(77,axiom,
( ( new_Addr @ ha )
= ( aa @ nat @ ( option @ nat ) @ ( some @ nat ) @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_RedNew_I1_J) ).
thf(389,plain,
( ( new_Addr @ ha )
= ( aa @ nat @ ( option @ nat ) @ ( some @ nat ) @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( option @ TB ),B: TA] :
( ( aa @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) @ ( aa @ ( option @ TA ) @ ( fun @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) ) @ ( bind @ TA @ TB ) @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) @ A )
= ( aa @ TA @ ( option @ TB ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_bind__lunit) ).
thf(542,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( option @ TB ),B: TA] :
( ( aa @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) @ ( aa @ ( option @ TA ) @ ( fun @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) ) @ ( bind @ TA @ TB ) @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) @ A )
= ( aa @ TA @ ( option @ TB ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(13,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(157,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( insert @ TA @ C @ B ) @ A ) )
<=> ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_insert__code) ).
thf(284,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( insert @ TA @ C @ B ) @ A ) )
=> ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) )
& ( ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( insert @ TA @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(86,axiom,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( hext @ E @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_hext__upd__obj) ).
thf(416,plain,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( hext @ E @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(325,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(11,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( collect @ TA @ A ) )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fimplies @ ( combb @ bool @ bool @ TA @ fNot @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_insert__Collect) ).
thf(152,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( collect @ TA @ A ) )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fimplies @ ( combb @ bool @ bool @ TA @ fNot @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(448,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(42,axiom,
! [A: bool,B: bool] :
( ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(261,plain,
! [A: bool,B: bool] :
( ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( option @ TA )] :
( ( aa @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) @ ( aa @ ( option @ TB ) @ ( fun @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) ) @ ( bind @ TB @ TA ) @ ( none @ TB ) ) @ A )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_bind__lzero) ).
thf(216,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( option @ TA )] :
( ( aa @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) @ ( aa @ ( option @ TB ) @ ( fun @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) ) @ ( bind @ TB @ TA ) @ ( none @ TB ) ) @ A )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ D @ C @ B )
=> ( ( hext @ C @ A )
=> ( oconf @ TA @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_oconf__hext) ).
thf(164,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ D @ C @ B )
=> ( ( hext @ C @ A )
=> ( oconf @ TA @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [TA: $tType,A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( preallocated @ ( start_heap @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_preallocated__start) ).
thf(179,plain,
! [TA: $tType,A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( preallocated @ ( start_heap @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(58,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(321,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: option @ TB] :
( ( aa @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) @ ( aa @ ( option @ TB ) @ ( fun @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) ) @ ( bind @ TB @ TA ) @ A ) @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_bind__rzero) ).
thf(376,plain,
! [TA: $tType,TB: $tType,A: option @ TB] :
( ( aa @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) @ ( aa @ ( option @ TB ) @ ( fun @ ( fun @ TB @ ( option @ TA ) ) @ ( option @ TA ) ) @ ( bind @ TB @ TA ) @ A ) @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(121,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( option @ TB )] :
( ( ( aa @ TA @ ( option @ TB ) @ C @ B )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ A ) @ ( ran @ TA @ TB @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_ranI) ).
thf(353,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( option @ TB )] :
( ( ( aa @ TA @ ( option @ TB ) @ C @ B )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ A ) @ ( ran @ TA @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(105,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_option_Oinject) ).
thf(480,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(80,axiom,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_option_Osimps_I2_J) ).
thf(397,plain,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(6,axiom,
! [TA: $tType,A: list @ char,B: list @ char] :
( ( ( new @ TA @ B )
= ( new @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_exp_Osimps_I1_J) ).
thf(132,plain,
! [TA: $tType,A: list @ char,B: list @ char] :
( ( ( ( new @ TA @ B )
= ( new @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( new @ TA @ B )
= ( new @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(109,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( insert @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_insert__absorb) ).
thf(507,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( insert @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(29,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ B @ A )
<=> ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_hext__def) ).
thf(206,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( hext @ B @ A )
=> ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) ) )
& ( ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) )
=> ( hext @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(53,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C != B )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insertE) ).
thf(307,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C != B )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( option @ TA )] :
~ ! [D: TB] :
( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ C @ B @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) @ D )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_map__upd__nonempty) ).
thf(248,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( option @ TA )] :
~ ! [D: TB] :
( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ C @ B @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) @ D )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(71,axiom,
! [TA: $tType,A: option @ TA,B: fun @ TA @ bool,C: bool] :
( ( pp @ ( aa @ ( option @ TA ) @ bool @ ( option_case @ bool @ TA @ C @ B ) @ A ) )
=> ( ( ( A
= ( none @ TA ) )
=> ~ ( pp @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ D ) )
=> ~ ( pp @ ( aa @ TA @ bool @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_option__caseE) ).
