TSTP Solution File: SWW474+6 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW474+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 12:24:16 EDT 2023
% Result : Theorem 107.60s 30.03s
% Output : Refutation 109.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 711
% Syntax : Number of formulae : 1372 ( 453 unt; 89 typ; 0 def)
% Number of atoms : 3097 (1087 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 82755 ( 322 ~; 79 |; 221 &;80629 @)
% ( 71 <=>;1433 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 92 ( 89 usr; 27 con; 0-4 aty)
% Number of variables : 4340 ( 0 ^;4284 !; 56 ?;4340 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i > $i > $i ).
thf(fun_type,type,
fun: $i > $i > $i ).
thf(hoare_1656922687triple_type,type,
hoare_1656922687triple: $i > $i ).
thf(state_type,type,
state: $i ).
thf(bool_type,type,
bool: $i ).
thf(hoare_279057269derivs_type,type,
hoare_279057269derivs: $i > $i ).
thf(pname_type,type,
pname: $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(com_type,type,
com: $i ).
thf(combb_type,type,
combb: $i > $i > $i > $i ).
thf(hoare_Mirabelle_MGT_type,type,
hoare_Mirabelle_MGT: $i ).
thf(body_1_type,type,
body_1: $i ).
thf(option_type,type,
option: $i > $i ).
thf(dom_type,type,
dom: $i > $i > $i ).
thf(body_type,type,
body: $i ).
thf(insert_type,type,
insert: $i > $i ).
thf(y_type,type,
y: $i ).
thf(bot_bot_type,type,
bot_bot: $i > $i ).
thf(ti_type,type,
ti: $i > $i > $i ).
thf(undefined_type,type,
undefined: $i > $i ).
thf(member_type,type,
member: $i > $i ).
thf(the_1_type,type,
the_1: $i > $i ).
thf(semilattice_sup_type,type,
semilattice_sup: $i > $o ).
thf(semilattice_sup_sup_type,type,
semilattice_sup_sup: $i > $i ).
thf(finite_finite_type,type,
finite_finite: $i > $i ).
thf(minus_minus_type,type,
minus_minus: $i > $i ).
thf(the_type,type,
the: $i > $i ).
thf(fNot_type,type,
fNot: $i ).
thf(semilattice_inf_inf_type,type,
semilattice_inf_inf: $i > $i ).
thf(minus_type,type,
minus: $i > $o ).
thf(semi_type,type,
semi: $i ).
thf(order_type,type,
order: $i > $o ).
thf(ord_type,type,
ord: $i > $o ).
thf(ord_less_eq_type,type,
ord_less_eq: $i > $i ).
thf(collect_type,type,
collect: $i > $i ).
thf(combs_type,type,
combs: $i > $i > $i > $i ).
thf(fconj_type,type,
fconj: $i ).
thf(combc_type,type,
combc: $i > $i > $i > $i ).
thf(fequal_type,type,
fequal: $i > $i ).
thf(some_type,type,
some: $i > $i ).
thf(fFalse_type,type,
fFalse: $i ).
thf(none_type,type,
none: $i > $i ).
thf(hoare_246368825triple_type,type,
hoare_246368825triple: $i > $i ).
thf(lattice_type,type,
lattice: $i > $o ).
thf(evalc_type,type,
evalc: $i ).
thf(skip_type,type,
skip: $i ).
thf(set_type,type,
set: $i > $i ).
thf(option_rec_type,type,
option_rec: $i > $i > $i ).
thf(fdisj_type,type,
fdisj: $i ).
thf(pn_type,type,
pn: $i ).
thf(override_on_type,type,
override_on: $i > $i > $i ).
thf(semilattice_inf_type,type,
semilattice_inf: $i > $o ).
thf(hoare_1924220188gleton_type,type,
hoare_1924220188gleton: $i ).
thf(fAll_type,type,
fAll: $i > $i ).
thf(fimplies_type,type,
fimplies: $i ).
thf(finite_comp_fun_idem_type,type,
finite_comp_fun_idem: $i > $i > $i ).
thf(while_type,type,
while: $i ).
thf(finite_finite_1_type,type,
finite_finite_1: $i > $o ).
thf(finite2073411215e_idem_type,type,
finite2073411215e_idem: $i > $i ).
thf(hoare_1312322281e_case_type,type,
hoare_1312322281e_case: $i > $i > $i ).
thf(bounded_lattice_bot_type,type,
bounded_lattice_bot: $i > $o ).
thf(inj_on_type,type,
inj_on: $i > $i > $i ).
thf(fun_upd_type,type,
fun_upd: $i > $i > $i ).
thf(finite1357897459simple_type,type,
finite1357897459simple: $i > $i > $i ).
thf(finite_folding_one_type,type,
finite_folding_one: $i > $i ).
thf(preorder_type,type,
preorder: $i > $o ).
thf(wt_type,type,
wt: $i ).
thf(the_elem_type,type,
the_elem: $i > $i ).
thf(wT_bodies_type,type,
wT_bodies: $i ).
thf(fTrue_type,type,
fTrue: $i ).
thf(finite908156982e_idem_type,type,
finite908156982e_idem: $i > $i > $i ).
thf(fold_graph_type,type,
fold_graph: $i > $i > $i ).
thf(combk_type,type,
combk: $i > $i > $i ).
thf(fa_type,type,
fa: $i ).
thf(bot_type,type,
bot: $i > $o ).
thf(distrib_lattice_type,type,
distrib_lattice: $i > $o ).
thf(combi_type,type,
combi: $i > $i ).
thf(if_type,type,
if: $i > $i ).
thf(hoare_2027193591valids_type,type,
hoare_2027193591valids: $i > $i ).
thf(hoare_1632998903le_rec_type,type,
hoare_1632998903le_rec: $i > $i > $i ).
thf(bounded_lattice_type,type,
bounded_lattice: $i > $o ).
thf(partial_flat_lub_type,type,
partial_flat_lub: $i > $i ).
thf(ab_group_add_type,type,
ab_group_add: $i > $o ).
thf(linorder_type,type,
linorder: $i > $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add: $i > $o ).
thf(sk80_type,type,
sk80: $i > $i ).
thf(sk95_type,type,
sk95: $i ).
thf(sk96_type,type,
sk96: $i ).
thf(202,axiom,
! [A: $i] :
( ( hAPP @ pname @ com @ body_1 @ A )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_com_Osimps_I19_J) ).
thf(1322,plain,
! [A: $i] :
( ( hAPP @ pname @ com @ body_1 @ A )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_UnE) ).
thf(1036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__surj) ).
thf(1501,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( ( hAPP @ A @ B @ E @ C )
= ( hAPP @ A @ B @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ F ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_inj__onD) ).
thf(1879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( ( hAPP @ A @ B @ E @ C )
= ( hAPP @ A @ B @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ F ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ D ) @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ H ) @ C ) )
=> ( ( hAPP @ A @ B @ F @ H )
= ( ti @ B @ E ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ G @ C )
= ( ti @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_folding__image__simple_Oneutral) ).
thf(1168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ D ) @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ H ) @ C ) )
=> ( ( hAPP @ A @ B @ F @ H )
= ( ti @ B @ E ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ G @ C )
= ( ti @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
=> ( ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
= ( ti @ ( fun @ A @ ( option @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_map__upd__triv) ).
thf(2072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
=> ( ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
= ( ti @ ( fun @ A @ ( option @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
<=> ( ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
& ( ( ti @ A @ C )
= ( ti @ A @ E ) ) )
| ( ( ( ti @ A @ B )
= ( ti @ A @ E ) )
& ( ( ti @ A @ C )
= ( ti @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_doubleton__eq__iff) ).
thf(1559,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
& ( ( ti @ A @ C )
= ( ti @ A @ E ) ) )
| ( ( ( ti @ A @ B )
= ( ti @ A @ E ) )
& ( ( ti @ A @ C )
= ( ti @ A @ D ) ) ) ) )
& ( ( ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
& ( ( ti @ A @ C )
= ( ti @ A @ E ) ) )
| ( ( ( ti @ A @ B )
= ( ti @ A @ E ) )
& ( ( ti @ A @ C )
= ( ti @ A @ D ) ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(4,axiom,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(628,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( combk @ ( option @ B ) @ A ) @ ( none @ B ) ) ) @ C ) @ ( none @ B ) ) @ D )
= ( none @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_empty__upd__none) ).
thf(1982,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( combk @ ( option @ B ) @ A ) @ ( none @ B ) ) ) @ C ) @ ( none @ B ) ) @ D )
= ( none @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(566,axiom,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( semilattice_sup_sup @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( semilattice_sup_sup @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_sup__fun__def) ).
thf(2559,plain,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( semilattice_sup_sup @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( semilattice_sup_sup @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(2331,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ state ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ state ) @ ( hAPP @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) ) ) ) ) @ ( fequal @ state ) ) ) ) @ B ) @ ( fequal @ state ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_MGT__alternI) ).
thf(1950,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ state ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ state ) @ ( hAPP @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) ) ) ) ) @ ( fequal @ state ) ) ) ) @ B ) @ ( fequal @ state ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ti @ B @ E )
= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ B @ E )
!= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_fun__upd__apply) ).
thf(1110,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ti @ B @ E )
= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ B @ E )
!= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_singleton__conv) ).
thf(1686,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ ( hAPP @ pname @ com @ body_1 @ A ) ) ) @ B ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ A ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ ( hAPP @ pname @ com @ body_1 @ A ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_MGT__BodyN) ).
thf(645,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ ( hAPP @ pname @ com @ body_1 @ A ) ) ) @ B ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ A ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ ( hAPP @ pname @ com @ body_1 @ A ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_weaken) ).
thf(892,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( semilattice_inf_inf @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( semilattice_inf_inf @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_inf__fun__def) ).
thf(2109,plain,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( semilattice_inf_inf @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( semilattice_inf_inf @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(445,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) )
<=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_le__inf__iff) ).
thf(2131,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ F )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ D ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ bool @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( fun @ bool @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( combc @ A @ bool @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ A @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ A @ ( fun @ bool @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ bool @ ( fun @ state @ bool ) ) @ A ) @ ( combc @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ A ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fconj ) ) @ C ) ) ) @ F ) ) @ D ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_constant) ).
thf(1454,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ F )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ D ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ bool @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( fun @ bool @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( combc @ A @ bool @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ A @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ A @ ( fun @ bool @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ bool @ ( fun @ state @ bool ) ) @ A ) @ ( combc @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ A ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fconj ) ) @ C ) ) ) @ F ) ) @ D ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(526,axiom,
! [A: $i] :
( ( ( ti @ bool @ A )
= fTrue )
| ( ( ti @ bool @ A )
= fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(2412,plain,
! [A: $i] :
( ( ( ti @ bool @ A )
= fTrue )
| ( ( ti @ bool @ A )
= fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(68,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
= ( collect @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
thf(846,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
= ( collect @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(577,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_sup_Oidem) ).
thf(2595,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_Un__insert__right) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_image__mono) ).
thf(1005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ C ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C ) ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_folding__image__simple_Ounion__inter) ).
thf(1882,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ C ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C ) ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(475,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D ) )
<=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_le__sup__iff) ).
thf(2231,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ B ) ) @ bool ) @ ( finite_comp_fun_idem @ A @ B ) )
= ( finite_comp_fun_idem @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocomp__fun__idem_res) ).
thf(2381,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ B ) ) @ bool ) @ ( finite_comp_fun_idem @ A @ B ) )
= ( finite_comp_fun_idem @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_pred__subset__eq) ).
thf(2395,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
<=> ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_ex__in__conv) ).
thf(1808,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) ) )
& ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(285,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_empty__iff) ).
thf(1618,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( skip
!= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_com_Osimps_I12_J) ).
thf(994,plain,
! [A: $i,B: $i] :
( skip
!= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( minus_minus @ ( fun @ B @ bool ) ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_image__diff__subset) ).
thf(2099,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( minus_minus @ ( fun @ B @ bool ) ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ C @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_imageI) ).
thf(1269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ C @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(264,axiom,
hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ fa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
thf(1533,plain,
hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(308,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) ) @ ( fun_upd @ A @ B ) )
= ( fun_upd @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Fun_Ofun__upd_res) ).
thf(1692,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) ) @ ( fun_upd @ A @ B ) )
= ( fun_upd @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ pname @ com @ body_1 @ A ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ A ) ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_evalc__elim__cases_I6_J) ).
thf(1173,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ pname @ com @ body_1 @ A ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ A ) ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_image__Un) ).
thf(2363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ D ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_insert__subset) ).
thf(1200,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) )
=> ? [E: $i] :
( ( hAPP @ A @ ( option @ B ) @ D @ C )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_domD) ).
thf(2309,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) )
=> ? [E: $i] :
( ( hAPP @ A @ ( option @ B ) @ D @ C )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ F ) @ G ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ C @ H ) @ I ) )
=> ! [J: $i] :
( ! [K: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ E @ K ) @ I ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ G @ K ) @ J ) ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ B @ H ) @ J ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ F ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_conseq12) ).
thf(762,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ F ) @ G ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ C @ H ) @ I ) )
=> ! [J: $i] :
( ! [K: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ E @ K ) @ I ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ G @ K ) @ J ) ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ B @ H ) @ J ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ F ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
<=> ? [C: $i,D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_nonempty__iff) ).
thf(1596,plain,
! [A: $i,B: $i] :
( ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ? [C: $i,D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) ) ) )
& ( ? [C: $i,D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(228,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ A ) ) @ ( semilattice_inf_inf @ A ) )
= ( semilattice_inf_inf @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Lattices_Osemilattice__inf__class_Oinf_res) ).
thf(1406,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ A ) ) @ ( semilattice_inf_inf @ A ) )
= ( semilattice_inf_inf @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(437,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ bool @ ( finite_comp_fun_idem @ A @ A ) @ ( semilattice_sup_sup @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_comp__fun__idem__sup) ).
thf(2104,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ bool @ ( finite_comp_fun_idem @ A @ A ) @ ( semilattice_sup_sup @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hoare_1656922687triple @ A ) @ B @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_1656922687triple @ A ) @ B ) @ ( hoare_1632998903le_rec @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ F ) )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ B @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) @ C @ D ) @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_triple_Orecs) ).
thf(2590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hoare_1656922687triple @ A ) @ B @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_1656922687triple @ A ) @ B ) @ ( hoare_1632998903le_rec @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ F ) )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ B @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) @ C @ D ) @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ E ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ C )
= ( ti @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_the1__equality) ).
thf(1401,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ E ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ C )
= ( ti @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(32,axiom,
! [A: $i] :
( skip
!= ( hAPP @ pname @ com @ body_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_com_Osimps_I18_J) ).
thf(738,plain,
! [A: $i] :
( skip
!= ( hAPP @ pname @ com @ body_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(739,plain,
~ ? [A: $i] :
( skip
= ( hAPP @ pname @ com @ body_1 @ A ) ),
inference(miniscope,[status(thm)],[738]) ).
thf(740,plain,
! [A: $i] :
( skip
!= ( hAPP @ pname @ com @ body_1 @ A ) ),
inference(cnf,[status(esa)],[739]) ).
thf(741,plain,
! [A: $i] :
( ( hAPP @ pname @ com @ body_1 @ A )
!= skip ),
inference(lifteq,[status(thm)],[740]) ).
thf(133,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( option @ A ) @ A ) @ ( the @ A ) )
= ( the @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Option_Othe_res) ).
thf(1073,plain,
! [A: $i] :
( ( ti @ ( fun @ ( option @ A ) @ A ) @ ( the @ A ) )
= ( the @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ B @ A ) ) @ ( combk @ A @ B ) )
= ( combk @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).
thf(1544,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ B @ A ) ) @ ( combk @ A @ B ) )
= ( combk @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(601,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_distrib__inf__le) ).
thf(2676,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(122,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( the_elem @ A ) )
= ( the_elem @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Othe__elem_res) ).
thf(1041,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( the_elem @ A ) )
= ( the_elem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ E ) @ C ) @ D ) ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_inj__on__fun__updI) ).
thf(861,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ E ) @ C ) @ D ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ D ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).
thf(1608,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ D ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(580,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ E @ F ) @ G ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( combk @ ( fun @ state @ bool ) @ A ) @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( combc @ state @ state @ bool ) @ ( fequal @ state ) ) @ G ) ) ) @ C ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( combk @ ( fun @ state @ bool ) @ A ) @ ( hAPP @ A @ ( fun @ state @ bool ) @ D @ F ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ C ) @ D ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_escape) ).
thf(2607,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ E @ F ) @ G ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( combk @ ( fun @ state @ bool ) @ A ) @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( combc @ state @ state @ bool ) @ ( fequal @ state ) ) @ G ) ) ) @ C ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( combk @ ( fun @ state @ bool ) @ A ) @ ( hAPP @ A @ ( fun @ state @ bool ) @ D @ F ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ C ) @ D ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
<=> ? [E: $i] :
( ( ti @ ( fun @ A @ ( option @ B ) ) @ C )
= ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( combk @ ( option @ B ) @ A ) @ ( none @ B ) ) ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_dom__eq__singleton__conv) ).
thf(1310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ? [E: $i] :
( ( ti @ ( fun @ A @ ( option @ B ) ) @ C )
= ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( combk @ ( option @ B ) @ A ) @ ( none @ B ) ) ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) ) )
& ( ? [E: $i] :
( ( ti @ ( fun @ A @ ( option @ B ) ) @ C )
= ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( combk @ ( option @ B ) @ A ) @ ( none @ B ) ) ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) )
=> ( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ A ) ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ pname @ com @ body_1 @ A ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_evalc_OBody) ).
