TSTP Solution File: SWW470+5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW470+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 12:24:01 EDT 2023
% Result : Theorem 90.97s 39.96s
% Output : Refutation 91.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 208
% Syntax : Number of formulae : 373 ( 152 unt; 45 typ; 0 def)
% Number of atoms : 748 ( 318 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 18356 ( 122 ~; 51 |; 82 &;17814 @)
% ( 21 <=>; 266 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 17 con; 0-4 aty)
% Number of variables : 1016 ( 0 ^; 969 !; 47 ?;1016 :)
% 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_509422987triple_type,type,
hoare_509422987triple: $i > $i ).
thf(x_a_type,type,
x_a: $i ).
thf(bool_type,type,
bool: $i ).
thf(hoare_122391849derivs_type,type,
hoare_122391849derivs: $i > $i ).
thf(g_type,type,
g: $i ).
thf(insert_type,type,
insert: $i > $i ).
thf(state_type,type,
state: $i ).
thf(com_type,type,
com: $i ).
thf(hoare_1008221573triple_type,type,
hoare_1008221573triple: $i > $i ).
thf(combk_type,type,
combk: $i > $i > $i ).
thf(fFalse_type,type,
fFalse: $i ).
thf(c_type,type,
c: $i ).
thf(combc_type,type,
combc: $i > $i > $i > $i ).
thf(combb_type,type,
combb: $i > $i > $i > $i ).
thf(combs_type,type,
combs: $i > $i > $i > $i ).
thf(fconj_type,type,
fconj: $i ).
thf(p_type,type,
p: $i ).
thf(fNot_type,type,
fNot: $i ).
thf(b_type,type,
b: $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(finite_finite_type,type,
finite_finite: $i > $o ).
thf(finite_finite_1_type,type,
finite_finite_1: $i > $i ).
thf(finite_fold1_type,type,
finite_fold1: $i > $i ).
thf(fdisj_type,type,
fdisj: $i ).
thf(finite_fold1Set_type,type,
finite_fold1Set: $i > $i ).
thf(collect_type,type,
collect: $i > $i ).
thf(semi_type,type,
semi: $i ).
thf(fequal_type,type,
fequal: $i > $i ).
thf(finite_fold_graph_type,type,
finite_fold_graph: $i > $i > $i ).
thf(skip_type,type,
skip: $i ).
thf(the_type,type,
the: $i > $i ).
thf(fimplies_type,type,
fimplies: $i ).
thf(hoare_885240885e_case_type,type,
hoare_885240885e_case: $i > $i > $i ).
thf(finite_folding_one_type,type,
finite_folding_one: $i > $i ).
thf(the_elem_type,type,
the_elem: $i > $i ).
thf(bot_type,type,
bot: $i > $o ).
thf(finite2073411215e_idem_type,type,
finite2073411215e_idem: $i > $i ).
thf(hoare_728318379le_rec_type,type,
hoare_728318379le_rec: $i > $i > $i ).
thf(fTrue_type,type,
fTrue: $i ).
thf(51,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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ G ) @ 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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ F ) @ G ) ) @ ( hAPP @ A @ A @ ( hAPP @ B @ ( fun @ A @ A ) @ C @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_fold__graph_OinsertI) ).
thf(350,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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ G ) @ 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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ F ) @ G ) ) @ ( hAPP @ A @ A @ ( hAPP @ B @ ( fun @ A @ A ) @ C @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(122,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_1 @ 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/sandbox/benchmark/theBenchmark.p',fact_96_folding__one__idem_Oinsert__idem) ).
thf(613,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_1 @ 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)],[122]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_40_empty__not__insert) ).
thf(234,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)],[20]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__insert) ).
thf(555,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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)],[105]) ).
thf(52,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) ) @ ( hoare_1008221573triple @ A ) )
= ( hoare_1008221573triple @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple_res) ).
thf(352,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) ) @ ( hoare_1008221573triple @ A ) )
= ( hoare_1008221573triple @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
thf(408,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)],[64]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ 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/sandbox/benchmark/theBenchmark.p',fact_91_finite__induct) ).