thf(366,plain,
! [TA: $tType,A: option @ TA,B: fun @ TA @ bool,C: bool] :
( ( pp @ ( aa @ ( option @ TA ) @ bool @ ( option_case @ bool @ TA @ C @ B ) @ A ) )
=> ( ( ( A
= ( none @ TA ) )
=> ~ ( pp @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ D ) )
=> ~ ( pp @ ( aa @ TA @ bool @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( ( D = C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= A ) )
& ( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_fun__upd__def) ).
thf(334,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( ( D = C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= A ) )
& ( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(67,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(349,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( ( D = C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= A ) )
& ( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_fun__upd__apply) ).
thf(297,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( ( D = C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= A ) )
& ( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB] :
( ( aa @ ( option @ TA ) @ ( option @ TB ) @ ( map @ TA @ TB @ B ) @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_option__map__Some) ).
thf(407,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB] :
( ( aa @ ( option @ TA ) @ ( option @ TB ) @ ( map @ TA @ TB @ B ) @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: fun @ TC @ ( option @ TB ),C: fun @ TB @ ( option @ TA )] :
( ( ( map_comp @ TB @ TA @ TC @ C @ B @ A )
= ( none @ TA ) )
<=> ( ( ( aa @ TC @ ( option @ TB ) @ B @ A )
= ( none @ TB ) )
| ? [D: TB] :
( ( ( aa @ TC @ ( option @ TB ) @ B @ A )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ D ) )
& ( ( aa @ TB @ ( option @ TA ) @ C @ D )
= ( none @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_map__comp__None__iff) ).
thf(197,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: fun @ TC @ ( option @ TB ),C: fun @ TB @ ( option @ TA )] :
( ( ( ( map_comp @ TB @ TA @ TC @ C @ B @ A )
= ( none @ TA ) )
=> ( ( ( aa @ TC @ ( option @ TB ) @ B @ A )
= ( none @ TB ) )
| ? [D: TB] :
( ( ( aa @ TC @ ( option @ TB ) @ B @ A )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ D ) )
& ( ( aa @ TB @ ( option @ TA ) @ C @ D )
= ( none @ TA ) ) ) ) )
& ( ( ( ( aa @ TC @ ( option @ TB ) @ B @ A )
= ( none @ TB ) )
| ? [D: TB] :
( ( ( aa @ TC @ ( option @ TB ) @ B @ A )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ D ) )
& ( ( aa @ TB @ ( option @ TA ) @ C @ D )
= ( none @ TA ) ) ) )
=> ( ( map_comp @ TB @ TA @ TC @ C @ B @ A )
= ( none @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(98,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(461,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: TA,B: option @ TB,C: fun @ TB @ TA] :
( ( ( aa @ ( option @ TB ) @ ( option @ TA ) @ ( map @ TB @ TA @ C ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
<=> ? [D: TB] :
( ( B
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ D ) )
& ( ( aa @ TB @ TA @ C @ D )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_option__map__eq__Some) ).
thf(493,plain,
! [TA: $tType,TB: $tType,A: TA,B: option @ TB,C: fun @ TB @ TA] :
( ( ( ( aa @ ( option @ TB ) @ ( option @ TA ) @ ( map @ TB @ TA @ C ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
=> ? [D: TB] :
( ( B
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ D ) )
& ( ( aa @ TB @ TA @ C @ D )
= A ) ) )
& ( ? [D: TB] :
( ( B
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ D ) )
& ( ( aa @ TB @ TA @ C @ D )
= A ) )
=> ( ( aa @ ( option @ TB ) @ ( option @ TA ) @ ( map @ TB @ TA @ C ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(96,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_insertI1) ).
thf(456,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(112,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool,D: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( ( insert @ TA @ D @ C )
= ( insert @ TA @ B @ A ) )
<=> ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( insert @ TA @ B @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( insert @ TA @ D @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_insert__eq__iff) ).
thf(519,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool,D: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( ( ( insert @ TA @ D @ C )
= ( insert @ TA @ B @ A ) )
=> ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( insert @ TA @ B @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( insert @ TA @ D @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) ) )
& ( ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( insert @ TA @ B @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( insert @ TA @ D @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) )
=> ( ( insert @ TA @ D @ C )
= ( insert @ TA @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(82,axiom,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(403,plain,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(69,axiom,
! [A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( hext @ C @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_hext__new) ).