thf(2035,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ A ) ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ pname @ com @ body_1 @ A ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( option @ A ) @ ( fun @ A @ bool ) @ ( set @ A ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Option_Oset_Osimps_I2_J) ).
thf(1735,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( option @ A ) @ ( fun @ A @ bool ) @ ( set @ A ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( bot @ B )
=> ! [C: $i] :
( ( hAPP @ A @ B @ ( bot_bot @ ( fun @ A @ B ) ) @ C )
= ( bot_bot @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_bot__apply) ).
thf(2448,plain,
! [A: $i,B: $i] :
( ( bot @ B )
=> ! [C: $i] :
( ( hAPP @ A @ B @ ( bot_bot @ ( fun @ A @ B ) ) @ C )
= ( bot_bot @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(58,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_inf__sup__aci_I1_J) ).
thf(814,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(209,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ A ) @ ( combi @ A ) )
= ( combi @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
thf(1342,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ A ) @ ( combi @ A ) )
= ( combi @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Collect__empty__eq) ).
thf(1354,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(245,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(1457,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1458,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(cnf,[status(esa)],[1457]) ).
thf(401,axiom,
hBOOL @ hoare_1924220188gleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1999,plain,
hBOOL @ hoare_1924220188gleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ B @ bool ) ) @ D ) @ E ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_image__Int__subset) ).
thf(797,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ B @ bool ) ) @ D ) @ E ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_Int__Un__distrib) ).
thf(2476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(20,axiom,
~ ( hBOOL @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(698,plain,
~ ( hBOOL @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_Diff__disjoint) ).
thf(1746,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
<=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Un__empty) ).
thf(1835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
& ( ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(421,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( bot_bot @ ( fun @ A @ bool ) ) @ B ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_bot__empty__eq) ).
thf(2046,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( bot_bot @ ( fun @ A @ bool ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( bot_bot @ ( fun @ A @ bool ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
<=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_ball__Un) ).
thf(2432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) ) ) )
& ( ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ B ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( combs @ A @ B @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ B ) ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ ( fun @ B @ B ) ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ B ) ) ) @ ( combs @ A @ B @ ( fun @ B @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ B @ ( fun @ B @ B ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ B @ ( fun @ B @ B ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ B @ ( fun @ B @ B ) ) ) ) @ ( combb @ bool @ ( fun @ B @ ( fun @ B @ B ) ) @ A ) @ ( if @ B ) ) @ C ) ) @ D ) ) @ E ) ) @ F )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ F ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ F ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_if__image__distrib) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ B ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( combs @ A @ B @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ B ) ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ ( fun @ B @ B ) ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ B ) ) ) @ ( combs @ A @ B @ ( fun @ B @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ B @ ( fun @ B @ B ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ B @ ( fun @ B @ B ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ B @ ( fun @ B @ B ) ) ) ) @ ( combb @ bool @ ( fun @ B @ ( fun @ B @ B ) ) @ A ) @ ( if @ B ) ) @ C ) ) @ D ) ) @ E ) ) @ F )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ F ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ F ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( order @ B )
=> ( order @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(1613,plain,
! [A: $i,B: $i] :
( ( order @ B )
=> ( order @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( ( finite_finite_1 @ B )
& ( finite_finite_1 @ A ) )
=> ( finite_finite_1 @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(2010,plain,
! [A: $i,B: $i] :
( ( ( finite_finite_1 @ B )
& ( finite_finite_1 @ A ) )
=> ( finite_finite_1 @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(375,axiom,
! [A: $i] :
( ( ab_group_add @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( minus_minus @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( minus_minus @ A ) @ D ) @ E ) )
=> ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
<=> ( ( ti @ A @ D )
= ( ti @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_diff__eq__diff__eq) ).
thf(1921,plain,
! [A: $i] :
( ( ab_group_add @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( minus_minus @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( minus_minus @ A ) @ D ) @ E ) )
=> ( ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ E ) ) )
& ( ( ( ti @ A @ D )
= ( ti @ A @ E ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ wT_bodies )
=> ( ( ( hAPP @ pname @ ( option @ com ) @ body @ A )
= ( hAPP @ com @ ( option @ com ) @ ( some @ com ) @ B ) )
=> ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_WT__bodiesD) ).
thf(1386,plain,
! [A: $i,B: $i] :
( ( hBOOL @ wT_bodies )
=> ( ( ( hAPP @ pname @ ( option @ com ) @ body @ A )
= ( hAPP @ com @ ( option @ com ) @ ( some @ com ) @ B ) )
=> ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) ) @ F )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( minus_minus @ ( fun @ B @ bool ) ) @ F ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ E ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) ) @ F )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_fun__upd__image) ).
thf(1366,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) ) @ F )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( minus_minus @ ( fun @ B @ bool ) ) @ F ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ E ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) ) @ F )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(552,axiom,
semilattice_inf @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).
thf(2516,plain,
semilattice_inf @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(186,axiom,
finite_finite_1 @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(1265,plain,
finite_finite_1 @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_2027193591valids @ state ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ A ) @ C ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ A ) @ C ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_MGF__complete) ).
thf(1887,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_2027193591valids @ state ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ A ) @ C ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ A ) @ C ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(108,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i,G: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ E ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ F ) @ G ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ E ) @ F ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ E ) @ G ) ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_distrib__imp2) ).
thf(1001,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i,G: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ E ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ F ) @ G ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ E ) @ F ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ E ) @ G ) ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_WTs__elim__cases_I6_J) ).
thf(2723,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_inf1D2) ).
thf(973,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_Un__Diff__cancel) ).
thf(1046,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(521,axiom,
! [A: $i] :
( ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ A )
= ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ ( fequal @ state ) ) @ A ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_MGT__def) ).
thf(2400,plain,
! [A: $i] :
( ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ A )
= ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ ( fequal @ state ) ) @ A ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(391,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
<=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( ti @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_le__iff__inf) ).
thf(1967,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( ti @ A @ B ) ) )
& ( ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( ti @ A @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ skip ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_hoare__derivs_OSkip) ).
thf(2531,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ skip ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(523,axiom,
! [A: $i] :
( ( ti @ ( option @ A ) @ ( none @ A ) )
= ( none @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Option_Ooption_ONone_res) ).
thf(2405,plain,
! [A: $i] :
( ( ti @ ( option @ A ) @ ( none @ A ) )
= ( none @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ A ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) ) @ ( override_on @ B @ A ) @ C ) @ D ) @ F ) @ E )
= ( hAPP @ B @ A @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_override__on__apply__in) ).
thf(2654,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ A ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) ) @ ( override_on @ B @ A ) @ C ) @ D ) @ F ) @ E )
= ( hAPP @ B @ A @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_folding__image__simple__idem_Ounion__idem) ).
thf(1409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(314,axiom,
! [A: $i] :
( ( distrib_lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_sup__inf__distrib1) ).
thf(1709,plain,
! [A: $i] :
( ( distrib_lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(236,axiom,
! [A: $i] :
( ( distrib_lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_inf__sup__distrib1) ).
thf(1430,plain,
! [A: $i] :
( ( distrib_lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite_OinsertI) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(299,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_inf__le2) ).
thf(1660,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(46,axiom,
( ( ti @ bool @ fFalse )
= fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
thf(785,plain,
( ( ti @ bool @ fFalse )
= fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ F ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ F ) )
& ( ( ti @ ( fun @ B @ bool ) @ E )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_finite__subset__image) ).
thf(1871,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ F ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ F ) )
& ( ( ti @ ( fun @ B @ bool ) @ E )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ A ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) ) @ ( override_on @ B @ A ) @ C ) @ D ) @ F ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_override__on__apply__notin) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ A ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) ) @ ( override_on @ B @ A ) @ C ) @ D ) @ F ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(471,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite_OemptyI) ).
thf(2217,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( preorder @ B )
=> ( preorder @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(917,plain,
! [A: $i,B: $i] :
( ( preorder @ B )
=> ( preorder @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( bot @ B )
=> ! [C: $i] :
( ( hAPP @ A @ B @ ( bot_bot @ ( fun @ A @ B ) ) @ C )
= ( bot_bot @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_bot__fun__def) ).
thf(1279,plain,
! [A: $i,B: $i] :
( ( bot @ B )
=> ! [C: $i] :
( ( hAPP @ A @ B @ ( bot_bot @ ( fun @ A @ B ) ) @ C )
= ( bot_bot @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( fAll @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fAll_1_1_U) ).
thf(2703,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( fAll @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Un__Int__distrib2) ).
thf(2735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
!= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_com_Osimps_I46_J) ).
thf(1985,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
!= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(598,axiom,
! [A: $i,B: $i] :
( ( minus @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( minus_minus @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( minus_minus @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_fun__diff__def) ).
thf(2667,plain,
! [A: $i,B: $i] :
( ( minus @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( minus_minus @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( minus_minus @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( semilattice_sup_sup @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( semilattice_sup_sup @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_sup__apply) ).
thf(719,plain,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( semilattice_sup_sup @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( semilattice_sup_sup @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(567,axiom,
! [A: $i] :
( ( linorder @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_linorder__linear) ).
thf(2562,plain,
! [A: $i] :
( ( linorder @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_Un__mono) ).
thf(2488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(247,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_inf__left__commute) ).
thf(1462,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(128,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B )
= ( ti @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_sup__absorb1) ).
thf(1059,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B )
= ( ti @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_Diff__Un) ).
thf(949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_folding__image__simple__idem_Osubset__idem) ).
thf(2571,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ! [F: $i,G: $i] :
( ( hAPP @ A @ A @ C @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ F ) @ G ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ A @ A @ C @ F ) ) @ ( hAPP @ A @ A @ C @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ A @ A @ C @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ A ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ A @ A ) @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_folding__one__idem_Ohom__commute) ).
thf(817,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ! [F: $i,G: $i] :
( ( hAPP @ A @ A @ C @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ F ) @ G ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ A @ A @ C @ F ) ) @ ( hAPP @ A @ A @ C @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ A @ A @ C @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ A ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ A @ A ) @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fold_graph @ B @ A ) @ C ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( minus_minus @ ( fun @ B @ bool ) ) @ G ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ F ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fold_graph @ B @ A ) @ C ) @ D ) @ G ) @ ( hAPP @ A @ A @ ( hAPP @ B @ ( fun @ A @ A ) @ C @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_fold__graph_H_Ointros_I2_J) ).
thf(1379,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fold_graph @ B @ A ) @ C ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( minus_minus @ ( fun @ B @ bool ) ) @ G ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ F ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fold_graph @ B @ A ) @ C ) @ D ) @ G ) @ ( hAPP @ A @ A @ ( hAPP @ B @ ( fun @ A @ A ) @ C @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(226,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_inf__commute) ).
thf(1398,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ C @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ C @ ( fun @ A @ B ) ) @ ( combc @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(2024,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ C @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ C @ ( fun @ A @ B ) ) @ ( combc @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_double__diff) ).
thf(1778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_Diff__insert2) ).
thf(2533,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_insert__compr) ).
thf(1232,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(355,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(1847,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_set__mp) ).
thf(2169,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(522,axiom,
( ( ti @ com @ skip )
= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Com_Ocom_OSKIP_res) ).
thf(2403,plain,
( ( ti @ com @ skip )
= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( bot_bot @ ( fun @ B @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_image__empty) ).
thf(1087,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( bot_bot @ ( fun @ B @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ C ) ) ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ C ) ) ) @ B ) )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Collect__conv__if2) ).
thf(1514,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ C ) ) ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ C ) ) ) @ B ) )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_equals0D) ).
thf(2301,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ( semilattice_inf @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).
thf(1815,plain,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ( semilattice_inf @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( bot @ B )
=> ( bot @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(2237,plain,
! [A: $i,B: $i] :
( ( bot @ B )
=> ( bot @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( option @ B ) @ A ) ) ) @ ( option_rec @ A @ B ) )
= ( option_rec @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Option_Ooption_Ooption__rec_res) ).
thf(756,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( option @ B ) @ A ) ) ) @ ( option_rec @ A @ B ) )
= ( option_rec @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ B ) ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Collect__disj__eq) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ B ) ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_UnI1) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(217,axiom,
! [A: $i] :
( ( ti @ ( fun @ bool @ ( fun @ A @ ( fun @ A @ A ) ) ) @ ( if @ A ) )
= ( if @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_If_res) ).
thf(1373,plain,
! [A: $i] :
( ( ti @ ( fun @ bool @ ( fun @ A @ ( fun @ A @ A ) ) ) @ ( if @ A ) )
= ( if @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ B @ A ) @ C ) )
<=> ( ( hAPP @ B @ A @ C @ D )
= ( ti @ A @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_fun__upd__idem__iff) ).
thf(2451,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ B @ A ) @ C ) )
=> ( ( hAPP @ B @ A @ C @ D )
= ( ti @ A @ E ) ) )
& ( ( ( hAPP @ B @ A @ C @ D )
= ( ti @ A @ E ) )
=> ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_Diff__mono) ).
thf(1334,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_subset__insert) ).
thf(1136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(359,axiom,
minus @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(1864,plain,
minus @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( ti @ ( option @ A ) @ B )
!= ( none @ A ) )
<=> ? [C: $i] :
( ( ti @ ( option @ A ) @ B )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_not__None__eq) ).
thf(1828,plain,
! [A: $i,B: $i] :
( ( ( ( ti @ ( option @ A ) @ B )
!= ( none @ A ) )
=> ? [C: $i] :
( ( ti @ ( option @ A ) @ B )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) ) )
& ( ? [C: $i] :
( ( ti @ ( option @ A ) @ B )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) )
=> ( ( ti @ ( option @ A ) @ B )
!= ( none @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(115,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
= ( fequal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
thf(1020,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
= ( fequal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(55,axiom,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ( finite_finite_1 @ ( option @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option_Ooption___Finite__Set_Ofinite) ).
thf(806,plain,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ( finite_finite_1 @ ( option @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( collect @ B ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combs @ B @ bool @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ B ) @ fconj ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combc @ B @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) ) @ D ) ) ) @ ( hAPP @ A @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( combc @ B @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ bool ) ) ) @ ( combb @ A @ ( fun @ A @ bool ) @ B ) @ ( fequal @ A ) ) @ C ) ) @ ( hAPP @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_pigeonhole__infinite) ).
thf(1183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( collect @ B ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combs @ B @ bool @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ B ) @ fconj ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combc @ B @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) ) @ D ) ) ) @ ( hAPP @ A @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( combc @ B @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ bool ) ) ) @ ( combb @ A @ ( fun @ A @ bool ) @ B ) @ ( fequal @ A ) ) @ C ) ) @ ( hAPP @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_subset__trans) ).
thf(905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(583,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ A ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ A ) @ ( combi @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_inj__on__id2) ).
thf(2616,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ A ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ A ) @ ( combi @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ( ( ( hAPP @ A @ B @ E @ D )
= ( hAPP @ A @ B @ E @ C ) )
<=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_inj__on__iff) ).
thf(1465,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ( ( ( ( hAPP @ A @ B @ E @ D )
= ( hAPP @ A @ B @ E @ C ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) )
& ( ( ( ti @ A @ D )
= ( ti @ A @ C ) )
=> ( ( hAPP @ A @ B @ E @ D )
= ( hAPP @ A @ B @ E @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(303,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( option @ A ) @ ( fun @ A @ bool ) ) @ ( set @ A ) )
= ( set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Option_Oset_res) ).
thf(1677,plain,
! [A: $i] :
( ( ti @ ( fun @ ( option @ A ) @ ( fun @ A @ bool ) ) @ ( set @ A ) )
= ( set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ F ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( minus_minus @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_inj__on__image__set__diff) ).
thf(2540,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ F ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( minus_minus @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ C ) ) ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ C ) ) ) @ B ) )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Collect__conv__if) ).
thf(687,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ C ) ) ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ C ) ) ) @ B ) )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( the_1 @ A ) )
= ( the_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_OThe_res) ).
thf(634,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( the_1 @ A ) )
= ( the_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(460,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_sup__ge1) ).
thf(2190,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(2483,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(75,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_inf__greatest) ).
thf(866,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_folding__image__simple__idem_Oinsert__idem) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ D @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_folding__one_Osingleton) ).
thf(2137,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ D @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(212,axiom,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( bot_bot @ A ) )
= ( bot_bot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_inf__bot__right) ).
thf(1351,plain,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( bot_bot @ A ) )
= ( bot_bot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(237,axiom,
! [A: $i] :
( ( bot @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( bot_bot @ A ) ) )
=> ( ( ti @ A @ B )
= ( bot_bot @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_le__bot) ).
thf(1433,plain,
! [A: $i] :
( ( bot @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( bot_bot @ A ) ) )
=> ( ( ti @ A @ B )
= ( bot_bot @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(69,axiom,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( bot_bot @ A ) ) @ B )
= ( bot_bot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_inf__bot__left) ).
thf(849,plain,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( bot_bot @ A ) ) @ B )
= ( bot_bot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(549,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_order__antisym) ).
thf(2508,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(40,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fdisj )
= fdisj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
thf(766,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fdisj )
= fdisj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( ( ord @ B )
& ( ord @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ E ) @ F ) )
=> ( ( ( hAPP @ A @ B @ C @ F )
= D )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ G ) ) @ ( hAPP @ A @ B @ C @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_ord__le__eq__subst) ).
thf(2618,plain,
! [A: $i,B: $i] :
( ( ( ord @ B )
& ( ord @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ E ) @ F ) )
=> ( ( ( hAPP @ A @ B @ C @ F )
= D )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ G ) ) @ ( hAPP @ A @ B @ C @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_folding__image__simple_Oinsert) ).