thf(762,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ 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)],[164]) ).
thf(137,axiom,
( ( ti @ com @ skip )
= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Com_Ocom_OSKIP_res) ).
thf(683,plain,
( ( ti @ com @ skip )
= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one_res) ).
thf(308,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)],[41]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',fact_57_equals0I) ).
thf(741,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)],[157]) ).
thf(13,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
thf(202,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( bot @ B )
=> ( bot @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(597,plain,
! [A: $i,B: $i] :
( ( bot @ B )
=> ( bot @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(59,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 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_theI) ).
thf(385,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 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(98,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_1 @ 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/sandbox/benchmark/theBenchmark.p',fact_88_folding__one_Oclosed) ).
thf(533,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_1 @ 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)],[98]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(500,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)],[89]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) @ E ) )
=> ~ ! [F: $i,G: $i] :
( ( ( 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 ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold_graph @ A @ A ) @ B ) @ F ) @ G ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insert__fold1SetE) ).
thf(320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) @ E ) )
=> ~ ! [F: $i,G: $i] :
( ( ( 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 ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold_graph @ A @ A ) @ B ) @ F ) @ G ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_18_Collect__empty__eq) ).
thf(257,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)],[26]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',fact_66_bot__empty__eq) ).
thf(389,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)],[60]) ).
thf(151,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 ) )
=> ? [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ H ) @ D ) @ I ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) )
& ! [J: $i] :
( ! [K: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ H @ K ) @ G ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ I @ K ) @ J ) ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ B @ F ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ D ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_conseq) ).
thf(724,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 ) )
=> ? [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ H ) @ D ) @ I ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) )
& ! [J: $i] :
( ! [K: $i] :
( ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ H @ K ) @ G ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ I @ K ) @ J ) ) )
=> ( hBOOL @ ( hAPP @ state @ bool @ ( hAPP @ A @ ( fun @ state @ bool ) @ B @ F ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ D ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one__idem_res) ).
thf(570,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)],[108]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
thf(619,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)],[124]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ C ) @ skip ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_hoare__derivs_OSkip) ).
thf(542,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ C ) @ skip ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(421,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)],[69]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',fact_21_ex__in__conv) ).
thf(606,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)],[121]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( finite_finite @ B )
& ( finite_finite @ A ) )
=> ( finite_finite @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(284,plain,
! [A: $i,B: $i] :
( ( ( finite_finite @ B )
& ( finite_finite @ A ) )
=> ( finite_finite @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(416,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)],[67]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(325,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)],[45]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(289,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)],[35]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(591,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)],[115]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(376,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',fact_15_Collect__conv__if) ).
thf(238,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)],[21]) ).
thf(50,axiom,
( ( ti @ bool @ fFalse )
= fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
thf(348,plain,
( ( ti @ bool @ fFalse )
= fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(84,axiom,
( ( ti @ ( fun @ bool @ bool ) @ fNot )
= fNot ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
thf(480,plain,
( ( ti @ ( fun @ bool @ bool ) @ fNot )
= fNot ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) @ D ) )
=> ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_fold1Set__nonempty) ).
thf(211,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) @ D ) )
=> ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',fact_37_doubleton__eq__iff) ).
thf(646,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)],[131]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_25_insertI2) ).
thf(602,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)],[119]) ).
thf(32,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 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_theI_H) ).
thf(280,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 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(154,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_finite_OemptyI) ).
thf(734,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(75,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fconj )
= fconj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
thf(453,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fconj )
= fconj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(65,axiom,
( ( ti @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ p )
= p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_P_res) ).
thf(411,plain,
( ( ti @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ p )
= p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',fact_30_insert__absorb2) ).
thf(248,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)],[23]) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(678,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)],[135]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(270,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)],[29]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( skip
!= ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_com_Osimps_I12_J) ).
thf(381,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)],[58]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_509422987triple @ A ) @ B ) ) @ ( hoare_885240885e_case @ A @ B ) )
= ( hoare_885240885e_case @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__case_res) ).