thf(356,plain,
! [A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( hext @ C @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_prod_Orecs) ).
thf(420,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(328,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(101,axiom,
wTrt @ p @ ha @ e @ ( new @ ( list @ char ) @ c ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_RedNew_I4_J) ).
thf(471,plain,
wTrt @ p @ ha @ e @ ( new @ ( list @ char ) @ c ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(4,axiom,
! [TA: $tType,A: option @ TA] :
( ( is_none @ TA @ A )
<=> ( A
= ( none @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_is__none__def) ).
thf(124,plain,
! [TA: $tType,A: option @ TA] :
( ( ( is_none @ TA @ A )
=> ( A
= ( none @ TA ) ) )
& ( ( A
= ( none @ TA ) )
=> ( is_none @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) )
=> ( hext @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_hextI) ).
thf(225,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) )
=> ( hext @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(65,axiom,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( preallocated @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_preallocated__upd__obj) ).
thf(343,plain,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( preallocated @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(44,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
| ~ ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(266,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
| ~ ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(111,axiom,
! [TA: $tType,A: option @ TA] :
( ! [B: TA] :
( A
!= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) )
<=> ( A
= ( none @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_not__Some__eq) ).
thf(513,plain,
! [TA: $tType,A: option @ TA] :
( ( ! [B: TA] :
( A
!= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) )
=> ( A
= ( none @ TA ) ) )
& ( ( A
= ( none @ TA ) )
=> ! [B: TA] :
( A
!= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Pair__eq) ).
thf(166,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: TA] :
( ( option_rec @ TA @ TB @ B @ A @ ( none @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_option_Orecs_I1_J) ).
thf(161,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: TA] :
( ( option_rec @ TA @ TB @ B @ A @ ( none @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_insert__compr) ).
thf(149,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_fun__upd__other) ).
thf(423,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( option @ TA ),C: TA,D: TB,E: fun @ TB @ ( option @ TA )] :
( ( ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ C ) )
= ( fun_upd @ TB @ ( option @ TA ) @ B @ D @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_map__upd__eqD1) ).
thf(191,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( option @ TA ),C: TA,D: TB,E: fun @ TB @ ( option @ TA )] :
( ( ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ C ) )
= ( fun_upd @ TB @ ( option @ TA ) @ B @ D @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(49,axiom,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ G @ F @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ F @ D )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( oconf @ TA @ G @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ F @ D @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_oconf__upd__obj) ).
thf(291,plain,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ G @ F @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ F @ D )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( oconf @ TA @ G @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ F @ D @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(114,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: option @ TA] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( set @ TA @ C ) ) )
=> ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( ( C
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_ospec) ).
thf(545,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: option @ TA] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( set @ TA @ C ) ) )
=> ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( ( C
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( option @ TB )] :
( ( ( aa @ TA @ ( option @ TB ) @ C @ B )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ A ) )
=> ( ( fun_upd @ TA @ ( option @ TB ) @ C @ B @ ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ A ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_map__upd__triv) ).
thf(391,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( option @ TB )] :
( ( ( aa @ TA @ ( option @ TB ) @ C @ B )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ A ) )
=> ( ( fun_upd @ TA @ ( option @ TB ) @ C @ B @ ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(92,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A )
!= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_option_Osimps_I3_J) ).
thf(445,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A )
!= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_split__paired__Ex) ).
thf(382,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(55,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(313,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(21,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ B )
=> ( ( hext @ B @ A )
=> ( preallocated @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_preallocated__hext) ).
thf(181,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ B )
=> ( ( hext @ B @ A )
=> ( preallocated @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB,D: fun @ TB @ TA] :
( ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ D @ C @ B ) @ C @ A )
= ( fun_upd @ TB @ TA @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_fun__upd__upd) ).
thf(187,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB,D: fun @ TB @ TA] :
( ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ D @ C @ B ) @ C @ A )
= ( fun_upd @ TB @ TA @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB] :
( ( map @ TA @ TB @ A )
= ( option_case @ ( option @ TB ) @ TA @ ( none @ TB ) @ ( combb @ TB @ ( option @ TB ) @ TA @ ( some @ TB ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Option_Omap__def) ).
thf(219,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB] :
( ( map @ TA @ TB @ A )
= ( option_case @ ( option @ TB ) @ TA @ ( none @ TB ) @ ( combb @ TB @ ( option @ TB ) @ TA @ ( some @ TB ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(87,axiom,
hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_RedNew_I5_J) ).
thf(419,plain,
hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(94,axiom,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( ( oconf @ TA @ D @ C @ A )
=> ( hconf @ TA @ D @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_hconf__new) ).