thf(2281,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(43,axiom,
( ( ti @ pname @ pn )
= pn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_pn_res) ).
thf(773,plain,
( ( ti @ pname @ pn )
= pn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(774,plain,
( ( ti @ pname @ pn )
= pn ),
inference(lifteq,[status(thm)],[773]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ti @ ( fun @ B @ bool ) @ D )
= ( bot_bot @ ( fun @ B @ bool ) ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( combk @ A @ B ) @ C ) ) @ D )
= ( bot_bot @ ( fun @ A @ bool ) ) ) )
& ( ( ( ti @ ( fun @ B @ bool ) @ D )
!= ( bot_bot @ ( fun @ B @ bool ) ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( combk @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_image__constant__conv) ).
thf(2371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ti @ ( fun @ B @ bool ) @ D )
= ( bot_bot @ ( fun @ B @ bool ) ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( combk @ A @ B ) @ C ) ) @ D )
= ( bot_bot @ ( fun @ A @ bool ) ) ) )
& ( ( ( ti @ ( fun @ B @ bool ) @ D )
!= ( bot_bot @ ( fun @ B @ bool ) ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( combk @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(403,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_inf__sup__ord_I3_J) ).
thf(2002,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Un__commute) ).
thf(998,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_Un__Int__crazy) ).
thf(2242,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(210,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_inf_Oidem) ).
thf(1345,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_Int__insert__right__if1) ).
thf(2392,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_Int__commute) ).
thf(1521,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(296,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D ) )
=> ~ ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_le__supE) ).
thf(1651,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D ) )
=> ~ ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ti @ B @ F )
= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) @ F )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ B @ F )
!= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) @ F )
= ( hAPP @ B @ A @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_fun__upd__def) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ti @ B @ F )
= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) @ F )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ B @ F )
!= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) @ F )
= ( hAPP @ B @ A @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_subset__insertI) ).
thf(2204,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) @ D ) )
<=> ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_insert__code) ).
thf(678,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) @ D ) )
=> ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ F ) @ G ) )
<=> ( ( B = E )
& ( C = F )
& ( D = G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_triple_Oinject) ).
thf(2574,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ F ) @ G ) )
=> ( ( B = E )
& ( C = F )
& ( D = G ) ) )
& ( ( ( B = E )
& ( C = F )
& ( D = G ) )
=> ( ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ F ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ D )
=> ( ( ti @ A @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ D ) ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ ( hAPP @ bool @ bool @ fNot @ D ) ) ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ C ) ) ) ) ) )
& ( ~ ( hBOOL @ D )
=> ( ( ti @ A @ C )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ D ) ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ ( hAPP @ bool @ bool @ fNot @ D ) ) ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_If__def) ).
thf(2118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ D )
=> ( ( ti @ A @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ D ) ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ ( hAPP @ bool @ bool @ fNot @ D ) ) ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ C ) ) ) ) ) )
& ( ~ ( hBOOL @ D )
=> ( ( ti @ A @ C )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ D ) ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ ( hAPP @ bool @ bool @ fNot @ D ) ) ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ E ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ F ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ C @ F ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_Int__Collect__mono) ).
thf(2660,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ E ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ F ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ C @ F ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( ord @ B )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_le__funI) ).
thf(2000,plain,
! [A: $i,B: $i] :
( ( ord @ B )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C )
= ( ti @ A @ B ) ) )
& ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_folding__one_Oremove) ).
thf(1730,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C )
= ( ti @ A @ B ) ) )
& ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Un__left__absorb) ).
thf(2646,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ D ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ F ) @ D ) )
=> ( ( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ C @ F ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_inj__on__def) ).
thf(925,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ D ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ F ) @ D ) )
=> ( ( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ C @ F ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ F ) ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ F ) @ D ) )
=> ( ( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ C @ F ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ D ) @ ( hAPP @ ( fun @ C @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ C @ A ) @ ( fun @ ( fun @ C @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ C @ A ) @ E ) @ F ) )
= ( hAPP @ ( fun @ C @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ C @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ C @ B ) @ ( hAPP @ ( fun @ C @ A ) @ ( fun @ C @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) @ ( combb @ A @ B @ C ) @ D ) @ E ) ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_image__image) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ D ) @ ( hAPP @ ( fun @ C @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ C @ A ) @ ( fun @ ( fun @ C @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ C @ A ) @ E ) @ F ) )
= ( hAPP @ ( fun @ C @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ C @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ C @ B ) @ ( hAPP @ ( fun @ C @ A ) @ ( fun @ C @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) @ ( combb @ A @ B @ C ) @ D ) @ E ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_Un__Diff__cancel2) ).
thf(1915,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ B ) ) @ C ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_finite__Collect__disjI) ).
thf(2093,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ B ) ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ B ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(492,axiom,
( ( hAPP @ pname @ ( option @ com ) @ body @ pn )
= ( hAPP @ com @ ( option @ com ) @ ( some @ com ) @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
thf(2296,plain,
( ( hAPP @ pname @ ( option @ com ) @ body @ pn )
= ( hAPP @ com @ ( option @ com ) @ ( some @ com ) @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_inj__on__Int) ).
thf(2307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(430,axiom,
! [A: $i,B: $i] :
( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_com_Osimps_I17_J) ).
thf(2083,plain,
! [A: $i,B: $i] :
( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(544,axiom,
! [A: $i,B: $i] :
( ( distrib_lattice @ B )
=> ( distrib_lattice @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Lattices_Odistrib__lattice) ).
thf(2496,plain,
! [A: $i,B: $i] :
( ( distrib_lattice @ B )
=> ( distrib_lattice @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_Int__insert__right__if0) ).
thf(2705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(2733,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(96,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_inf__sup__aci_I3_J) ).
thf(952,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(486,axiom,
! [A: $i] :
( ( linorder @ A )
=> ! [B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_linorder__le__cases) ).
thf(2277,plain,
! [A: $i] :
( ( linorder @ A )
=> ! [B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(146,axiom,
( ( ti @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ hoare_Mirabelle_MGT )
= hoare_Mirabelle_MGT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__nrugjuseim_OMGT_res) ).
thf(1123,plain,
( ( ti @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ hoare_Mirabelle_MGT )
= hoare_Mirabelle_MGT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ( lattice @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).
thf(820,plain,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ( lattice @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( inj_on @ B @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_finite__imageD) ).
thf(1666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( inj_on @ B @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_sup__Un__eq) ).
thf(1487,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(629,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(cnf,[status(esa)],[628]) ).
thf(630,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(lifteq,[status(thm)],[629]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ? [D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_mk__disjoint__insert) ).
thf(1824,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ? [D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(414,axiom,
hBOOL @ ( hAPP @ com @ bool @ wt @ skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_WT_OSkip) ).
thf(2032,plain,
hBOOL @ ( hAPP @ com @ bool @ wt @ skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_Int__insert__left__if0) ).
thf(729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_elem @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_the__elem__eq) ).
thf(1274,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_elem @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_Diff__Int2) ).
thf(2673,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(1723,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( bot_bot @ ( fun @ A @ bool ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) )
<=> ( ( ti @ ( fun @ B @ bool ) @ D )
= ( bot_bot @ ( fun @ B @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_empty__is__image) ).
thf(910,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( bot_bot @ ( fun @ A @ bool ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) )
=> ( ( ti @ ( fun @ B @ bool ) @ D )
= ( bot_bot @ ( fun @ B @ bool ) ) ) )
& ( ( ( ti @ ( fun @ B @ bool ) @ D )
= ( bot_bot @ ( fun @ B @ bool ) ) )
=> ( ( bot_bot @ ( fun @ A @ bool ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cut) ).
thf(1223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_folding__one_Ounion__disjoint) ).
thf(894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(579,axiom,
( ( hBOOL @ hoare_1924220188gleton )
<=> ? [A: $i,B: $i] : A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_state__not__singleton__def) ).
thf(2601,plain,
( ( ( hBOOL @ hoare_1924220188gleton )
=> ? [A: $i,B: $i] : A != B )
& ( ? [A: $i,B: $i] : A != B
=> ( hBOOL @ hoare_1924220188gleton ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(529,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ hoare_1924220188gleton )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( hAPP @ pname @ ( fun @ ( fun @ pname @ bool ) @ bool ) @ ( member @ pname ) @ C ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ ( hAPP @ pname @ com @ body_1 @ C ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ com @ bool @ wt @ A ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_MGF__lemma1) ).
thf(2428,plain,
! [A: $i,B: $i] :
( ( hBOOL @ hoare_1924220188gleton )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( hAPP @ pname @ ( fun @ ( fun @ pname @ bool ) @ bool ) @ ( member @ pname ) @ C ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ ( hAPP @ pname @ com @ body_1 @ C ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ com @ bool @ wt @ A ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( inj_on @ A @ B ) )
= ( inj_on @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Fun_Oinj__on_res) ).
thf(2249,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( inj_on @ A @ B ) )
= ( inj_on @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ A ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) ) @ ( override_on @ B @ A ) @ C ) @ D ) @ E ) @ F )
= ( hAPP @ B @ A @ D @ F ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ A ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) ) @ ( override_on @ B @ A ) @ C ) @ D ) @ E ) @ F )
= ( hAPP @ B @ A @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_override__on__def) ).
thf(778,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ A ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) ) @ ( override_on @ B @ A ) @ C ) @ D ) @ E ) @ F )
= ( hAPP @ B @ A @ D @ F ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ A ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ A ) ) ) @ ( override_on @ B @ A ) @ C ) @ D ) @ E ) @ F )
= ( hAPP @ B @ A @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_subset__insert__iff) ).
thf(1238,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_folding__one__idem_Ounion__idem) ).
thf(2015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_Diff__subset__conv) ).
thf(1423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(374,axiom,
hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( finite_finite @ ( hoare_1656922687triple @ state ) ) @ fa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(1920,plain,
hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( finite_finite @ ( hoare_1656922687triple @ state ) ) @ fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
thf(625,plain,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_finite__UnI) ).
thf(852,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(13,axiom,
! [A: $i] :
( ( minus @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ A ) ) @ ( minus_minus @ A ) )
= ( minus_minus @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).
thf(665,plain,
! [A: $i] :
( ( minus @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ A ) ) @ ( minus_minus @ A ) )
= ( minus_minus @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ti @ B @ F )
!= ( ti @ B @ G ) )
=> ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) ) @ G ) @ E )
= ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ G ) @ E ) ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_fun__upd__twist) ).
thf(1624,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ti @ B @ F )
!= ( ti @ B @ G ) )
=> ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) ) @ G ) @ E )
= ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ G ) @ E ) ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ F @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ B @ G ) @ H ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_conseq2) ).
thf(830,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ F @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ B @ G ) @ H ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_folding__one_Oinsert) ).
thf(1159,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_predicate1I) ).
thf(1079,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(325,axiom,
~ ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( member @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ fa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(1740,plain,
~ ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( member @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ fa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( ord @ B )
=> ( ord @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(1106,plain,
! [A: $i,B: $i] :
( ( ord @ B )
=> ( ord @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ pname @ com @ body_1 @ A )
= ( hAPP @ pname @ com @ body_1 @ B ) )
<=> ( ( ti @ pname @ A )
= ( ti @ pname @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_com_Osimps_I6_J) ).
thf(2464,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ pname @ com @ body_1 @ A )
= ( hAPP @ pname @ com @ body_1 @ B ) )
=> ( ( ti @ pname @ A )
= ( ti @ pname @ B ) ) )
& ( ( ( ti @ pname @ A )
= ( ti @ pname @ B ) )
=> ( ( hAPP @ pname @ com @ body_1 @ A )
= ( hAPP @ pname @ com @ body_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ I ) )
=> ( ! [J: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ F @ J ) ) @ ( hAPP @ B @ com @ G @ J ) ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ H @ J ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ C @ J ) ) @ ( hAPP @ B @ com @ G @ J ) ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ D @ J ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ B @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ com ) @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ B @ com ) @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ B @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ B ) @ ( hoare_246368825triple @ A ) ) @ F ) ) @ G ) ) @ H ) ) @ I ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ B @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ com ) @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ B @ com ) @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ B @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ B ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ G ) ) @ D ) ) @ I ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_finite__pointwise) ).
thf(1938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ I ) )
=> ( ! [J: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ F @ J ) ) @ ( hAPP @ B @ com @ G @ J ) ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ H @ J ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ C @ J ) ) @ ( hAPP @ B @ com @ G @ J ) ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ D @ J ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ B @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ com ) @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ B @ com ) @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ B @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ B ) @ ( hoare_246368825triple @ A ) ) @ F ) ) @ G ) ) @ H ) ) @ I ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ B @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ B @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ B @ com ) @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ B @ com ) @ ( fun @ B @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ B @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ B @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ B @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ B ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ G ) ) @ D ) ) @ I ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(570,axiom,
hBOOL @ wT_bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2570,plain,
hBOOL @ wT_bodies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(699,plain,
~ ( hBOOL @ fFalse ),
inference(polarity_switch,[status(thm)],[698]) ).
thf(2756,plain,
( ( hBOOL @ wT_bodies )
!= ( hBOOL @ fFalse ) ),
inference(paramod_ordered,[status(thm)],[2570,699]) ).
thf(2758,plain,
wT_bodies != fFalse,
inference(simp,[status(thm)],[2756]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_Diff__idemp) ).
thf(2628,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( hAPP @ bool @ ( fun @ A @ ( fun @ A @ A ) ) @ ( if @ A ) @ fFalse ) @ B ) @ C )
= ( ti @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(2670,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( hAPP @ bool @ ( fun @ A @ ( fun @ A @ A ) ) @ ( if @ A ) @ fFalse ) @ B ) @ C )
= ( ti @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(498,axiom,
( ( ti @ bool @ fTrue )
= fTrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
thf(2312,plain,
( ( ti @ bool @ fTrue )
= fTrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(2313,plain,
( ( ti @ bool @ fTrue )
= fTrue ),
inference(lifteq,[status(thm)],[2312]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ B @ C @ D )
= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_fun__upd__idem) ).
thf(1128,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ B @ C @ D )
= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(290,axiom,
! [A: $i] :
( ( hBOOL @ ( ti @ bool @ A ) )
<=> ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(1634,plain,
! [A: $i] :
( ( ( hBOOL @ ( ti @ bool @ A ) )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ ( ti @ bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(474,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) ) @ ( hoare_2027193591valids @ A ) )
= ( hoare_2027193591valids @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__valids_res) ).
thf(2228,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) ) @ ( hoare_2027193591valids @ A ) )
= ( hoare_2027193591valids @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_folding__one__idem_Oinsert__idem) ).
thf(2112,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ D ) ) ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ ( hAPP @ pname @ com @ body_1 @ D ) ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_weak__Body) ).
thf(710,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ D ) ) ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ ( hAPP @ pname @ com @ body_1 @ D ) ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( option @ A ) @ ( fun @ A @ bool ) @ ( set @ A ) @ C ) ) )
<=> ( ( ti @ ( option @ A ) @ C )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_elem__set) ).
thf(742,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( option @ A ) @ ( fun @ A @ bool ) @ ( set @ A ) @ C ) ) )
=> ( ( ti @ ( option @ A ) @ C )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) ) )
& ( ( ( ti @ ( option @ A ) @ C )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( option @ A ) @ ( fun @ A @ bool ) @ ( set @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_inj__on__diff) ).
thf(2498,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) ) @ ( image @ A @ B ) )
= ( image @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).
thf(2115,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) ) @ ( image @ A @ B ) )
= ( image @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( bounded_lattice @ B )
=> ( bounded_lattice @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).
thf(1762,plain,
! [A: $i,B: $i] :
( ( bounded_lattice @ B )
=> ( bounded_lattice @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(345,axiom,
bounded_lattice @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).
thf(1804,plain,
bounded_lattice @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(204,axiom,
! [A: $i] :
( ( distrib_lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_sup__inf__distrib2) ).
thf(1328,plain,
! [A: $i] :
( ( distrib_lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ com @ bool @ wt @ A ) )
=> ~ ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_WTs__elim__cases_I4_J) ).
thf(2631,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ com @ bool @ wt @ A ) )
=> ~ ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ A ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ B ) ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( finite_finite @ pname ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_MGT__Body) ).
thf(1755,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ A ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ B ) ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( finite_finite @ pname ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(482,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_inf__le1) ).
thf(2268,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(104,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_inf__sup__aci_I2_J) ).
thf(989,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(479,axiom,
( ( hBOOL @ hoare_1924220188gleton )
=> ! [A: $i] :
~ ! [B: $i] : B = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_single__stateE) ).
thf(2245,plain,
( ( hBOOL @ hoare_1924220188gleton )
=> ! [A: $i] :
~ ! [B: $i] : B = A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(380,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_sup__least) ).
thf(1936,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
<=> ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_insert__ident) ).
thf(1534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ B ) ) )
& ( ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) )
=> ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_While) ).
thf(1794,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) )
=> ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(113,axiom,
( ( ti @ com @ y )
= y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_y_res) ).
thf(1016,plain,
( ( ti @ com @ y )
= y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1017,plain,
( ( ti @ com @ y )
= y ),
inference(lifteq,[status(thm)],[1016]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
<=> ! [D: $i] :
( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( none @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_dom__eq__empty__conv) ).
thf(2692,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ! [D: $i] :
( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( none @ B ) ) )
& ( ! [D: $i] :
( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( none @ B ) )
=> ( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(1587,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( override_on @ A @ ( option @ B ) ) @ C ) @ D ) @ E ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_dom__override__on) ).