thf(297,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_509422987triple @ A ) @ B ) ) @ ( hoare_885240885e_case @ A @ B ) )
= ( hoare_885240885e_case @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) @ E ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_empty__fold__graphE) ).
thf(424,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) @ E ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1,conjecture,
hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ x_a ) @ g ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ x_a ) @ ( fun @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ x_a ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) @ ( hAPP @ com @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) ) ) @ ( hoare_1008221573triple @ x_a ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( combk @ ( fun @ state @ bool ) @ x_a ) @ ( hAPP @ bool @ ( fun @ state @ bool ) @ ( combk @ bool @ state ) @ fFalse ) ) ) @ c ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) ) @ ( combc @ x_a @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ x_a ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ x_a ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fconj ) ) @ p ) ) ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( combb @ bool @ bool @ state ) @ fNot ) @ b ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ x_a ) @ g ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ x_a ) @ ( fun @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ x_a ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) @ ( hAPP @ com @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) ) ) @ ( hoare_1008221573triple @ x_a ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( combk @ ( fun @ state @ bool ) @ x_a ) @ ( hAPP @ bool @ ( fun @ state @ bool ) @ ( combk @ bool @ state ) @ fFalse ) ) ) @ c ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) ) @ ( combc @ x_a @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ x_a ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ x_a ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fconj ) ) @ p ) ) ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( combb @ bool @ bool @ state ) @ fNot ) @ b ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(165,plain,
~ ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ x_a ) @ g ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ x_a ) @ ( fun @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ x_a ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) @ ( hAPP @ com @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ x_a ) ) ) @ ( hoare_1008221573triple @ x_a ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( combk @ ( fun @ state @ bool ) @ x_a ) @ ( hAPP @ bool @ ( fun @ state @ bool ) @ ( combk @ bool @ state ) @ fFalse ) ) ) @ c ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ x_a @ ( fun @ state @ bool ) ) ) @ ( combc @ x_a @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ x_a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ x_a ) @ ( combs @ state @ bool @ bool ) ) @ ( hAPP @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ x_a @ ( fun @ state @ bool ) ) @ ( fun @ x_a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ x_a ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fconj ) ) @ p ) ) ) @ ( hAPP @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( combb @ bool @ bool @ state ) @ fNot ) @ b ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) ) @ ( finite_fold1 @ A ) )
= ( finite_fold1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofold1_res) ).
thf(192,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) ) @ ( finite_fold1 @ A ) )
= ( finite_fold1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',fact_19_empty__iff) ).
thf(693,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)],[140]) ).
thf(81,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( the_elem @ A ) )
= ( the_elem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Othe__elem_res) ).
thf(467,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( the_elem @ A ) )
= ( the_elem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(86,axiom,
( ( ti @ ( fun @ state @ bool ) @ b )
= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_b_res) ).
thf(484,plain,
( ( ti @ ( fun @ state @ bool ) @ b )
= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cut) ).
thf(197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hoare_509422987triple @ A ) @ B @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_509422987triple @ A ) @ B ) @ ( hoare_885240885e_case @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ 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/sandbox/benchmark/theBenchmark.p',fact_42_triple_Osimps_I2_J) ).
thf(522,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hoare_509422987triple @ A ) @ B @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_509422987triple @ A ) @ B ) @ ( hoare_885240885e_case @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ 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)],[94]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(461,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)],[79]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(757,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)],[162]) ).
thf(145,axiom,
finite_finite @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(710,plain,
finite_finite @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(224,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)],[18]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( bot @ B )
=> ! [C: $i] :
( ( hAPP @ A @ B @ ( bot_bot @ ( fun @ A @ B ) ) @ C )
= ( bot_bot @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_bot__fun__def) ).
thf(519,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)],[93]) ).
thf(4,axiom,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(169,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(125,axiom,
( ( ti @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ g )
= g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_G_res) ).