thf(451,plain,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( ( oconf @ TA @ D @ C @ A )
=> ( hconf @ TA @ D @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB] :
( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) @ A @ ( none @ TA ) ) @ B )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_empty__upd__none) ).
thf(318,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB] :
( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) @ A @ ( none @ TA ) ) @ B )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_split__paired__All) ).
thf(303,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: option @ TA,B: fun @ TA @ TB] :
( ( ( aa @ ( option @ TA ) @ ( option @ TB ) @ ( map @ TA @ TB @ B ) @ A )
= ( none @ TB ) )
<=> ( A
= ( none @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_option__map__is__None) ).
thf(271,plain,
! [TA: $tType,TB: $tType,A: option @ TA,B: fun @ TA @ TB] :
( ( ( ( aa @ ( option @ TA ) @ ( option @ TB ) @ ( map @ TA @ TB @ B ) @ A )
= ( none @ TB ) )
=> ( A
= ( none @ TA ) ) )
& ( ( A
= ( none @ TA ) )
=> ( ( aa @ ( option @ TA ) @ ( option @ TB ) @ ( map @ TA @ TB @ B ) @ A )
= ( none @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ TA] :
( ( aa @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_fun__upd__same) ).
thf(477,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ TA] :
( ( aa @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(115,axiom,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ F @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( ( oconf @ TA @ F @ E @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) )
=> ( hconf @ TA @ F @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_hconf__upd__obj) ).
thf(552,plain,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ F @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( ( oconf @ TA @ F @ E @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) )
=> ( hconf @ TA @ F @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_insertI2) ).
thf(323,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ TB] :
( ( ( aa @ TA @ TB @ C @ B )
= A )
=> ( ( fun_upd @ TA @ TB @ C @ B @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_fun__upd__idem) ).
thf(251,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ TB] :
( ( ( aa @ TA @ TB @ C @ B )
= A )
=> ( ( fun_upd @ TA @ TB @ C @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(12,axiom,
! [TA: $tType] : ( is_none @ TA @ ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_is__none__code_I1_J) ).
thf(155,plain,
! [TA: $tType] : ( is_none @ TA @ ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( hext @ E @ A )
=> ( wTrt @ F @ A @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_WTrt__hext__mono) ).
thf(130,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( hext @ E @ A )
=> ( wTrt @ F @ A @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(79,axiom,
! [TA: $tType,A: option @ TA,B: option @ TA] :
( ( quickcheck_orelse @ TA @ B @ A )
= ( aa @ ( option @ TA ) @ ( option @ TA ) @ ( option_case @ ( option @ TA ) @ TA @ A @ ( some @ TA ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_) ).
thf(394,plain,
! [TA: $tType,A: option @ TA,B: option @ TA] :
( ( quickcheck_orelse @ TA @ B @ A )
= ( aa @ ( option @ TA ) @ ( option @ TA ) @ ( option_case @ ( option @ TA ) @ TA @ A @ ( some @ TA ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(118,axiom,
! [A: nat,B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( new_Addr @ B )
= ( aa @ nat @ ( option @ nat ) @ ( some @ nat ) @ A ) )
=> ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ A )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_new__Addr__SomeD) ).
thf(563,plain,
! [A: nat,B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( new_Addr @ B )
= ( aa @ nat @ ( option @ nat ) @ ( some @ nat ) @ A ) )
=> ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ A )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: fun @ TB @ ( option @ TA )] :
( ( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ C ) ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
<=> ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( aa @ TB @ ( option @ TA ) @ E @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_map__upd__Some__unfold) ).
thf(426,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: fun @ TB @ ( option @ TA )] :
( ( ( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ C ) ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
=> ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( aa @ TB @ ( option @ TA ) @ E @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) ) )
& ( ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( aa @ TB @ ( option @ TA ) @ E @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) )
=> ( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ C ) ) @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(72,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: list @ ( product_prod @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ty ),C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( fields @ TA @ D @ C @ B )
=> ( oconf @ TA @ D @ A @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ ( init_fields @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_oconf__init__fields) ).
thf(374,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: list @ ( product_prod @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ty ),C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( fields @ TA @ D @ C @ B )
=> ( oconf @ TA @ D @ A @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ ( init_fields @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(255,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ ( option @ TA ),B: TC,C: fun @ TC @ ( option @ TB )] :
( ( ( aa @ TC @ ( option @ TB ) @ C @ B )
= ( none @ TB ) )
=> ( ( map_comp @ TB @ TA @ TC @ A @ C @ B )
= ( none @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_map__comp__simps_I1_J) ).