thf(1683,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( override_on @ A @ ( option @ B ) ) @ C ) @ D ) @ E ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ ( fun @ B @ bool ) @ A ) @ bool ) ) ) ) @ ( finite908156982e_idem @ A @ B ) )
= ( finite908156982e_idem @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple__idem_res) ).
thf(1082,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ ( fun @ B @ bool ) @ A ) @ bool ) ) ) ) @ ( finite908156982e_idem @ A @ B ) )
= ( finite908156982e_idem @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Un__upper1) ).
thf(1361,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_Int__empty__left) ).
thf(1964,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(195,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_inf__sup__ord_I1_J) ).
thf(1292,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_Int__insert__left__if1) ).
thf(2080,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(463,axiom,
bounded_lattice_bot @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__bot) ).
thf(2196,plain,
bounded_lattice_bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(7,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_sup__left__idem) ).
thf(637,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Diff__Int__distrib2) ).
thf(2613,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_insert__compr__raw) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(232,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_empty__subsetI) ).
thf(1419,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
<=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_bex__Un) ).
thf(1889,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) ) ) )
& ( ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ D ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
& ( hBOOL @ ( hAPP @ A @ bool @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_2027193591valids @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_2027193591valids @ A ) @ B ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Body__sound__lemma) ).
thf(1644,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_2027193591valids @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_2027193591valids @ A ) @ B ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_Int__lower1) ).
thf(2649,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_insert__commute) ).
thf(970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(548,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i,G: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ E ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ F ) @ G ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ E ) @ F ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ E ) @ G ) ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_distrib__imp1) ).
thf(2504,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i,G: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ E ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ F ) @ G ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ E ) @ F ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ E ) @ G ) ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(578,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_le__infE) ).
thf(2598,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) ) ) @ ( fold_graph @ A @ B ) )
= ( fold_graph @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nitpick_Ofold__graph_H_res) ).
thf(1131,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) ) ) @ ( fold_graph @ A @ B ) )
= ( fold_graph @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_DiffI) ).
thf(1932,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(405,axiom,
! [A: $i] :
( ( ord @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( D = B )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_ord__le__eq__trans) ).
thf(2006,plain,
! [A: $i] :
( ( ord @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( D = B )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( option @ A ) @ A @ ( the @ A ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_the_Osimps) ).
thf(1799,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( option @ A ) @ A @ ( the @ A ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_equalityD1) ).
thf(1947,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(316,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_le__supI) ).
thf(1715,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_1656922687triple @ A ) @ B ) ) @ ( hoare_1632998903le_rec @ A @ B ) )
= ( hoare_1632998903le_rec @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__rec_res) ).
thf(1720,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_1656922687triple @ A ) @ B ) ) @ ( hoare_1632998903le_rec @ A @ B ) )
= ( hoare_1632998903le_rec @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(447,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ti @ A @ C )
= ( hAPP @ A @ A @ D @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ E ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ G ) @ F ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ D @ G ) ) @ ( hAPP @ A @ A @ D @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ D @ B ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_xt1_I15_J) ).
thf(2140,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ti @ A @ C )
= ( hAPP @ A @ A @ D @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ E ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ G ) @ F ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ D @ G ) ) @ ( hAPP @ A @ A @ D @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ D @ B ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(288,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hoare_246368825triple @ A ) )
= ( hoare_246368825triple @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple_res) ).
thf(1627,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hoare_246368825triple @ A ) )
= ( hoare_246368825triple @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(10,axiom,
( ( ti @ ( fun @ bool @ bool ) @ fNot )
= fNot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
thf(647,plain,
( ( ti @ ( fun @ bool @ bool ) @ fNot )
= fNot ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_finite__subset) ).
thf(1263,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_Diff__empty) ).
thf(2125,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_Int__insert__left) ).
thf(1099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(1150,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_Un__absorb2) ).
thf(1478,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ ( hAPP @ pname @ com @ body_1 @ C ) ) @ D ) ) @ E ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ C ) ) ) @ D ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ ( hAPP @ pname @ com @ body_1 @ C ) ) @ D ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_BodyN) ).
thf(2536,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ ( hAPP @ pname @ com @ body_1 @ C ) ) @ D ) ) @ E ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ ( hAPP @ ( option @ com ) @ com @ ( the @ com ) @ ( hAPP @ pname @ ( option @ com ) @ body @ C ) ) ) @ D ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ E ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ ( hAPP @ pname @ com @ body_1 @ C ) ) @ D ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(197,axiom,
! [A: $i] :
( ( distrib_lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_inf__sup__distrib2) ).
thf(1297,plain,
! [A: $i] :
( ( distrib_lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(603,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_sup__inf__absorb) ).
thf(2681,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B ) ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_folding__one_Ounion__inter) ).
thf(1451,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B ) ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(495,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_inf__sup__aci_I5_J) ).
thf(2304,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__Collect__conjI) ).
thf(1530,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ ( fun @ B @ bool ) @ E )
= ( ti @ ( fun @ B @ bool ) @ F ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ G ) @ F ) )
=> ( ( hAPP @ B @ A @ C @ G )
= ( hAPP @ B @ A @ D @ G ) ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_image__cong) ).
thf(1539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ ( fun @ B @ bool ) @ E )
= ( ti @ ( fun @ B @ bool ) @ F ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ G ) @ F ) )
=> ( ( hAPP @ B @ A @ C @ G )
= ( hAPP @ B @ A @ D @ G ) ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_insert__inter__insert) ).
thf(1266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
<=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
| ? [C: $i,D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_finite_Osimps) ).
thf(2153,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
| ? [C: $i,D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) ) )
& ( ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
| ? [C: $i,D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(2387,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(302,axiom,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i,C: $i] :
( ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( bot_bot @ A ) )
<=> ( ( ( ti @ A @ B )
= ( bot_bot @ A ) )
& ( ( ti @ A @ C )
= ( bot_bot @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_sup__eq__bot__iff) ).
thf(1668,plain,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i,C: $i] :
( ( ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( bot_bot @ A ) )
=> ( ( ( ti @ A @ B )
= ( bot_bot @ A ) )
& ( ( ti @ A @ C )
= ( bot_bot @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( bot_bot @ A ) )
& ( ( ti @ A @ C )
= ( bot_bot @ A ) ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( bot_bot @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_Diff__insert) ).
thf(1974,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( semilattice_inf_inf @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( semilattice_inf_inf @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_inf__apply) ).
thf(1759,plain,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( semilattice_inf_inf @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( semilattice_inf_inf @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(224,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_subset__refl) ).
thf(1393,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
& ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_image__iff) ).
thf(2634,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
& ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
& ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_insert__absorb) ).
thf(1991,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ hoare_1924220188gleton )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ state ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ state ) @ ( hAPP @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) ) ) ) ) @ ( fequal @ state ) ) ) ) @ B ) @ ( fequal @ state ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_MGT__alternD) ).
thf(792,plain,
! [A: $i,B: $i] :
( ( hBOOL @ hoare_1924220188gleton )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) @ ( hAPP @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ state ) ) ) @ ( hoare_246368825triple @ state ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ state ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ state ) @ ( hAPP @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) ) ) ) ) @ ( fequal @ state ) ) ) ) @ B ) @ ( fequal @ state ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ A @ D )
= ( hAPP @ B @ A @ E @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_image__eqI) ).
thf(631,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ A @ D )
= ( hAPP @ B @ A @ E @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(632,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ti @ A @ D )
!= ( hAPP @ B @ A @ E @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ E ) @ C ) ) ) ),
inference(cnf,[status(esa)],[631]) ).
thf(633,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ti @ A @ D )
!= ( hAPP @ B @ A @ E @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ E ) @ C ) ) ) ),
inference(lifteq,[status(thm)],[632]) ).
thf(309,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_sup_Oassoc) ).
thf(1695,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( ord @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ C ) ) @ ( hAPP @ A @ B @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_le__funD) ).
thf(1071,plain,
! [A: $i,B: $i] :
( ( ord @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ C ) ) @ ( hAPP @ A @ B @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(524,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).
thf(2408,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) )
<=> ( ( hAPP @ A @ ( option @ B ) @ D @ C )
!= ( none @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_domIff) ).
thf(2221,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) )
=> ( ( hAPP @ A @ ( option @ B ) @ D @ C )
!= ( none @ B ) ) )
& ( ( ( hAPP @ A @ ( option @ B ) @ D @ C )
!= ( none @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(590,axiom,
hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( finite_finite @ pname ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_finite__dom__body) ).
thf(2645,plain,
hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( finite_finite @ pname ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(561,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_sup__commute) ).
thf(2546,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(2246,plain,
( ( hBOOL @ hoare_1924220188gleton )
=> ~ ? [A: $i] :
! [B: $i] : B = A ),
inference(miniscope,[status(thm)],[2245]) ).
thf(2247,plain,
! [A: $i] :
( ~ ( hBOOL @ hoare_1924220188gleton )
| ( ( sk80 @ A )
!= A ) ),
inference(cnf,[status(esa)],[2246]) ).
thf(2248,plain,
! [A: $i] :
( ( ( sk80 @ A )
!= A )
| ~ ( hBOOL @ hoare_1924220188gleton ) ),
inference(lifteq,[status(thm)],[2247]) ).
thf(2760,plain,
! [A: $i] :
( ( ( sk80 @ A )
!= A )
| ~ $true ),
inference(rewrite,[status(thm)],[2248,1999]) ).
thf(2761,plain,
! [A: $i] :
( ( sk80 @ A )
!= A ),
inference(simp,[status(thm)],[2760]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Un__left__commute) ).
thf(1712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rev__finite__subset) ).
thf(1054,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ C ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ E ) )
= ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ F ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ G ) ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_map__upd__eqD1) ).
thf(1996,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ C ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ E ) )
= ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ F ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ G ) ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_insert__not__empty) ).
thf(2729,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fold_graph @ B @ A ) @ C ) @ D ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_fold__graph_H_Ointros_I1_J) ).
thf(1764,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fold_graph @ B @ A ) @ C ) @ D ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) ) @ ( dom @ A @ B ) )
= ( dom @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Map_Odom_res) ).
thf(1680,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) ) @ ( dom @ A @ B ) )
= ( dom @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) ) @ ( combb @ A @ B @ C ) )
= ( combb @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
thf(1698,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) ) @ ( combb @ A @ B @ C ) )
= ( combb @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ state @ bool @ B @ C ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ B ) @ A ) ) @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_evalc_OWhileFalse) ).
thf(2585,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ state @ bool @ B @ C ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ B ) @ A ) ) @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(62,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_inf__sup__absorb) ).
thf(824,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_insert__Diff__if) ).
thf(2524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( option @ B ) ) ) @ ( combs @ A @ ( option @ B ) @ ( option @ B ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) @ ( combs @ A @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) @ A ) @ ( if @ ( option @ B ) ) ) @ C ) ) @ D ) ) @ E ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ E ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_dom__if) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( option @ B ) ) ) @ ( combs @ A @ ( option @ B ) @ ( option @ B ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) @ ( combs @ A @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ ( option @ B ) ) ) @ A ) @ ( if @ ( option @ B ) ) ) @ C ) ) @ D ) ) @ E ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ E ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ pname @ com @ body_1 @ A )
!= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_com_Osimps_I59_J) ).
thf(1510,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ pname @ com @ body_1 @ A )
!= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(485,axiom,
( ( ti @ ( fun @ pname @ com ) @ body_1 )
= body_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Com_Ocom_OBODY_res) ).
thf(2275,plain,
( ( ti @ ( fun @ pname @ com ) @ body_1 )
= body_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( bounded_lattice @ B )
=> ( bounded_lattice_bot @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__bot) ).
thf(2033,plain,
! [A: $i,B: $i] :
( ( bounded_lattice @ B )
=> ( bounded_lattice_bot @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_folding__image__simple_Ounion__disjoint) ).
thf(975,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(619,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_Int__lower2) ).
thf(2727,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) )
=> ~ ( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_inf1E) ).
thf(732,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) )
=> ~ ( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_UnCI) ).
thf(2657,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( option @ B ) @ bool ) ) @ ( fun @ ( option @ B ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( option @ B ) @ bool ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ bool ) ) @ ( hAPP @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ bool ) ) @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ bool ) ) ) @ ( combb @ ( option @ B ) @ ( fun @ ( option @ B ) @ bool ) @ A ) @ ( fequal @ ( option @ B ) ) ) @ C ) ) @ ( none @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_dom__def) ).
thf(1752,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( option @ B ) @ bool ) ) @ ( fun @ ( option @ B ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( option @ B ) @ bool ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ bool ) ) @ ( hAPP @ ( fun @ ( option @ B ) @ ( fun @ ( option @ B ) @ bool ) ) @ ( fun @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ bool ) ) ) @ ( combb @ ( option @ B ) @ ( fun @ ( option @ B ) @ bool ) @ A ) @ ( fequal @ ( option @ B ) ) ) @ C ) ) @ ( none @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Un__empty__right) ).
thf(1929,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(551,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ ( option @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ ( option @ A ) ) @ ( some @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_inj__Some) ).
thf(2514,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ ( option @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ ( option @ A ) ) @ ( some @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ I ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C ) ) )
=> ( ( hAPP @ A @ B @ G @ I )
= ( ti @ B @ F ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_folding__image__simple_Ounion__inter__neutral) ).
thf(875,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ I ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C ) ) )
=> ( ( hAPP @ A @ B @ G @ I )
= ( ti @ B @ F ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(311,axiom,
preorder @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(1701,plain,
preorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_Diff__triv) ).
thf(2716,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_theI_H) ).
thf(1226,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_inj__on__empty) ).
thf(1007,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_domI) ).
thf(694,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(284,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_inf_Ocommute) ).
thf(1615,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( partial_flat_lub @ A ) @ C ) @ B )
= ( ti @ A @ C ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( partial_flat_lub @ A ) @ C ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_flat__lub__def) ).
thf(1784,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( partial_flat_lub @ A ) @ C ) @ B )
= ( ti @ A @ C ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( partial_flat_lub @ A ) @ C ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(67,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( insert @ A ) )
= ( insert @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
thf(843,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( insert @ A ) )
= ( insert @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fimplies ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_insert__Collect) ).
thf(1125,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fimplies ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(235,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_inf__sup__ord_I4_J) ).
thf(1428,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_elem @ A ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fun @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ bool ) ) @ ( combb @ ( fun @ A @ bool ) @ bool @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fequal @ ( fun @ A @ bool ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ A @ bool ) ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_the__elem__def) ).
thf(2193,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_elem @ A ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fun @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ bool ) ) @ ( combb @ ( fun @ A @ bool ) @ bool @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fequal @ ( fun @ A @ bool ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ A @ bool ) ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ F ) ) @ D ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ G ) ) @ ( hAPP @ A @ B @ C @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_order__subst2) ).
thf(2326,plain,
! [A: $i,B: $i] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ F ) ) @ D ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ G ) ) @ ( hAPP @ A @ B @ C @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_Diff__partition) ).
thf(2293,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ B ) )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_Diff__insert__absorb) ).
thf(1271,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(47,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_inf__left__idem) ).
thf(787,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(623,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ skip ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_evalc_OSkip) ).
thf(2738,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ skip ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_theI) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1,conjecture,
hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(624,plain,
~ ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(2757,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
!= ( hBOOL @ wT_bodies ) ),
inference(paramod_ordered,[status(thm)],[2570,624]) ).
thf(2759,plain,
( ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) )
!= wT_bodies ),
inference(simp,[status(thm)],[2757]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ E ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ E ) )
& ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ E ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ D ) ) )
= ( bot_bot @ ( fun @ B @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_inj__on__Un) ).
thf(1090,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ E ) )
& ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ E ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ D ) ) )
= ( bot_bot @ ( fun @ B @ bool ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ E ) )
& ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ E ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ D ) ) )
= ( bot_bot @ ( fun @ B @ bool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_Int__assoc) ).
thf(2425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_finite__induct) ).
thf(1258,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(537,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_le__infI1) ).
thf(2474,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_Int__empty__right) ).
thf(672,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Un__upper2) ).
thf(1139,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( ( ord @ B )
& ( ord @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( D
= ( hAPP @ B @ A @ E @ F ) )
=> ( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ F ) @ C ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ B @ A @ E @ G ) ) @ ( hAPP @ B @ A @ E @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ ( hAPP @ B @ A @ E @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_ord__eq__le__subst) ).
thf(1503,plain,
! [A: $i,B: $i] :
( ( ( ord @ B )
& ( ord @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( D
= ( hAPP @ B @ A @ E @ F ) )
=> ( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ F ) @ C ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ B @ A @ E @ G ) ) @ ( hAPP @ B @ A @ E @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ ( hAPP @ B @ A @ E @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_Int__iff) ).
thf(919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(565,axiom,
( ( ti @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ fa )
= fa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_Fa_res) ).
thf(2557,plain,
( ( ti @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ fa )
= fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ D @ E ) )
=> ( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ E ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ D ) @ B ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ D ) @ B ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_evalc_OWhileTrue) ).
thf(804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ D @ E ) )
=> ( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ E ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ D ) @ B ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ D ) @ B ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_Int__absorb1) ).
thf(2148,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(500,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
<=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( ti @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_le__iff__sup) ).
thf(2319,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( ti @ A @ C ) ) )
& ( ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( ti @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
=> ( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_insertE) ).
thf(1194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
=> ( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_inf1D1) ).
thf(2361,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Int__Diff) ).
thf(900,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D )
= ( bot_bot @ ( fun @ B @ bool ) ) )
<=> ( ( ti @ ( fun @ A @ bool ) @ D )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_image__is__empty) ).
thf(1282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D )
= ( bot_bot @ ( fun @ B @ bool ) ) )
=> ( ( ti @ ( fun @ A @ bool ) @ D )
= ( bot_bot @ ( fun @ A @ bool ) ) ) )
& ( ( ( ti @ ( fun @ A @ bool ) @ D )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D )
= ( bot_bot @ ( fun @ B @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) )
| ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(1117,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) )
| ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ C ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_finite__empty__induct) ).
thf(1011,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ C ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ B @ A @ D @ E ) ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ H ) @ G ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ B @ A @ D @ H ) ) @ ( hAPP @ B @ A @ D @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ B @ A @ D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_xt3) ).
thf(1524,plain,
! [A: $i,B: $i] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ B @ A @ D @ E ) ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ H ) @ G ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ B @ A @ D @ H ) ) @ ( hAPP @ B @ A @ D @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ B @ A @ D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(489,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_inf_Oleft__idem) ).
thf(2284,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ C ) @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_com_Osimps_I5_J) ).
thf(1492,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ C ) @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_folding__one__idem_Osubset__idem) ).
thf(2378,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ C ) @ D ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ C @ B ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_folding__one__idem_Oidem) ).
thf(2197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ C ) @ D ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ C @ B ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(558,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_inf__sup__ord_I2_J) ).
thf(2538,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ C ) @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_com_Osimps_I3_J) ).
thf(1853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ C ) @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_subset__inj__on) ).
thf(2151,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(589,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ A ) ) @ ( semilattice_sup_sup @ A ) )
= ( semilattice_sup_sup @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Lattices_Osemilattice__sup__class_Osup_res) ).
thf(2642,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ A ) ) @ ( semilattice_sup_sup @ A ) )
= ( semilattice_sup_sup @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ) @ C ) @ D ) )
=> ( ( ( D = C )
=> ( hBOOL @ ( hAPP @ state @ bool @ A @ C ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ state @ bool @ A @ C ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ C ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ) @ E ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_evalc__WHILE__case) ).
thf(2415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ) @ C ) @ D ) )
=> ( ( ( D = C )
=> ( hBOOL @ ( hAPP @ state @ bool @ A @ C ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ state @ bool @ A @ C ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ C ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ) @ E ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(543,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ ( hAPP @ B @ A @ C @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_insert__image) ).
thf(2493,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ ( hAPP @ B @ A @ C @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ B ) ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_Collect__conj__eq) ).
thf(880,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ B ) ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Un__absorb) ).
thf(649,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(218,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( ( ti @ A @ C )
= ( ti @ A @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_xt1_I4_J) ).
thf(1376,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( ( ti @ A @ C )
= ( ti @ A @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_subset__insertI2) ).
thf(1439,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rev__image__eqI) ).
thf(863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(163,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_distrib__sup__le) ).
thf(1175,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Un__iff) ).
thf(2180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(57,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) ) @ ( hoare_279057269derivs @ A ) )
= ( hoare_279057269derivs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__derivs_res) ).
thf(811,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) ) @ ( hoare_279057269derivs @ A ) )
= ( hoare_279057269derivs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(72,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_sup_Oleft__commute) ).
thf(858,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_equals0I) ).
thf(1630,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ B @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ D @ G ) @ H ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_conseq1) ).
thf(1821,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ B @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ D @ G ) @ H ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ B ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_sup1E) ).
thf(1862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ti @ ( option @ A ) @ B )
!= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) )
<=> ( ( ti @ ( option @ A ) @ B )
= ( none @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_not__Some__eq) ).
thf(700,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ti @ ( option @ A ) @ B )
!= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) )
=> ( ( ti @ ( option @ A ) @ B )
= ( none @ A ) ) )
& ( ( ( ti @ ( option @ A ) @ B )
= ( none @ A ) )
=> ! [C: $i] :
( ( ti @ ( option @ A ) @ B )
!= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(525,axiom,
( ( ti @ bool @ hoare_1924220188gleton )
= hoare_1924220188gleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__nrugjuseim_Ostate__not__singleton_res) ).
thf(2410,plain,
( ( ti @ bool @ hoare_1924220188gleton )
= hoare_1924220188gleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_finite__Int) ).
thf(1556,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
!= ( hAPP @ pname @ com @ body_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_com_Osimps_I48_J) ).
thf(668,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
!= ( hAPP @ pname @ com @ body_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_insert__is__Un) ).
thf(2461,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_finite__Diff2) ).
thf(1339,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_insert__absorb2) ).
thf(2610,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(499,axiom,
! [A: $i] :
( ( ordered_ab_group_add @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( minus_minus @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( minus_minus @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_diff__eq__diff__less__eq) ).
thf(2314,plain,
! [A: $i] :
( ( ordered_ab_group_add @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( minus_minus @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( minus_minus @ A ) @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) ) )
& ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( option @ A ) @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( option @ A ) @ B ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( option @ A ) @ B ) ) @ ( option_rec @ B @ A ) @ C ) @ D ) @ ( none @ A ) )
= ( ti @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_option_Orecs_I1_J) ).
thf(2625,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( option @ A ) @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( option @ A ) @ B ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( option @ A ) @ B ) ) @ ( option_rec @ B @ A ) @ C ) @ D ) @ ( none @ A ) )
= ( ti @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(52,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ bool @ ( finite_comp_fun_idem @ A @ A ) @ ( semilattice_inf_inf @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_comp__fun__idem__inf) ).
thf(799,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ bool @ ( finite_comp_fun_idem @ A @ A ) @ ( semilattice_inf_inf @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ B @ E )
!= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_fun__upd__other) ).
thf(1162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ B @ E )
!= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(576,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_subsetD) ).
thf(2593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B )
!= ( none @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_option_Osimps_I3_J) ).
thf(1029,plain,
! [A: $i,B: $i] :
( ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B )
!= ( none @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(93,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) ) @ ( finite_folding_one @ A ) )
= ( finite_folding_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one_res) ).
thf(943,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) ) @ ( finite_folding_one @ A ) )
= ( finite_folding_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) )
<=> ( ( ( ( ti @ A @ F )
= ( ti @ A @ D ) )
& ( ( ti @ B @ E )
= ( ti @ B @ G ) ) )
| ( ( ( ti @ A @ F )
!= ( ti @ A @ D ) )
& ( ( hAPP @ A @ ( option @ B ) @ C @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_map__upd__Some__unfold) ).
thf(2252,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) )
=> ( ( ( ( ti @ A @ F )
= ( ti @ A @ D ) )
& ( ( ti @ B @ E )
= ( ti @ B @ G ) ) )
| ( ( ( ti @ A @ F )
!= ( ti @ A @ D ) )
& ( ( hAPP @ A @ ( option @ B ) @ C @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) ) ) ) )
& ( ( ( ( ( ti @ A @ F )
= ( ti @ A @ D ) )
& ( ( ti @ B @ E )
= ( ti @ B @ G ) ) )
| ( ( ( ti @ A @ F )
!= ( ti @ A @ D ) )
& ( ( hAPP @ A @ ( option @ B ) @ C @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) ) ) )
=> ( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_singleton__inject) ).
thf(2664,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_the__sym__eq__trivial) ).
thf(1177,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_folding__image__simple_Oremove) ).
thf(1381,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(502,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ bool @ ( finite_comp_fun_idem @ A @ ( fun @ A @ bool ) ) @ ( insert @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_comp__fun__idem__insert) ).
thf(2329,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ bool @ ( finite_comp_fun_idem @ A @ ( fun @ A @ bool ) ) @ ( insert @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(386,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ A ) ) @ ( partial_flat_lub @ A ) )
= ( partial_flat_lub @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Partial__Function_Oflat__lub_res) ).
thf(1952,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ A ) ) @ ( partial_flat_lub @ A ) )
= ( partial_flat_lub @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(427,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( finite_finite @ A ) )
= ( finite_finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
thf(2075,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( finite_finite @ A ) )
= ( finite_finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combs @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ ( hAPP @ A @ C @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(1926,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combs @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ ( hAPP @ A @ C @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(618,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_sup__ge2) ).
thf(2725,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_Int__left__commute) ).
thf(868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(80,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
<=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_order__eq__iff) ).
thf(883,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(336,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_sup_Oleft__idem) ).
thf(1775,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(436,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_emptyE) ).
thf(2101,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_insert__Diff__single) ).
thf(1250,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( ti @ A @ B ) ) )
& ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_folding__one_Oinsert__remove) ).
thf(2207,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( ti @ A @ B ) ) )
& ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(346,axiom,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( bot_bot @ A ) ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_sup__bot__left) ).
thf(1805,plain,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( bot_bot @ A ) ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hoare_1656922687triple @ A ) @ B @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_1656922687triple @ A ) @ B ) @ ( hoare_1312322281e_case @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ F ) )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ B @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) @ C @ D ) @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_triple_Osimps_I2_J) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hoare_1656922687triple @ A ) @ B @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_1656922687triple @ A ) @ B ) @ ( hoare_1312322281e_case @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ D ) @ E ) @ F ) )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ B @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) @ C @ D ) @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( ( ti @ A @ C )
!= ( ti @ A @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ F ) )
=> ( ( hAPP @ A @ B @ E @ C )
!= ( hAPP @ A @ B @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_inj__on__contraD) ).
thf(2212,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( ( ti @ A @ C )
!= ( ti @ A @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ F ) )
=> ( ( hAPP @ A @ B @ E @ C )
!= ( hAPP @ A @ B @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ! [E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ C @ E ) @ F ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ F ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ D @ B ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_folding__one_Oclosed) ).
thf(2171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite_folding_one @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ! [E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ C @ E ) @ F ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ F ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ D @ B ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_Int__absorb2) ).
thf(1213,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_DiffE) ).
thf(768,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(63,axiom,
! [A: $i] :
( ( ord @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( ord_less_eq @ A ) )
= ( ord_less_eq @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
thf(827,plain,
! [A: $i] :
( ( ord @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( ord_less_eq @ A ) )
= ( ord_less_eq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ C @ F ) ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_image__subsetI) ).
thf(2051,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ C @ F ) ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(123,axiom,
( ( ti @ bool @ wT_bodies )
= wT_bodies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Com_OWT__bodies_res) ).
thf(1044,plain,
( ( ti @ bool @ wT_bodies )
= wT_bodies ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i] :
( ( bot_bot @ ( fun @ A @ bool ) )
!= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_empty__not__insert) ).
thf(2550,plain,
! [A: $i,B: $i,C: $i] :
( ( bot_bot @ ( fun @ A @ bool ) )
!= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(134,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_inf__idem) ).
thf(1076,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(477,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( option @ A ) ) @ ( some @ A ) )
= ( some @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Option_Ooption_OSome_res) ).
thf(2239,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( option @ A ) ) @ ( some @ A ) )
= ( some @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( order @ B )
& ( ord @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ E ) ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ E ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ H ) @ G ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ H ) ) @ ( hAPP @ A @ B @ D @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ C ) ) @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_xt2) ).
thf(675,plain,
! [A: $i,B: $i] :
( ( ( order @ B )
& ( ord @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ E ) ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ E ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ H ) @ G ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ H ) ) @ ( hAPP @ A @ B @ D @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ C ) ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ D ) @ E ) @ F ) @ G ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ D @ C ) @ C )
= ( ti @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_folding__image__simple__idem_Oidem) ).
thf(1662,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ D ) @ E ) @ F ) @ G ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ D @ C ) @ C )
= ( ti @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_Un__least) ).
thf(795,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_Un__Int__distrib) ).
thf(2471,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) )
<=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_option_Oinject) ).
thf(1905,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) )
& ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
=> ( ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_finite__Diff) ).
thf(2037,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_hoare__derivs_OBody) ).
thf(1277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(150,axiom,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_finite__code) ).
thf(1134,plain,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(34,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_xt1_I5_J) ).
thf(749,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_finite__Un) ).
thf(2684,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
!= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_com_Osimps_I47_J) ).
thf(939,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
!= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(36,axiom,
( ( ti @ ( fun @ pname @ ( option @ com ) ) @ body )
= body ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Com_Obody_res) ).
thf(754,plain,
( ( ti @ ( fun @ pname @ ( option @ com ) ) @ body )
= body ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(125,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
<=> ( ( ti @ A @ C )
= ( ti @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_order__antisym__conv) ).
thf(1049,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ B ) ) )
& ( ( ( ti @ A @ C )
= ( ti @ A @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
<=> ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_insert__iff) ).
thf(2054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
=> ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_finite__insert) ).
thf(722,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_set__rev__mp) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(568,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B )
= ( ti @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_inf__absorb2) ).
thf(2564,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ B )
= ( ti @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(569,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_inf__sup__aci_I6_J) ).
thf(2567,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ D ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_Int__Collect) ).
thf(1547,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ D @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ bool @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(493,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_inf__sup__aci_I7_J) ).
thf(2298,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_insertCI) ).
thf(712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ~ ! [F: $i] :
( ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_imageE) ).
thf(1025,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ~ ! [F: $i] :
( ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(461,axiom,
lattice @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).
thf(2192,plain,
lattice @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(407,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_sup__idem) ).
thf(2012,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_Diff__cancel) ).
thf(1605,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_folding__image__simple__idem_Oin__idem) ).
thf(1941,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite908156982e_idem @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ B @ H @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ C ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_derivs__insertD) ).
thf(2678,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ C ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(616,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_sup_Ocommute) ).
thf(2720,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_finite__Diff__insert) ).
thf(640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E ) ) @ D ) @ F )
= ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_fun__upd__upd) ).
thf(1961,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E ) ) @ D ) @ F )
= ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(176,axiom,
order @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(1225,plain,
order @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(22,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( ti @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_sup__absorb2) ).
thf(707,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C )
= ( ti @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_insertI1) ).
thf(1230,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ ( fun @ B @ bool ) @ A ) @ bool ) ) ) ) @ ( finite1357897459simple @ A @ B ) )
= ( finite1357897459simple @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple_res) ).
thf(1484,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ ( fun @ B @ bool ) @ A ) @ bool ) ) ) ) @ ( finite1357897459simple @ A @ B ) )
= ( finite1357897459simple @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(2745,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) )
!= ( hBOOL @ hoare_1924220188gleton ) ),
inference(paramod_ordered,[status(thm)],[1999,624]) ).
thf(2747,plain,
( ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ y ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) )
!= hoare_1924220188gleton ),
inference(simp,[status(thm)],[2745]) ).
thf(433,axiom,
ord @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(2092,plain,
ord @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(452,axiom,
! [A: $i] :
( ( preorder @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_order__trans) ).
thf(2165,plain,
! [A: $i] :
( ( preorder @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ D @ E ) )
=> ( ( ti @ ( fun @ A @ B ) @ C )
= ( ti @ ( fun @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(1300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ D @ E ) )
=> ( ( ti @ ( fun @ A @ B ) @ C )
= ( ti @ ( fun @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
<=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_singleton__iff) ).
thf(1186,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) )
& ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( option @ A ) @ bool ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ ( option @ A ) @ bool ) ) @ ( image @ B @ ( option @ A ) ) @ ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ C ) @ E ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ D ) ) ) @ F )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( option @ A ) @ bool ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ ( option @ A ) @ bool ) ) @ ( image @ B @ ( option @ A ) ) @ C ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_image__map__upd) ).
thf(1038,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( option @ A ) @ bool ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ ( option @ A ) @ bool ) ) @ ( image @ B @ ( option @ A ) ) @ ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ C ) @ E ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ D ) ) ) @ F )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( option @ A ) @ bool ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ ( option @ A ) @ bool ) ) @ ( image @ B @ ( option @ A ) ) @ C ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_thin) ).
thf(1869,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_1656922687triple @ A ) @ B ) ) @ ( hoare_1312322281e_case @ A @ B ) )
= ( hoare_1312322281e_case @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__case_res) ).
thf(840,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_1656922687triple @ A ) @ B ) ) @ ( hoare_1312322281e_case @ A @ B ) )
= ( hoare_1312322281e_case @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_sup1CI) ).
thf(1235,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(505,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) ) @ ( finite2073411215e_idem @ A ) )
= ( finite2073411215e_idem @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one__idem_res) ).
thf(2337,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) ) @ ( finite2073411215e_idem @ A ) )
= ( finite2073411215e_idem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_equalityE) ).
thf(1317,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(420,axiom,
! [A: $i] :
( ( preorder @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_order__refl) ).
thf(2044,plain,
! [A: $i] :
( ( preorder @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(273,axiom,
! [A: $i] :
( ( hBOOL @ hoare_1924220188gleton )
=> ( ( hBOOL @ wT_bodies )
=> ( ( hBOOL @ ( hAPP @ com @ bool @ wt @ A ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_MGF) ).
thf(1579,plain,
! [A: $i] :
( ( hBOOL @ hoare_1924220188gleton )
=> ( ( hBOOL @ wT_bodies )
=> ( ( hBOOL @ ( hAPP @ com @ bool @ wt @ A ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ state ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ state ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ com @ ( hoare_1656922687triple @ state ) @ hoare_Mirabelle_MGT @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(324,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fimplies )
= fimplies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
thf(1738,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fimplies )
= fimplies ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_empty__Diff) ).
thf(1336,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ F ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_inj__on__image__Int) ).
thf(907,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ F ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ C ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_insert__mono) ).
thf(2219,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(394,axiom,
( ( ti @ ( fun @ com @ ( fun @ com @ com ) ) @ semi )
= semi ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Com_Ocom_OSemi_res) ).