thf(458,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ ( option @ TA ),B: TC,C: fun @ TC @ ( option @ TB )] :
( ( ( aa @ TC @ ( option @ TB ) @ C @ B )
= ( none @ TB ) )
=> ( ( map_comp @ TB @ TA @ TC @ A @ C @ B )
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB,C: TB] :
( ( option_rec @ TB @ TA @ C @ B @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
= ( aa @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_option_Orecs_I2_J) ).
thf(194,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB,C: TB] :
( ( option_rec @ TB @ TA @ C @ B @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
= ( aa @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( option @ TB ),B: fun @ TB @ ( option @ TC ),C: TA] :
( ( map_comp @ TB @ TC @ TA @ B @ A @ C )
= ( aa @ ( option @ TB ) @ ( option @ TC ) @ ( option_case @ ( option @ TC ) @ TB @ ( none @ TC ) @ B ) @ ( aa @ TA @ ( option @ TB ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_map__comp__def) ).
thf(263,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( option @ TB ),B: fun @ TB @ ( option @ TC ),C: TA] :
( ( map_comp @ TB @ TC @ TA @ B @ A @ C )
= ( aa @ ( option @ TB ) @ ( option @ TC ) @ ( option_case @ ( option @ TC ) @ TB @ ( none @ TC ) @ B ) @ ( aa @ TA @ ( option @ TB ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: TA] :
( ( aa @ ( option @ TB ) @ TA @ ( option_case @ TA @ TB @ B @ A ) @ ( none @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_option_Osimps_I4_J) ).
thf(310,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: TA] :
( ( aa @ ( option @ TB ) @ TA @ ( option_case @ TA @ TB @ B @ A ) @ ( none @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(19,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ C @ B )
=> ( ( hext @ B @ A )
=> ( hext @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_hext__trans) ).
thf(177,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ C @ B )
=> ( ( hext @ B @ A )
=> ( hext @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(62,axiom,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) )
=> ( oconf @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_hconfD) ).
thf(331,plain,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) )
=> ( oconf @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(99,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( ( ( insert @ TA @ C @ B )
= ( insert @ TA @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_insert__ident) ).
thf(463,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( ( ( ( insert @ TA @ C @ B )
= ( insert @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( insert @ TA @ C @ B )
= ( insert @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(70,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ B @ A )
<=> ( ! [C: nat,D: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D ) )
=> ( oconf @ TA @ B @ A @ D ) )
& ( preallocated @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_hconf__def) ).
thf(359,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( ( hconf @ TA @ B @ A )
=> ( ! [C: nat,D: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D ) )
=> ( oconf @ TA @ B @ A @ D ) )
& ( preallocated @ A ) ) )
& ( ( ! [C: nat,D: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D ) )
=> ( oconf @ TA @ B @ A @ D ) )
& ( preallocated @ A ) )
=> ( hconf @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( option @ TB )] :
( ( ( aa @ TA @ ( option @ TB ) @ C @ B )
= ( none @ TB ) )
=> ( ( ran @ TA @ TB @ ( fun_upd @ TA @ ( option @ TB ) @ C @ B @ ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ A ) ) )
= ( insert @ TB @ A @ ( ran @ TA @ TB @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_ran__map__upd) ).
thf(386,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( option @ TB )] :
( ( ( aa @ TA @ ( option @ TB ) @ C @ B )
= ( none @ TB ) )
=> ( ( ran @ TA @ TB @ ( fun_upd @ TA @ ( option @ TB ) @ C @ B @ ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ A ) ) )
= ( insert @ TB @ A @ ( ran @ TA @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( insert @ TA @ A @ B )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_insert__compr__raw) ).
thf(143,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( insert @ TA @ A @ B )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,axiom,
! [TA: $tType,A: option @ TA] :
( ( aa @ ( fun @ TA @ ( option @ TA ) ) @ ( option @ TA ) @ ( aa @ ( option @ TA ) @ ( fun @ ( fun @ TA @ ( option @ TA ) ) @ ( option @ TA ) ) @ ( bind @ TA @ TA ) @ A ) @ ( some @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_bind__runit) ).
thf(258,plain,
! [TA: $tType,A: option @ TA] :
( ( aa @ ( fun @ TA @ ( option @ TA ) ) @ ( option @ TA ) @ ( aa @ ( option @ TA ) @ ( fun @ ( fun @ TA @ ( option @ TA ) ) @ ( option @ TA ) ) @ ( bind @ TA @ TA ) @ A ) @ ( some @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ TA,D: TB,E: TB] :
( ( E != D )
=> ( ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ E @ B ) @ D @ A )
= ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ D @ A ) @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_fun__upd__twist) ).