thf(1980,plain,
( ( ti @ ( fun @ com @ ( fun @ com @ com ) ) @ semi )
= semi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(444,axiom,
! [A: $i,B: $i] :
( ( minus @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( minus_minus @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( minus_minus @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_minus__apply) ).
thf(2128,plain,
! [A: $i,B: $i] :
( ( minus @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ B ) ) @ ( minus_minus @ ( fun @ A @ B ) ) @ C ) @ D ) @ E )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ ( minus_minus @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(137,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_le__supI1) ).
thf(1085,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_inf1I) ).
thf(1658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(608,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_le__infI) ).
thf(2701,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(56,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( ti @ A @ C )
= ( ti @ A @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_xt1_I3_J) ).
thf(808,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( ti @ A @ C )
= ( ti @ A @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ bool @ ( finite_finite @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( collect @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( combc @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).
thf(1934,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ bool @ ( finite_finite @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( collect @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( combc @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(546,axiom,
! [A: $i,B: $i] :
( ( minus @ B )
=> ( minus @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(2500,plain,
! [A: $i,B: $i] :
( ( minus @ B )
=> ( minus @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_set__eq__subset) ).
thf(1766,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
<=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_all__not__in__conv) ).
thf(1141,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ) )
& ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(312,axiom,
! [A: $i,B: $i] :
~ ! [C: $i,D: $i,E: $i] :
( B
!= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ D ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_triple_Oexhaust) ).
thf(1702,plain,
! [A: $i,B: $i] :
~ ! [C: $i,D: $i,E: $i] :
( B
!= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ C ) @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ B @ B ) ) @ bool @ ( finite_comp_fun_idem @ A @ B ) @ E ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ A @ ( fun @ B @ B ) @ E @ C ) @ ( hAPP @ B @ B @ ( hAPP @ A @ ( fun @ B @ B ) @ E @ C ) @ D ) )
= ( hAPP @ B @ B @ ( hAPP @ A @ ( fun @ B @ B ) @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_comp__fun__idem_Ofun__left__idem) ).
thf(2543,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ B @ B ) ) @ bool @ ( finite_comp_fun_idem @ A @ B ) @ E ) )
=> ( ( hAPP @ B @ B @ ( hAPP @ A @ ( fun @ B @ B ) @ E @ C ) @ ( hAPP @ B @ B @ ( hAPP @ A @ ( fun @ B @ B ) @ E @ C ) @ D ) )
= ( hAPP @ B @ B @ ( hAPP @ A @ ( fun @ B @ B ) @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Un__empty__left) ).
thf(2711,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(328,axiom,
! [A: $i] :
( ( bot @ A )
=> ( ( ti @ A @ ( bot_bot @ A ) )
= ( bot_bot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
thf(1749,plain,
! [A: $i] :
( ( bot @ A )
=> ( ( ti @ A @ ( bot_bot @ A ) )
= ( bot_bot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ F ) @ G ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ G ) @ B ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ F ) @ B ) ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_Comp) ).
thf(727,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ F ) @ G ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ G ) @ B ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ E ) @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ F ) @ B ) ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_Int__greatest) ).
thf(1802,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(116,axiom,
( ( ti @ ( fun @ com @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ evalc )
= evalc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Natural_Oevalc_res) ).
thf(1023,plain,
( ( ti @ ( fun @ com @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ evalc )
= evalc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_sup1I2) ).
thf(2279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_predicate1D) ).
thf(1955,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(2145,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(1585,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ E ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ E )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ E ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_finite__ne__induct) ).
thf(978,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ E ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ E )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ E ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( hAPP @ bool @ ( fun @ A @ ( fun @ A @ A ) ) @ ( if @ A ) @ fTrue ) @ B ) @ C )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(2511,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( hAPP @ bool @ ( fun @ A @ ( fun @ A @ A ) ) @ ( if @ A ) @ fTrue ) @ B ) @ C )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_DiffD1) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(413,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ D ) @ B ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_inf__mono) ).
thf(2030,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ D ) @ B ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ A ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ C ) @ A ) ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_evalc_OSemi) ).
thf(1421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ A ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ C ) @ A ) ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ~ ! [D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_Set_Oset__insert) ).
thf(2479,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ~ ! [D: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(246,axiom,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( bot_bot @ A ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_sup__bot__right) ).
thf(1459,plain,
! [A: $i] :
( ( bounded_lattice_bot @ A )
=> ! [B: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( bot_bot @ A ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(165,axiom,
! [A: $i] :
( ( bot_bot @ ( fun @ A @ bool ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ bool @ ( fun @ A @ bool ) @ ( combk @ bool @ A ) @ fFalse ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_empty__def) ).
thf(1180,plain,
! [A: $i] :
( ( bot_bot @ ( fun @ A @ bool ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ bool @ ( fun @ A @ bool ) @ ( combk @ bool @ A ) @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_Int__def) ).
thf(1553,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(349,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ pname @ com @ body_1 @ A ) ) )
=> ~ ! [B: $i] :
( ( hAPP @ pname @ ( option @ com ) @ body @ A )
!= ( hAPP @ com @ ( option @ com ) @ ( some @ com ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_WTs__elim__cases_I7_J) ).
thf(1817,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ pname @ com @ body_1 @ A ) ) )
=> ~ ! [B: $i] :
( ( hAPP @ pname @ ( option @ com ) @ body @ A )
!= ( hAPP @ com @ ( option @ com ) @ ( some @ com ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(470,axiom,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(2215,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Un__insert__left) ).
thf(759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(194,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_inf__assoc) ).
thf(1289,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_Diff__subset) ).
thf(771,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_sup1I1) ).
thf(1108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_IntE) ).
thf(2458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(cnf,[status(esa)],[625]) ).
thf(627,plain,
! [B: $i,A: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(lifteq,[status(thm)],[626]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(1918,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_in__mono) ).
thf(1649,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(157,axiom,
( ( ti @ ( fun @ ( fun @ state @ bool ) @ ( fun @ com @ com ) ) @ while )
= while ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Com_Ocom_OWhile_res) ).
thf(1157,plain,
( ( ti @ ( fun @ ( fun @ state @ bool ) @ ( fun @ com @ com ) ) @ while )
= while ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(428,axiom,
! [A: $i] :
( ( bot @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( bot_bot @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_bot__least) ).
thf(2078,plain,
! [A: $i] :
( ( bot @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( bot_bot @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_folding__image__simple_Oinsert__remove) ).
thf(1844,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ E ) @ F ) @ G ) @ H ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ B @ B @ ( hAPP @ B @ ( fun @ B @ B ) @ E @ ( hAPP @ A @ B @ G @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ B @ H @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_rev__predicate1D) ).
thf(903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(507,axiom,
! [A: $i] :
( ( ord @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( C = D )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_ord__eq__le__trans) ).
thf(2347,plain,
! [A: $i] :
( ( ord @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( C = D )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ pname @ com @ body_1 @ A )
!= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_com_Osimps_I49_J) ).
thf(1654,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ pname @ com @ body_1 @ A )
!= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_inf__Int__eq) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(338,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_sup__assoc) ).
thf(1781,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
<=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_subset__empty) ).
thf(1216,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) ) )
& ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(2602,plain,
( ( ( hBOOL @ hoare_1924220188gleton )
=> ~ ! [A: $i,B: $i] : A = B )
& ( ~ ! [A: $i,B: $i] : A = B
=> ( hBOOL @ hoare_1924220188gleton ) ) ),
inference(miniscope,[status(thm)],[2601]) ).
thf(2604,plain,
( ~ ( hBOOL @ hoare_1924220188gleton )
| ( sk95 != sk96 ) ),
inference(cnf,[status(esa)],[2602]) ).
thf(2606,plain,
( ( sk96 != sk95 )
| ~ ( hBOOL @ hoare_1924220188gleton ) ),
inference(lifteq,[status(thm)],[2604]) ).
thf(2742,plain,
( ( sk96 != sk95 )
| ~ $true ),
inference(rewrite,[status(thm)],[2606,1999]) ).
thf(2743,plain,
sk96 != sk95,
inference(simp,[status(thm)],[2742]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ A ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ A @ A ) @ ( combi @ A ) ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_image__ident) ).
thf(1448,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ A ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ A @ A ) @ ( combi @ A ) ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_Un__Diff__Int) ).
thf(2490,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Un__assoc) ).
thf(2187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(223,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_sup__left__commute) ).
thf(1390,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_com_Osimps_I13_J) ).
thf(1575,plain,
! [A: $i,B: $i] :
( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_insert__Diff) ).
thf(1590,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ B ) ) ) ) @ ( override_on @ A @ B ) )
= ( override_on @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Fun_Ooverride__on_res) ).
thf(1646,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ B ) ) ) ) @ ( override_on @ A @ B ) )
= ( override_on @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(203,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_xt1_I6_J) ).
thf(1326,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ ( hAPP @ B @ A @ E @ F ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ F ) @ C ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ B @ A @ E @ G ) ) @ ( hAPP @ B @ A @ E @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ ( hAPP @ B @ A @ E @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_order__subst1) ).
thf(1639,plain,
! [A: $i,B: $i] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ ( hAPP @ B @ A @ E @ F ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ F ) @ C ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ B @ A @ E @ G ) ) @ ( hAPP @ B @ A @ E @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ ( hAPP @ B @ A @ E @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ( semilattice_sup @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__sup) ).
thf(1903,plain,
! [A: $i,B: $i] :
( ( lattice @ B )
=> ( semilattice_sup @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(564,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ C ) @ D ) @ E ) @ F ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ F @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( ti @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_folding__image__simple_Oempty) ).
thf(2554,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) @ ( hAPP @ ( fun @ B @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ B ) @ bool ) ) ) @ ( finite1357897459simple @ B @ A ) @ C ) @ D ) @ E ) @ F ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ B @ F @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( ti @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(129,axiom,
! [A: $i] :
( ( ( ti @ bool @ A )
= fTrue )
| ( ( ti @ bool @ A )
= fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(1062,plain,
! [A: $i] :
( ( ( ti @ bool @ A )
= fTrue )
| ( ( ti @ bool @ A )
= fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_Diff__Int__distrib) ).
thf(1481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(94,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_inf_Oassoc) ).
thf(946,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
=> ( ( ti @ A @ D )
!= ( ti @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_disjoint__iff__not__equal) ).
thf(652,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
=> ( ( ti @ A @ D )
!= ( ti @ A @ E ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
=> ( ( ti @ A @ D )
!= ( ti @ A @ E ) ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(404,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ bool @ ( finite_comp_fun_idem @ A @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) ) @ ( combb @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ A ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( combc @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ A @ bool ) ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_comp__fun__idem__remove) ).
thf(2004,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ bool @ ( finite_comp_fun_idem @ A @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) ) @ ( combb @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ A ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( combc @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ A @ bool ) ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(786,plain,
( ( ti @ bool @ fFalse )
= fFalse ),
inference(lifteq,[status(thm)],[785]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( ord @ B )
=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ C ) @ D ) )
<=> ! [E: $i] : ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_le__fun__def) ).
thf(1253,plain,
! [A: $i,B: $i] :
( ( ord @ B )
=> ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ C ) @ D ) )
=> ! [E: $i] : ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) ) )
& ( ! [E: $i] : ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ C @ E ) ) @ ( hAPP @ A @ B @ D @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_Un__Int__assoc__eq) ).
thf(963,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_UnI2) ).
thf(2167,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_insertI2) ).
thf(2273,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_singletonE) ).
thf(2174,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(2389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(307,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_inf__sup__aci_I8_J) ).
thf(1689,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(516,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_inf_Oleft__commute) ).
thf(2384,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ D ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_equalityI) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_insert__Diff1) ).
thf(1294,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
!= ( hAPP @ pname @ com @ body_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_com_Osimps_I58_J) ).
thf(1444,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B )
!= ( hAPP @ pname @ com @ body_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_IntD2) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1045,plain,
( ( ti @ bool @ wT_bodies )
= wT_bodies ),
inference(lifteq,[status(thm)],[1044]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_equalityD2) ).
thf(716,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_subsetI) ).
thf(1706,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(168,axiom,
hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ fa ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(1193,plain,
hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ fa ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ state ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) @ ( hAPP @ ( fun @ com @ ( hoare_1656922687triple @ state ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( hoare_1656922687triple @ state ) ) ) @ ( combb @ com @ ( hoare_1656922687triple @ state ) @ pname ) @ hoare_Mirabelle_MGT ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ bool ) @ ( dom @ pname @ com ) @ body ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_Collect__mono) ).
thf(1348,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_Diff__iff) ).
thf(2287,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_Int__insert__right) ).
thf(2517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_diff__single__insert) ).
thf(1725,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(388,axiom,
! [A: $i] :
( ( preorder @ A )
=> ! [B: $i,C: $i] :
( ( B = C )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_order__eq__refl) ).
thf(1957,plain,
! [A: $i] :
( ( preorder @ A )
=> ! [B: $i,C: $i] :
( ( B = C )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Un__def) ).
thf(2587,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ C ) @ D ) @ E ) @ D )
= ( ti @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_fun__upd__same) ).
thf(1395,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ C ) @ D ) @ E ) @ D )
= ( ti @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( hAPP @ A @ A @ ( combi @ A ) @ B )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(1593,plain,
! [A: $i,B: $i] :
( ( hAPP @ A @ A @ ( combi @ A ) @ B )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(2950,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) )
| ( ( hBOOL @ wT_bodies )
!= ( hBOOL @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2570,1458]) ).
thf(2951,plain,
~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ wT_bodies ) ),
inference(pattern_uni,[status(thm)],[2950:[bind(A,$thf( wT_bodies ))]]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( combk @ A @ B ) @ C ) ) @ E )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_image__constant) ).
thf(1876,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( combk @ A @ B ) @ C ) ) @ E )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ D ) ) @ body_1 ) ) @ E ) ) @ F ) ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ D ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ E ) ) @ F ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( hAPP @ pname @ ( fun @ ( fun @ pname @ bool ) @ bool ) @ ( member @ pname ) @ B ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ D @ B ) ) @ ( hAPP @ pname @ com @ body_1 @ B ) ) @ ( hAPP @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ E @ B ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Body1) ).
thf(790,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ D ) ) @ body_1 ) ) @ E ) ) @ F ) ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( image @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( hoare_1656922687triple @ A ) ) ) @ ( combs @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ com ) @ ( fun @ pname @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( combs @ pname @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hAPP @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) @ ( fun @ ( fun @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( fun @ pname @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) ) ) @ ( combb @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ pname ) @ ( hoare_246368825triple @ A ) ) @ D ) ) @ ( hAPP @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) @ ( hAPP @ ( fun @ ( option @ com ) @ com ) @ ( fun @ ( fun @ pname @ ( option @ com ) ) @ ( fun @ pname @ com ) ) @ ( combb @ ( option @ com ) @ com @ pname ) @ ( the @ com ) ) @ body ) ) ) @ E ) ) @ F ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( hAPP @ pname @ ( fun @ ( fun @ pname @ bool ) @ bool ) @ ( member @ pname ) @ B ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ D @ B ) ) @ ( hAPP @ pname @ com @ body_1 @ B ) ) @ ( hAPP @ pname @ ( fun @ A @ ( fun @ state @ bool ) ) @ E @ B ) ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__imageI) ).
thf(1757,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ skip ) @ A ) @ B ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_evalc__elim__cases_I1_J) ).
thf(735,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ skip ) @ A ) @ B ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) )
=> ( ( hBOOL @ ( hAPP @ com @ bool @ wt @ A ) )
=> ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_WT_OSemi) ).
thf(1642,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ com @ bool @ wt @ B ) )
=> ( ( hBOOL @ ( hAPP @ com @ bool @ wt @ A ) )
=> ( hBOOL @ ( hAPP @ com @ bool @ wt @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_IntI) ).
thf(752,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( bot_bot @ ( fun @ A @ bool ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_empty__Collect__eq) ).
thf(833,plain,
! [A: $i,B: $i] :
( ( ( ( bot_bot @ ( fun @ A @ bool ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ( bot_bot @ ( fun @ A @ bool ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(615,axiom,
semilattice_sup @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__sup) ).
thf(2719,plain,
semilattice_sup @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( none @ A )
!= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_option_Osimps_I2_J) ).
thf(854,plain,
! [A: $i,B: $i] :
( ( none @ A )
!= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(199,axiom,
! [A: $i] :
( ( bot @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( bot_bot @ A ) ) )
<=> ( ( ti @ A @ B )
= ( bot_bot @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_bot__unique) ).
thf(1303,plain,
! [A: $i] :
( ( bot @ A )
=> ! [B: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( bot_bot @ A ) ) )
=> ( ( ti @ A @ B )
= ( bot_bot @ A ) ) )
& ( ( ( ti @ A @ B )
= ( bot_bot @ A ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ ( bot_bot @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_insert__def) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( ord @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ C ) ) @ ( hAPP @ A @ B @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_le__funE) ).
thf(1148,plain,
! [A: $i,B: $i] :
( ( ord @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ B ) ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ B @ ( fun @ B @ bool ) @ ( ord_less_eq @ B ) @ ( hAPP @ A @ B @ D @ C ) ) @ ( hAPP @ A @ B @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_IntD1) ).
thf(1436,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(215,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fAll @ A ) )
= ( fAll @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fAll_res) ).
thf(1363,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fAll @ A ) )
= ( fAll @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ B @ ( fun @ A @ C ) ) ) @ ( combc @ A @ B @ C ) )
= ( combc @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
thf(2334,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ B @ ( fun @ A @ C ) ) ) @ ( combc @ A @ B @ C ) )
= ( combc @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(2744,plain,
( ( hBOOL @ hoare_1924220188gleton )
!= ( hBOOL @ fFalse ) ),
inference(paramod_ordered,[status(thm)],[1999,699]) ).
thf(2746,plain,
hoare_1924220188gleton != fFalse,
inference(simp,[status(thm)],[2744]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combb @ C @ B @ A ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ D @ ( hAPP @ A @ C @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(897,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combb @ C @ B @ A ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ D @ ( hAPP @ A @ C @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_the__eq__trivial) ).
thf(1056,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ ( hAPP @ ( option @ A ) @ ( fun @ A @ bool ) @ ( set @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ E ) ) )
=> ( ( ( ti @ ( option @ A ) @ D )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ospec) ).
thf(2366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ ( hAPP @ ( option @ A ) @ ( fun @ A @ bool ) @ ( set @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ E ) ) )
=> ( ( ( ti @ ( option @ A ) @ D )
= ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(2404,plain,
( ( ti @ com @ skip )
= skip ),
inference(lifteq,[status(thm)],[2403]) ).
thf(613,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_le__infI2) ).
thf(2714,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i] :
( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( none @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_map__upd__nonempty) ).
thf(1065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i] :
( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( none @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(97,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) )
=> ( ( ( hAPP @ A @ A @ B @ D )
= ( ti @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ G ) @ F ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ B @ G ) ) @ ( hAPP @ A @ A @ B @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_xt1_I16_J) ).
thf(955,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) )
=> ( ( ( hAPP @ A @ A @ B @ D )
= ( ti @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ G ) @ F ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ B @ G ) ) @ ( hAPP @ A @ A @ B @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ B ) ) ) @ ( override_on @ A @ B ) @ C ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( ti @ ( fun @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_override__on__emptyset) ).
thf(2651,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ B ) ) ) @ ( override_on @ A @ B ) @ C ) @ D ) @ ( bot_bot @ ( fun @ A @ bool ) ) )
= ( ti @ ( fun @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ C ) @ A ) )
=> ( A = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_com__det) ).
thf(2201,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ C ) @ A ) )
=> ( A = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Un__absorb1) ).
thf(801,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_asm) ).
thf(1989,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_singleton__conv2) ).
thf(1033,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_folding__one__idem_Oin__idem) ).
thf(1197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ ( fun @ A @ bool ) @ A ) @ bool ) @ ( finite2073411215e_idem @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ D @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ A @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_set__diff__eq) ).
thf(960,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ B )
= ( ti @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_the__equality) ).
thf(1473,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ B @ D ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_1 @ A ) @ B )
= ( ti @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
<=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_subset__Un__eq) ).
thf(2340,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) ) )
& ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_Int__left__absorb) ).
thf(1165,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B ) ) @ C ) @ D ) )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ A ) @ C ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_evalc__elim__cases_I4_J) ).
thf(2021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B ) ) @ C ) @ D ) )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ A ) @ C ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ state @ ( fun @ state @ bool ) @ ( hAPP @ com @ ( fun @ state @ ( fun @ state @ bool ) ) @ evalc @ B ) @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ F ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ F ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_finite__subset__induct) ).
thf(2063,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( bot_bot @ ( fun @ A @ bool ) ) ) )
=> ( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ F ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ F ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ C ) ) ) @ ( combs @ A @ B @ C ) )
= ( combs @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
thf(1610,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ C ) ) ) @ ( combs @ A @ B @ C ) )
= ( combs @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_insert__dom) ).
thf(1742,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ bool ) @ ( dom @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(562,axiom,
bot @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(2549,plain,
bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(2502,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(393,axiom,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_inf__sup__aci_I4_J) ).
thf(1977,plain,
! [A: $i] :
( ( lattice @ A )
=> ! [B: $i,C: $i] :
( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) )
= ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ E ) ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) )
<=> ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_inj__on__Un__image__eq__iff) ).
thf(1152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( inj_on @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ D ) @ E ) ) )
=> ( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) )
=> ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ E ) ) )
& ( ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ E ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(1384,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_Int__absorb) ).
thf(1582,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(105,axiom,
( ( ti @ ( fun @ com @ bool ) @ wt )
= wt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Com_OWT_res) ).
thf(992,plain,
( ( ti @ ( fun @ com @ bool ) @ wt )
= wt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(61,axiom,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_finite) ).
thf(822,plain,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( skip
!= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_com_Osimps_I16_J) ).
thf(871,plain,
! [A: $i,B: $i] :
( skip
!= ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_Diff__Int) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ F ) @ E ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_subset__image__iff) ).
thf(2353,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ F ) @ E ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ F ) @ E ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_DiffD2) ).
thf(1885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(607,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fconj )
= fconj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
thf(2699,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fconj )
= fconj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
| ( ( ti @ ( fun @ A @ bool ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_subset__singletonD) ).
thf(2270,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( bot_bot @ ( fun @ A @ bool ) ) )
| ( ( ti @ ( fun @ A @ bool ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Int__Un__distrib2) ).
thf(1621,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_Un__Diff) ).
thf(1331,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_sup_sup @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( minus_minus @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(1944,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(111,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_le__supI2) ).
thf(1009,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ C ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(467,axiom,
distrib_lattice @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Odistrib__lattice) ).
thf(2206,plain,
distrib_lattice @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_Int__mono) ).
thf(2690,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ D ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( semilattice_inf_inf @ ( fun @ A @ bool ) ) @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(409,axiom,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( ti @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_inf__absorb1) ).
thf(2018,plain,
! [A: $i] :
( ( semilattice_inf @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_inf_inf @ A ) @ B ) @ C )
= ( ti @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ ( hAPP @ A @ B @ C @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_image__insert) ).
thf(775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ ( hAPP @ A @ B @ C @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_2027193591valids @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_hoare__sound) ).
thf(2351,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_2027193591valids @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( combc @ A @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ A @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ A @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ A ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ A ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fconj ) ) @ C ) ) ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( combb @ bool @ bool @ state ) @ fNot ) @ D ) ) ) @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ D ) @ E ) ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_LoopF) ).
thf(1069,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ bool ) @ ( hoare_279057269derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( hAPP @ ( hoare_1656922687triple @ A ) @ ( fun @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) @ ( insert @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_1656922687triple @ A ) ) ) @ ( hoare_246368825triple @ A ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( combc @ A @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ A @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ A @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ A ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ A @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ A ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fconj ) ) @ C ) ) ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( combb @ bool @ bool @ state ) @ fNot ) @ D ) ) ) @ ( hAPP @ com @ com @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ com @ com ) @ while @ D ) @ E ) ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_1656922687triple @ A ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( option @ A ) @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( option @ A ) @ B ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( option @ A ) @ B ) ) @ ( option_rec @ B @ A ) @ C ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ E ) )
= ( hAPP @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_option_Orecs_I2_J) ).
thf(1912,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( option @ A ) @ B @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( option @ A ) @ B ) @ ( hAPP @ B @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( option @ A ) @ B ) ) @ ( option_rec @ B @ A ) @ C ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ E ) )
= ( hAPP @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ ( hAPP @ B @ A @ C @ D ) )
= ( ti @ ( fun @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_fun__upd__triv) ).
thf(2177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ ( hAPP @ B @ A @ C @ D ) )
= ( ti @ ( fun @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(231,axiom,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ D ) @ B ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_sup__mono) ).
thf(1417,plain,
! [A: $i] :
( ( semilattice_sup @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ D ) @ B ) ) @ ( hAPP @ A @ A @ ( hAPP @ A @ ( fun @ A @ A ) @ ( semilattice_sup_sup @ A ) @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( hAPP @ B @ ( fun @ A @ B ) @ ( combk @ B @ A ) @ C ) @ D )
= ( ti @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(2106,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( hAPP @ B @ ( fun @ A @ B ) @ ( combk @ B @ A ) @ C ) @ D )
= ( ti @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(2087,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
= ( hAPP @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(10434,plain,
$false,
inference(cvc4,[status(thm)],[1322,1036,1501,1879,1168,2072,1559,628,1982,2559,2331,1950,1110,1686,645,892,2109,2131,1454,2412,846,2595,1850,1005,1882,2231,2381,2395,1808,1618,994,2099,1269,1533,1692,1173,2363,1200,2309,762,1596,1406,2104,2590,1401,741,1073,1544,2676,1041,861,1608,2607,1310,2035,1735,2448,814,1342,1354,1458,1999,797,2476,698,1746,1835,2046,2432,1441,1613,2010,1921,1386,1366,2516,1265,1887,1001,2723,973,1046,2400,1967,2531,2405,2654,1409,1709,1430,2039,1660,785,1871,2708,2217,917,1279,2703,2735,1985,2667,719,2562,2488,1462,1059,949,2571,817,1379,1398,2024,1778,2533,1232,1847,2169,2403,1087,1514,2301,1815,2237,756,2027,2090,1373,2451,1334,1136,1864,1828,1020,806,1183,905,2616,1465,1677,2540,687,634,2190,2483,866,1796,2137,1351,1433,849,2508,766,2618,2281,774,2371,2002,998,2242,1345,2392,1521,1651,1206,2204,678,2574,2118,2660,2000,1730,2646,925,1470,1915,2093,2296,2307,2083,2496,2705,2733,952,2277,1123,820,1666,1487,630,1824,2032,729,1274,2673,1723,910,1223,894,2601,2428,2249,778,1238,2015,1423,1920,625,852,665,1457,1624,830,1159,1079,1740,1106,2464,1938,2758,2628,2670,2313,1128,1634,2228,2112,710,742,2498,2115,1762,1804,1328,2631,1755,2268,989,2245,1936,1534,1794,1017,2692,1587,1683,1082,1361,1964,1292,2312,2080,2196,637,2613,1791,1016,1419,1889,1644,2649,970,2504,2598,1131,1932,2006,1799,1947,1715,1720,2140,1627,647,1263,2125,1099,1150,1478,2536,1297,2681,1451,738,2304,1530,1539,1266,2153,2387,1668,1974,1759,1393,2634,1991,792,633,1695,1071,2408,2221,2645,2546,2761,1712,1054,773,1996,2729,1764,1680,1698,2585,824,2570,2524,1727,1510,2275,2033,975,2727,732,2657,1752,1929,2514,875,1701,2716,1226,1007,694,1615,1784,843,1125,1428,2193,2326,2293,1271,787,2738,1865,2759,1090,2425,1258,2474,672,1139,1503,919,2557,804,2148,2319,1194,2361,900,1282,1117,1011,1524,2284,1492,2378,2197,2538,1853,2151,2642,2415,2493,880,649,1376,1439,863,1175,2180,811,631,858,1630,1821,1862,700,2410,1556,668,2461,1339,2610,2314,2625,799,1162,2593,1029,943,2252,2664,1177,1381,2329,1952,2075,1926,2725,868,883,1775,2101,1250,2207,1805,2069,2212,2171,1213,768,827,2051,1044,2550,1076,2239,675,1662,795,2471,1905,2037,1277,1134,749,2684,939,754,1049,2054,722,1018,2564,2567,1547,2298,712,1025,2192,2012,1605,1941,2678,2720,640,1961,1225,707,1230,1484,2747,2092,2165,1300,1186,1038,1869,840,1235,2337,1317,2044,1579,1738,1336,907,2219,1980,2128,1085,1658,2701,808,1934,2500,1766,1141,1702,2543,2711,1749,727,1802,1023,2279,1955,2145,1585,978,2511,1717,2030,1421,2479,1459,1180,1553,1817,2215,759,1289,771,1108,2458,627,1918,1649,1157,2078,1844,903,2347,1654,1412,1781,1216,2743,1448,2490,2187,1390,1575,1590,1646,1326,1639,1903,2554,1062,1481,946,652,2004,786,1253,699,963,2167,2273,2174,2389,1689,2384,2041,1294,1444,1994,1045,716,1706,1193,1348,2287,2517,1725,1957,2587,1395,1593,2951,1876,790,1757,735,1642,752,833,2719,854,1303,1527,1148,1436,1363,2334,2746,897,1056,2366,2404,2714,1065,955,2651,2201,801,1989,1033,1197,960,1473,2340,1165,2021,2063,1610,1742,2549,2502,1977,1152,1384,1582,992,822,871,1120,624,2353,1885,2699,2270,1621,1331,1944,1009,2206,2690,2018,775,2351,1069,1912,2177,1417,2106,2087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW474+6 : TPTP v8.1.2. Released v5.3.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n003.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 22:12:16 EDT 2023
% 0.22/0.36 % CPUTime :
% 0.85/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.89/1.11 % [INFO] Parsing done (271ms).
% 1.89/1.11 % [INFO] Running in sequential loop mode.
% 2.61/1.32 % [INFO] eprover registered as external prover.
% 2.61/1.32 % [INFO] cvc4 registered as external prover.
% 2.61/1.32 % [INFO] Scanning for conjecture ...
% 3.22/1.50 % [INFO] Found a conjecture and 621 axioms. Running axiom selection ...
% 4.03/1.71 % [INFO] Axiom selection finished. Selected 621 axioms (removed 0 axioms).
% 5.76/2.42 % [INFO] Problem is first-order (TPTP FOF).
% 5.76/2.46 % [INFO] Type checking passed.
% 5.76/2.46 % [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 ...
% 107.60/30.03 % External prover 'cvc4' found a proof!
% 107.60/30.03 % [INFO] Killing All external provers ...