thf(158,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ TA,D: TB,E: TB] :
( ( E != D )
=> ( ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ E @ B ) @ D @ A )
= ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ D @ A ) @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
( ( new_Addr @ ha )
= ( aa @ nat @ ( option @ nat ) @ ( some @ nat ) @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( new_Addr @ ha )
!= ( aa @ nat @ ( option @ nat ) @ ( some @ nat ) @ a ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
( ( new_Addr @ ha )
!= ( aa @ nat @ ( option @ nat ) @ ( some @ nat ) @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( option @ TB ),B: TA,C: TC,D: fun @ TC @ ( option @ TA )] :
( ( ( aa @ TC @ ( option @ TA ) @ D @ C )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) )
=> ( ( map_comp @ TA @ TB @ TC @ A @ D @ C )
= ( aa @ TA @ ( option @ TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_map__comp__simps_I2_J) ).
thf(510,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( option @ TB ),B: TA,C: TC,D: fun @ TC @ ( option @ TA )] :
( ( ( aa @ TC @ ( option @ TA ) @ D @ C )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) )
=> ( ( map_comp @ TA @ TB @ TC @ A @ D @ C )
= ( aa @ TA @ ( option @ TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB,C: TB] :
( ( aa @ ( option @ TA ) @ TB @ ( option_case @ TB @ TA @ C @ B ) @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
= ( aa @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_option_Osimps_I5_J) ).
thf(346,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB,C: TB] :
( ( aa @ ( option @ TA ) @ TB @ ( option_case @ TB @ TA @ C @ B ) @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
= ( aa @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(56,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(315,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(85,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
<=> ? [B: TA] :
( A
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_not__None__eq) ).
thf(410,plain,
! [TA: $tType,A: option @ TA] :
( ( ( A
!= ( none @ TA ) )
=> ? [B: TA] :
( A
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) )
& ( ? [B: TA] :
( A
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) )
=> ( A
!= ( none @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(9,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( insert @ TA @ C @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ ( insert @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_insert__commute) ).
thf(146,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( insert @ TA @ C @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ ( insert @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(83,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(405,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(25,axiom,
fields @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ c @ fDTs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_RedNew_I2_J) ).
thf(190,plain,
fields @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ c @ fDTs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(22,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(183,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( option @ TB ),B: fun @ TC @ ( option @ TA ),C: option @ TC] :
( ( aa @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) @ ( aa @ ( option @ TA ) @ ( fun @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) ) @ ( bind @ TA @ TB ) @ ( aa @ ( fun @ TC @ ( option @ TA ) ) @ ( option @ TA ) @ ( aa @ ( option @ TC ) @ ( fun @ ( fun @ TC @ ( option @ TA ) ) @ ( option @ TA ) ) @ ( bind @ TC @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ ( fun @ TC @ ( option @ TB ) ) @ ( option @ TB ) @ ( aa @ ( option @ TC ) @ ( fun @ ( fun @ TC @ ( option @ TB ) ) @ ( option @ TB ) ) @ ( bind @ TC @ TB ) @ C ) @ ( combc @ TC @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) @ ( combb @ ( option @ TA ) @ ( fun @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) ) @ TC @ ( bind @ TA @ TB ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_bind__assoc) ).
thf(294,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( option @ TB ),B: fun @ TC @ ( option @ TA ),C: option @ TC] :
( ( aa @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) @ ( aa @ ( option @ TA ) @ ( fun @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) ) @ ( bind @ TA @ TB ) @ ( aa @ ( fun @ TC @ ( option @ TA ) ) @ ( option @ TA ) @ ( aa @ ( option @ TC ) @ ( fun @ ( fun @ TC @ ( option @ TA ) ) @ ( option @ TA ) ) @ ( bind @ TC @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ ( fun @ TC @ ( option @ TB ) ) @ ( option @ TB ) @ ( aa @ ( option @ TC ) @ ( fun @ ( fun @ TC @ ( option @ TB ) ) @ ( option @ TB ) ) @ ( bind @ TC @ TB ) @ C ) @ ( combc @ TC @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) @ ( combb @ ( option @ TA ) @ ( fun @ ( fun @ TA @ ( option @ TB ) ) @ ( option @ TB ) ) @ TC @ ( bind @ TA @ TB ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(45,axiom,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ E @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( oconf @ TA @ E @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ B @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_oconf__new) ).