% 107.60/30.03 % Time passed: 29516ms (effective reasoning time: 28912ms)
% 107.60/30.03 % 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)>
% 107.60/30.03 % Axioms used in derivation (621): fact_252_com_Osimps_I49_J, fact_145_xt1_I6_J, arity_HOL_Obool___Finite__Set_Ofinite, fact_93_imageE, arity_HOL_Obool___Orderings_Oorder, fact_208_sup__idem, fact_362_sup__inf__distrib2, help_fimplies_2_1_U, fact_154_order__eq__refl, fact_364_inf__bot__left, fact_216_le__supI2, tsy_c_fconj_res, fact_173_conseq2, fact_63_doubleton__eq__iff, fact_315_Int__left__commute, fact_215_sup__absorb2, fact_327_Int__Un__distrib2, fact_8_finite__Collect__subsets, fact_56_image__iff, fact_339_Int__insert__right__if0, fact_163_le__funE, fact_331_Int__greatest, fact_365_inf_Oidem, fact_343_inf__sup__ord_I1_J, fact_15_image__constant, fact_303_IntI, tsy_c_Orderings_Obot__class_Obot_res, fact_127_Un__empty__right, arity_HOL_Obool___Orderings_Oord, fact_206_inf__sup__aci_I5_J, tsy_v_y_res, tsy_c_Fun_Ooverride__on_res, help_COMBS_1_1_U, fact_286_evalc_OWhileFalse, fact_27_Collect__empty__eq, fact_23_equalityI, fact_149_xt1_I4_J, fact_172_conseq1, fact_353_le__infI, fact_255_com_Osimps_I12_J, fact_251_com_Osimps_I17_J, fact_88_Collect__conv__if2, fact_430_Diff__idemp, fact_48_set__rev__mp, fact_146_xt1_I5_J, fact_190_elem__set, tsy_c_Com_Ocom_OBODY_res, fact_28_empty__iff, arity_HOL_Obool___Orderings_Opreorder, fact_271_folding__image__simple__idem_Oin__idem, tsy_c_COMBK_res, help_fconj_3_1_U, fact_24_subsetD, arity_fun___Orderings_Obot, fact_465_fun__upd__upd, fact_211_sup__mono, fact_424_insert__Diff__if, fact_62_singletonE, fact_317_Int__assoc, fact_192_sup__fun__def, fact_38_insert__code, fact_261_folding__one_Osingleton, fact_119_Un__assoc, tsy_c_Option_Ooption_ONone_res, fact_350_le__infI2, fact_371_inf_Oleft__idem, fact_455_comp__fun__idem__insert, fact_196_sup__assoc, fact_34_finite, fact_55_imageI, fact_44_insertI1, fact_59_image__ident, fact_460_map__upd__eqD1, fact_495_option_Osimps_I2_J, tsy_c_fimplies_res, fact_464_fun__upd__idem__iff, fact_209_sup_Oidem, fact_357_inf__sup__absorb, fact_50_equalityD2, fact_1_asm, fact_436_fun__diff__def, fact_168_BodyN, fact_468_fun__upd__twist, tsy_c_member_res, fact_9_finite__imageI, fact_281_MGT__alternI, tsy_c_Lattices_Osemilattice__sup__class_Osup_res, fact_110_weak__Body, fact_139_Un__upper1, arity_fun___Orderings_Oord, fact_164_le__funD, fact_398_DiffI, fact_332_Int__absorb1, tsy_c_Lattices_Osemilattice__inf__class_Oinf_res, help_COMBI_1_1_U, conj_3, fact_41_insert__absorb2, fact_359_inf__sup__distrib1, fact_96_subsetI, fact_319_IntD2, tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__valids_res, tsy_c_Com_OWT__bodies_res, fact_489_inj__Some, fact_92_WT__bodiesD, fact_160_le__bot, fact_138_Un__upper2, fact_3_thin, fact_256_com_Osimps_I13_J, fact_257_folding__one_Oinsert, arity_HOL_Obool___Groups_Ominus, fact_335_Int__lower1, fact_79_subset__insert, fact_306_inf1E, fact_418_Un__Diff__Int, fact_401_Diff__Int__distrib, tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__derivs_res, fact_277_mk__disjoint__insert, fact_179_rev__predicate1D, fact_417_Diff__Un, fact_202_sup__left__idem, fact_0_empty, arity_HOL_Obool___Lattices_Odistrib__lattice, fact_442_finite__empty__induct, fact_330_Int__mono, tsy_c_Map_Odom_res, fact_403_Diff__Int__distrib2, fact_16_insert__dom, fact_428_set__diff__eq, fact_158_constant, fact_264_theI_H, fact_104_domD, fact_348_le__inf__iff, fact_95_WTs__elim__cases_I7_J, fact_188_triple_Orecs, fact_334_Int__lower2, fact_230_folding__one__idem_Oinsert__idem, fact_234_com_Osimps_I18_J, fact_184_sup__Un__eq, fact_345_inf__sup__ord_I2_J, fact_177_hoare__sound, tsy_c_Fun_Oinj__on_res, fact_366_inf__idem, tsy_c_hAPP_res, fact_108_nonempty__iff, fact_384_Un__Int__assoc__eq, fact_372_inf__sup__aci_I4_J, fact_169_finite__pointwise, fact_298_ord__le__eq__subst, fact_46_subset__trans, tsy_c_Set_OCollect_res, fact_328_Un__Int__distrib, fact_250_com_Osimps_I16_J, fact_61_singleton__inject, fact_342_Int__insert__right, fact_313_Int__commute, fact_305_inf1I, fact_449_override__on__def, fact_236_folding__one__idem_Oin__idem, fact_259_the__eq__trivial, arity_fun___Lattices_Olattice, fact_479_inj__on__image__set__diff, fact_274_image__cong, fact_42_insert__Collect, fact_20_emptyE, fact_269_folding__image__simple__idem_Osubset__idem, tsy_c_hAPP_arg1, fact_396_folding__one_Oremove, fact_370_inf__commute, fact_197_inf__sup__aci_I6_J, fact_473_dom__eq__singleton__conv, fact_381_distrib__sup__le, fact_297_xt1_I16_J, fact_112_UnE, fact_142_insert__is__Un, fact_390_folding__image__simple_Ounion__disjoint, fact_214_sup__absorb1, fact_229_hoare__derivs_OSkip, fact_57_finite__Collect__disjI, tsy_c_Orderings_Oord__class_Oless__eq_res, arity_HOL_Obool___Lattices_Obounded__lattice__bot, help_fNot_2_1_U, fact_186_le__funI, fact_391_folding__image__simple_Ounion__inter, fact_54_rev__image__eqI, fact_275_Collect__mono, fact_376_inf__left__commute, fact_282_MGT__def, tsy_c_COMBC_res, fact_10_empty__subsetI, fact_496_option_Orecs_I1_J, fact_136_Un__absorb1, tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple_res, fact_105_the__elem__eq, arity_fun___Lattices_Odistrib__lattice, fact_90_singleton__conv2, fact_326_Un__Int__distrib2, help_fNot_1_1_U, fact_369_inf__sup__aci_I1_J, fact_486_inj__on__def, fact_380_inf__apply, fact_45_equalityE, fact_414_Diff__partition, tsy_c_COMBS_res, fact_379_inf__assoc, fact_267_triple_Oexhaust, fact_416_Diff__Int, fact_159_Body1, fact_382_distrib__inf__le, fact_238_LoopF, fact_84_image__mono, fact_80_insert__subset, fact_301_folding__one_Ounion__inter, fact_459_image__map__upd, fact_133_Un__mono, fact_378_inf__sup__aci_I2_J, fact_290_com__det, fact_205_sup__commute, fact_150_ord__le__eq__trans, fact_429_Diff__iff, fact_492_not__None__eq, help_fFalse_1_1_T, fact_258_If__def, fact_312_Int__def, fact_233_com_Osimps_I19_J, fact_135_Un__absorb2, fact_29_empty__Collect__eq, fact_323_inf1D1, fact_22_insertE, tsy_c_fFalse_res, tsy_c_Com_Ocom_OSKIP_res, fact_183_pred__subset__eq, fact_25_image__eqI, tsy_c_hBOOL_arg1, fact_333_Int__absorb2, fact_117_ball__Un, fact_134_Un__least, fact_289_evalc_OSkip, fact_440_folding__image__simple_Oremove, fact_470_fun__upd__idem, fact_321_Int__Collect, fact_198_sup_Oassoc, tsy_c_Com_Ocom_OSemi_res, fact_21_insertCI, fact_406_Diff__insert__absorb, fact_167_bot__fun__def, fact_340_insert__inter__insert, fact_437_minus__apply, fact_132_Un__insert__right, fact_221_inf__sup__ord_I4_J, fact_432_DiffD2, fact_121_Un__left__commute, fact_425_double__diff, fact_170_escape, fact_446_diff__eq__diff__eq, tsy_c_Com_OWT_res, fact_346_inf__le2, fact_475_empty__upd__none, fact_101_pigeonhole__infinite, conj_2, fact_201_sup_Oleft__commute, fact_85_subset__image__iff, fact_128_Un__empty__left, fact_355_inf__mono, tsy_c_Finite__Set_Ocomp__fun__idem_res, fact_457_fold__graph_H_Ointros_I2_J, fact_276_predicate1I, tsy_c_Finite__Set_Ofinite_res, fact_498_finite__imageD, fact_456_fun__upd__image, fact_453_comp__fun__idem__inf, fact_294_xt2, help_COMBB_1_1_U, fact_199_sup__left__commute, fact_397_folding__one_Oinsert__remove, help_If_1_1_T, fact_329_Int__Un__distrib, arity_HOL_Obool___Lattices_Osemilattice__inf, arity_fun___Orderings_Oorder, tsy_c_Set_Othe__elem_res, fact_476_map__upd__nonempty, help_fdisj_1_1_U, fact_383_image__Int__subset, fact_120_Un__iff, fact_307_finite__Int, fact_266_theI, fact_156_linorder__linear, fact_175_sup1E, fact_148_order__antisym, fact_472_inj__on__Un, fact_114_triple_Oinject, fact_375_inf__sup__aci_I3_J, fact_147_order__trans, fact_116_UnI1, fact_182_sup1I1, tsy_c_hAPP_arg2, fact_491_domIff, arity_fun___Orderings_Opreorder, fact_431_DiffD1, fact_71_empty__is__image, fact_451_comp__fun__idem__remove, fact_249_While, help_fconj_2_1_U, tsy_c_Fun_Ofun__upd_res, tsy_c_Finite__Set_Ofolding__one__idem_res, tsy_c_COMBB_res, tsy_c_fNot_res, tsy_c_HOL_OThe_res, tsy_c_Set_Oimage_res, fact_447_override__on__apply__in, help_fAll_1_1_U, fact_118_bex__Un, fact_12_finite_OemptyI, fact_144_linorder__le__cases, fact_471_fun__upd__def, tsy_c_Hoare__Mirabelle__nrugjuseim_OMGT_res, fact_474_inj__on__empty, fact_185_conseq12, fact_262_the__equality, arity_fun___Lattices_Osemilattice__inf, fact_49_in__mono, fact_361_inf__sup__distrib2, fact_325_Un__Int__crazy, fact_310_Int__empty__left, fact_102_com_Osimps_I6_J, fact_349_le__infI1, fact_488_subset__inj__on, fact_33_finite__code, fact_494_option_Osimps_I3_J, fact_228_folding__one__idem_Osubset__idem, fact_194_single__stateE, fact_435_Un__Diff__cancel, fact_415_Diff__subset__conv, fact_130_finite__Un, fact_452_comp__fun__idem_Ofun__left__idem, fact_337_Int__insert__right__if1, fact_300_ord__eq__le__subst, fact_292_evalc__WHILE__case, fact_485_inj__on__contraD, fact_247_com_Osimps_I59_J, fact_433_Un__Diff, tsy_c_HOL_Oundefined_res, fact_244_com_Osimps_I47_J, fact_181_sup1I2, tsy_c_Finite__Set_Ofolding__one_res, fact_299_order__subst2, fact_484_inj__on__iff, fact_98_finite__dom__body, fact_450_flat__lub__def, fact_180_predicate1D, fact_5_hoare__derivs_Oinsert, fact_367_inf__fun__def, fact_83_image__insert, help_ti_idem, fact_444_override__on__emptyset, fact_203_inf__sup__aci_I8_J, help_fequal_1_1_T, fact_103_MGT__Body, fact_232_folding__one__idem_Oidem, arity_HOL_Obool___Lattices_Osemilattice__sup, fact_360_sup__inf__distrib1, fact_111_UnCI, fact_352_inf__absorb2, fact_311_Int__absorb, fact_458_fun__upd__triv, tsy_c_fequal_res, fact_124_Un__def, fact_482_inj__on__Un__image__eq__iff, fact_246_com_Osimps_I5_J, fact_204_sup_Oleft__idem, fact_81_subset__insertI, arity_fun___Finite__Set_Ofinite, fact_97_finite__subset__image, tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__case_res, fact_43_insert__compr, fact_368_inf_Ocommute, fact_6_derivs__insertD, fact_405_insert__Diff, fact_161_bot__unique, fact_377_inf_Oassoc, fact_76_mem__def, fact_254_WT_OSemi, fact_426_Diff__mono, fact_295_xt1_I15_J, fact_422_finite__Diff2, fact_291_evalc__elim__cases_I4_J, fact_462_map__upd__Some__unfold, fact_389_distrib__imp2, fact_490_dom__def, fact_68_subset__empty, fact_51_equalityD1, fact_314_Int__left__absorb, fact_318_IntD1, fact_155_order__eq__iff, fact_191_ospec, fact_70_image__empty, fact_237_folding__one__idem_Ohom__commute, fact_374_inf_Oleft__commute, fact_481_inj__on__image__Int, fact_94_finite__subset__induct, fact_248_com_Osimps_I58_J, help_If_3_1_T, fact_395_folding__image__simple_Oneutral, help_fdisj_2_1_U, tsy_c_Set_Oinsert_res, fact_86_domI, tsy_v_pn_res, arity_HOL_Obool___Lattices_Obounded__lattice, fact_195_state__not__singleton__def, fact_284_evalc__elim__cases_I6_J, fact_419_Diff__cancel, fact_13_finite__Collect__conjI, fact_129_finite__UnI, tsy_c_Option_Oset_res, help_If_2_1_T, help_COMBK_1_1_U, fact_74_insert__mono, fact_223_inf__sup__ord_I3_J, fact_373_inf__left__idem, fact_420_Diff__empty, tsy_c_Com_Obody_res, fact_338_Int__insert__left__if0, fact_113_Collect__disj__eq, fact_47_set__mp, fact_438_subset__insert__iff, fact_351_inf__absorb1, fact_316_Int__iff, fact_466_fun__upd__same, fact_336_Int__insert__left__if1, fact_411_Diff__disjoint, fact_171_Body__sound__lemma, fact_220_sup__ge2, fact_193_sup__apply, fact_58_insert__compr__raw, fact_477_inj__on__fun__updI, fact_11_finite_OinsertI, fact_279_equals0I, fact_213_le__supI, fact_392_folding__image__simple_Oempty, conj_6, fact_35_insert__absorb, fact_394_folding__image__simple_Ounion__inter__neutral, fact_174_MGF__complete, fact_151_xt1_I3_J, fact_356_le__infE, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, fact_200_inf__sup__aci_I7_J, fact_165_le__fun__def, conj_1, fact_413_image__diff__subset, fact_131_Un__insert__left, fact_296_order__subst1, help_fequal_2_1_T, fact_387_Int__Collect__mono, fact_100_finite_Osimps, fact_439_diff__single__insert, fact_445_diff__eq__diff__less__eq, fact_423_insert__Diff1, fact_178_bot__empty__eq, fact_344_inf__le1, fact_31_all__not__in__conv, fact_421_empty__Diff, fact_72_finite__subset, fact_36_insertI2, fact_89_singleton__conv, fact_270_folding__image__simple__idem_Oidem, fact_143_hoare__derivs_OBody, fact_125_Un__absorb, fact_242_WTs__elim__cases_I4_J, fact_162_bot__least, fact_99_finite__induct, help_fconj_1_1_U, fact_427_Diff__subset, tsy_c_Hoare__Mirabelle__nrugjuseim_Ostate__not__singleton_res, help_fdisj_3_1_U, tsy_c_Option_Othe_res, fact_231_finite__ne__induct, fact_140_image__Un, fact_212_sup__least, tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__rec_res, fact_263_folding__one_Oclosed, fact_469_fun__upd__other, fact_210_le__supE, fact_137_subset__Un__eq, fact_320_Collect__conj__eq, fact_187_triple_Osimps_I2_J, fact_225_sup__bot__right, fact_157_option_Oinject, fact_224_sup__eq__bot__iff, fact_272_folding__image__simple__idem_Oinsert__idem, arity_Option_Ooption___Finite__Set_Ofinite, fact_265_the1__equality, fact_278_Set_Oset__insert, help_fFalse_1_1_U, fact_288_evalc_OSemi, tsy_c_Com_Ocom_OWhile_res, fact_480_inj__on__Int, fact_73_rev__finite__subset, fact_67_finite__insert, fact_487_inj__on__id2, fact_497_dom__eq__empty__conv, fact_107_order__refl, fact_240_the__elem__def, fact_253_com_Osimps_I48_J, fact_18_subset__singletonD, fact_243_com_Osimps_I46_J, fact_245_com_Osimps_I3_J, fact_91_MGF__lemma1, fact_388_distrib__imp1, fact_60_image__image, arity_HOL_Obool___Lattices_Olattice, fact_434_Un__Diff__cancel2, fact_19_MGF, fact_109_the_Osimps, fact_64_singleton__iff, fact_82_insert__image, fact_304_IntE, fact_280_MGT__alternD, fact_189_Option_Oset_Osimps_I2_J, fact_52_set__eq__subset, fact_322_inf__Int__eq, fact_2_weaken, fact_287_evalc_OWhileTrue, fact_402_Int__Diff, fact_461_map__upd__triv, fact_77_Collect__def, fact_404_Diff__Int2, fact_87_Collect__conv__if, fact_17_finite__surj, fact_106_image__subsetI, fact_66_empty__not__insert, fact_37_insert__ident, tsy_c_Finite__Set_Ofolding__image__simple_res, fact_324_inf1D2, fact_386_dom__if, conj_4, fact_283_evalc_OBody, fact_30_ex__in__conv, fact_4_cut, fact_363_inf__bot__right, fact_14_image__constant__conv, fact_400_finite__Diff, fact_65_insert__not__empty, tsy_c_COMBI_res, fact_26_equals0D, fact_385_if__image__distrib, arity_fun___Lattices_Osemilattice__sup, fact_40_insert__commute, tsy_c_Groups_Ominus__class_Ominus_res, arity_fun___Lattices_Obounded__lattice__bot, fact_302_folding__one_Ounion__disjoint, fact_407_insert__Diff__single, tsy_c_Option_Ooption_Ooption__rec_res, fact_153_order__antisym__conv, fact_7_MGT__BodyN, fact_75_ext, fact_478_inj__on__diff, fact_152_ord__eq__le__trans, fact_218_le__sup__iff, fact_308_disjoint__iff__not__equal, fact_219_le__iff__sup, help_fimplies_1_1_U, fact_227_folding__one__idem_Ounion__idem, tsy_c_Partial__Function_Oflat__lub_res, fact_122_Un__left__absorb, fact_217_le__supI1, fact_293_xt3, fact_268_folding__image__simple__idem_Ounion__idem, tsy_v_Fa_res, fact_39_insert__iff, fact_241_WTs__elim__cases_I6_J, tsy_c_Option_Ooption_OSome_res, fact_467_fun__upd__apply, conj_5, fact_32_empty__def, help_fimplies_3_1_U, fact_260_the__sym__eq__trivial, conj_0, fact_285_evalc__elim__cases_I1_J, fact_126_Un__empty, arity_fun___Lattices_Obounded__lattice, fact_207_sup_Ocommute, fact_448_override__on__apply__notin, fact_309_Int__empty__right, tsy_c_Finite__Set_Ofolding__image__simple__idem_res, fact_412_Diff__triv, fact_443_dom__override__on, fact_69_image__is__empty, fact_273_option_Orecs_I2_J, fact_408_Diff__insert2, fact_463_fold__graph_H_Ointros_I1_J, fact_441_folding__image__simple_Oinsert__remove, fact_341_Int__insert__left, tsy_c_fdisj_res, fact_176_sup1CI, fact_358_sup__inf__absorb, fact_239_Comp, fact_454_comp__fun__idem__sup, fact_226_sup__bot__left, tsy_c_fAll_res, tsy_c_If_res, fact_141_insert__def, fact_78_subset__insertI2, arity_fun___Groups_Ominus, fact_235_WT_OSkip, tsy_c_Natural_Oevalc_res, fact_393_folding__image__simple_Oinsert, fact_410_finite__Diff__insert, fact_53_subset__refl, fact_123_Un__commute, tsy_c_Nitpick_Ofold__graph_H_res, fact_347_le__iff__inf, tsy_c_fTrue_res, fact_115_UnI2, fact_493_not__Some__eq, fact_409_Diff__insert, fact_222_sup__ge1, fact_399_DiffE, fact_166_bot__apply, fact_354_inf__greatest, fact_483_inj__onD
% 107.60/30.03 % No. of inferences in proof: 1283
% 107.60/30.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 29516 ms resp. 28912 ms w/o parsing
% 109.18/30.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 109.18/30.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------