thf(268,plain,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ E @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( oconf @ TA @ E @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ B @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB] :
( ( fun_upd @ TA @ TB @ B @ A @ ( aa @ TA @ TB @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_fun__upd__triv) ).
thf(474,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB] :
( ( fun_upd @ TA @ TB @ B @ A @ ( aa @ TA @ TB @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(81,axiom,
! [A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( preallocated @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_preallocated__new) ).
thf(400,plain,
! [A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( preallocated @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(36,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_option_Oexhaust) ).
thf(239,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(37,axiom,
! [TA: $tType,A: option @ TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( set @ TA @ A ) ) )
<=> ( A
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_elem__set) ).
thf(242,plain,
! [TA: $tType,A: option @ TA,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( set @ TA @ A ) ) )
=> ( A
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) ) )
& ( ( A
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( set @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( option @ TB ),D: fun @ TB @ ( option @ TA )] :
( ( ( map_comp @ TB @ TA @ TC @ D @ C @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
<=> ? [E: TB] :
( ( ( aa @ TC @ ( option @ TB ) @ C @ B )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ E ) )
& ( ( aa @ TB @ ( option @ TA ) @ D @ E )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_map__comp__Some__iff) ).
thf(277,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( option @ TB ),D: fun @ TB @ ( option @ TA )] :
( ( ( ( map_comp @ TB @ TA @ TC @ D @ C @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) )
=> ? [E: TB] :
( ( ( aa @ TC @ ( option @ TB ) @ C @ B )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ E ) )
& ( ( aa @ TB @ ( option @ TA ) @ D @ E )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) )
& ( ? [E: TB] :
( ( ( aa @ TC @ ( option @ TB ) @ C @ B )
= ( aa @ TB @ ( option @ TB ) @ ( some @ TB ) @ E ) )
& ( ( aa @ TB @ ( option @ TA ) @ D @ E )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) )
=> ( ( map_comp @ TB @ TA @ TC @ D @ C @ B )
= ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TC @ ( option @ TB ),B: TC] :
( ( map_comp @ TB @ TA @ TC @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) @ A @ B )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_map__comp__empty_I2_J) ).
thf(442,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TC @ ( option @ TB ),B: TC] :
( ( map_comp @ TB @ TA @ TC @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) @ A @ B )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ TA] :
( ( ( fun_upd @ TB @ TA @ C @ B @ A )
= C )
<=> ( ( aa @ TB @ TA @ C @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_fun__upd__idem__iff) ).
thf(501,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ TA] :
( ( ( ( fun_upd @ TB @ TA @ C @ B @ A )
= C )
=> ( ( aa @ TB @ TA @ C @ B )
= A ) )
& ( ( ( aa @ TB @ TA @ C @ B )
= A )
=> ( ( fun_upd @ TB @ TA @ C @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(106,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
<=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_insert__iff) ).
thf(486,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(100,axiom,
! [TA: $tType,A: TA] :
~ ( is_none @ TA @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_is__none__code_I2_J) ).
thf(469,plain,
! [TA: $tType,A: TA] :
~ ( is_none @ TA @ ( aa @ TA @ ( option @ TA ) @ ( some @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA] :
( ( aa @ ( option @ TB ) @ ( option @ TA ) @ ( map @ TB @ TA @ A ) @ ( none @ TB ) )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_option__map__None) ).
thf(560,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA] :
( ( aa @ ( option @ TB ) @ ( option @ TA ) @ ( map @ TB @ TA @ A ) @ ( none @ TB ) )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(32,axiom,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: list @ char,C: nat,D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ E @ D )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ B @ A ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ B @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_hext__objD) ).
thf(222,plain,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: list @ char,C: nat,D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ E @ D )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ B @ A ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ C )
= ( aa @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(95,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(454,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(566,plain,
$false,
inference(e,[status(thm)],[379,231,138,234,555,472,340,174,185,389,542,157,284,416,325,152,448,261,216,164,179,321,376,121,353,480,397,132,507,206,307,248,366,334,349,297,407,197,461,493,456,519,403,356,420,328,471,124,225,343,266,513,166,161,149,423,191,291,545,391,445,382,313,181,187,219,419,451,318,303,271,477,552,323,251,155,130,394,563,426,374,255,458,194,263,310,177,331,463,359,386,143,258,158,119,510,346,315,410,146,405,190,183,294,268,474,400,239,242,277,442,501,486,469,560,222,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW551_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 21:59:10 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.12 % [INFO] Parsing done (229ms).
% 1.61/1.13 % [INFO] Running in sequential loop mode.
% 2.41/1.33 % [INFO] eprover registered as external prover.
% 2.41/1.33 % [INFO] cvc4 registered as external prover.
% 2.41/1.33 % [INFO] Scanning for conjecture ...
% 2.63/1.45 % [INFO] Found a conjecture and 116 axioms. Running axiom selection ...
% 3.09/1.53 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 3.93/1.71 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.93/1.73 % [INFO] Type checking passed.
% 3.93/1.73 % [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 ...
% 49.05/34.20 % External prover 'e' found a proof!
% 49.05/34.20 % [INFO] Killing All external provers ...
% 49.05/34.20 % Time passed: 33681ms (effective reasoning time: 33070ms)
% 49.05/34.20 % 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)>
% 49.05/34.20 % Axioms used in derivation (116): fact_30_map__upd__eqD1, help_fimplies_2_1_U, fact_67_hext__trans, fact_8_bind__lunit, help_COMBS_1_1_U, fact_41_option_Oexhaust, fact_63_hconf__def, fact_73_hext__def, fact_42_split__paired__All, fact_34_option_Osimps_I2_J, fact_90_insert__absorb, fact_97_insert__compr, fact_81_ran__map__upd, fact_93_insert__ident, fact_31_map__upd__triv, fact_37_option__caseE, fact_72_preallocated__hext, fact_18_bind__rzero, fact_12_map__comp__simps_I2_J, fact_29_map__comp__simps_I1_J, fact_95_insert__commute, fact_7_option_Osimps_I5_J, fact_49_fun__upd__twist, fact_33_option_Osimps_I3_J, fact_55_, fact_46_fun__upd__def, help_fNot_2_1_U, fact_13_bind__assoc, fact_69_preallocated__new, fact_89_insertE, fact_92_insert__eq__iff, fact_74_WTrt__hext__mono, fact_15_not__Some__eq, fact_4_option_Orecs_I2_J, help_fNot_1_1_U, fact_25_map__comp__def, fact_20_map__comp__empty_I2_J, fact_11_ranI, fact_48_fun__upd__other, fact_36_ospec, fact_0_RedNew_I1_J, fact_14_not__None__eq, fact_71_hext__objD, fact_54_prod_Orecs, fact_70_preallocated__upd__obj, help_COMBB_1_1_U, fact_87_insert__iff, fact_35_bind__runit, fact_44_RedNew_I4_J, fact_53_exp_Osimps_I1_J, fact_38_fun__upd__triv, fact_24_is__none__def, help_fdisj_1_1_U, fact_79_preallocated__start, fact_28_option_Osimps_I4_J, fact_62_oconf__init__fields, fact_88_insertCI, fact_22_map__upd__nonempty, fact_78_hextI, fact_10_map__comp__Some__iff, fact_1_option_Oinject, fact_52_split__paired__Ex, fact_40_fun__upd__apply, fact_50_fun__upd__same, help_fequal_1_1_T, fact_76_mem__def, fact_27_option_Orecs_I1_J, fact_66_hext__refl, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_68_oconf__hext, fact_84_option__map__is__None, fact_45_Pair__inject, fact_3_elem__set, fact_17_empty__upd__none, fact_96_insert__Collect, fact_83_option__map__eq__Some, help_COMBC_1_1_U, fact_51_fun__upd__idem__iff, fact_64_hext__new, fact_16_bind__lzero, help_fequal_2_1_T, fact_85_option__map__None, fact_80_Option_Omap__def, fact_82_option__map__Some, help_fdisj_3_1_U, fact_98_insertI1, fact_6_RedNew_I3_J, fact_57_hconf__new, fact_65_hext__upd__obj, fact_43_Pair__eq, fact_2_new__Addr__SomeD, fact_23_is__none__code_I1_J, fact_9_RedNew_I5_J, fact_77_Collect__def, fact_60_oconf__upd__obj, fact_59_hconfD, help_pp_1_1_U, fact_99_insert__compr__raw, fact_56_disjE__realizer2, help_fimplies_1_1_U, fact_61_oconf__new, fact_5_is__none__code_I2_J, fact_75_ext, fact_58_hconf__upd__obj, help_fimplies_3_1_U, fact_86_insert__absorb2, fact_47_fun__upd__idem, fact_32_map__upd__Some__unfold, fact_26_map__comp__None__iff, fact_19_map__comp__empty_I1_J, help_pp_2_1_U, fact_94_insert__code, fact_21_RedNew_I2_J, fact_39_fun__upd__upd, fact_91_insertI2
% 49.05/34.20 % No. of inferences in proof: 236
% 49.05/34.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 33681 ms resp. 33070 ms w/o parsing
% 49.51/34.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 49.51/34.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------