thf(622,plain,
( ( ti @ ( fun @ ( hoare_509422987triple @ x_a ) @ bool ) @ g )
= g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_elem @ A ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ 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/sandbox/benchmark/theBenchmark.p',fact_51_the__elem__def) ).
thf(738,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the_elem @ A ) @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ 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)],[156]) ).
thf(77,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fimplies )
= fimplies ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
thf(457,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fimplies )
= fimplies ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_509422987triple @ A ) @ B ) ) @ ( hoare_728318379le_rec @ A @ B ) )
= ( hoare_728318379le_rec @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rec_res) ).
thf(721,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_509422987triple @ A ) @ B ) ) @ ( hoare_728318379le_rec @ A @ B ) )
= ( hoare_728318379le_rec @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( finite_fold1 @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_fold1__def) ).
thf(503,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( finite_fold1 @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ D )
=> ( ( ti @ A @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ 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 @ 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/sandbox/benchmark/theBenchmark.p',fact_56_If__def) ).
thf(633,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ D )
=> ( ( ti @ A @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ 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 @ 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)],[128]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',fact_39_insert__not__empty) ).
thf(311,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)],[42]) ).
thf(97,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(530,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(132,axiom,
! [A: $i] :
( ( finite_finite @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_finite__code) ).
thf(662,plain,
! [A: $i] :
( ( finite_finite @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ F )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ C ) @ D ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ 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_509422987triple @ A ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_constant) ).
thf(718,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ F )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ C ) @ D ) @ E ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ 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_509422987triple @ A ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_33_insertI1) ).
thf(430,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)],[72]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( finite_fold1 @ 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 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_fold1__singleton) ).
thf(264,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( finite_fold1 @ 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 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(745,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)],[158]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(573,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)],[109]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite_Osimps) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ 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_1 @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
~ ( hBOOL @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(176,plain,
~ ( hBOOL @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',fact_35_singleton__inject) ).
thf(286,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)],[34]) ).
thf(146,axiom,
bot @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(711,plain,
bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(14,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
= ( collect @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
thf(204,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
= ( collect @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ B @ A ) ) @ ( combk @ A @ B ) )
= ( combk @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).
thf(413,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)],[66]) ).
thf(111,axiom,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(579,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',fact_32_insert__compr) ).
thf(291,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)],[36]) ).
thf(120,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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_fold__graph_OemptyI) ).
thf(604,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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ ( bot_bot @ ( fun @ B @ bool ) ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite_1 @ B ) @ E ) )
=> ? [F: $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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ E ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_finite__imp__fold__graph) ).
thf(406,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite_1 @ B ) @ E ) )
=> ? [F: $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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ E ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',fact_10_insertCI) ).
thf(172,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)],[5]) ).
thf(155,axiom,
( ( ti @ com @ c )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_c_res) ).
thf(736,plain,
( ( ti @ com @ c )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_17_equals0D) ).
thf(567,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)],[107]) ).
thf(22,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold1Set @ A ) )
= ( finite_fold1Set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofold1Set_res) ).
thf(245,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold1Set @ A ) )
= ( finite_fold1Set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
thf(616,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)],[123]) ).
thf(118,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_1 @ A ) @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ D @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( finite_fold1 @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_folding__one_Oeq__fold) ).
thf(599,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_1 @ A ) @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ D @ B )
= ( hAPP @ ( fun @ A @ bool ) @ A @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( finite_fold1 @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(83,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( insert @ A ) )
= ( insert @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
thf(477,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)],[83]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( bot @ B )
=> ! [C: $i] :
( ( hAPP @ A @ B @ ( bot_bot @ ( fun @ A @ B ) ) @ C )
= ( bot_bot @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_bot__apply) ).
thf(594,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)],[116]) ).
thf(24,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
= ( fequal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
thf(251,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
= ( fequal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',fact_22_all__not__in__conv) ).
thf(626,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)],[127]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',fact_24_insert__absorb) ).
thf(345,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)],[49]) ).
thf(104,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( finite_finite_1 @ A ) )
= ( finite_finite_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
thf(552,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( finite_finite_1 @ A ) )
= ( finite_finite_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ D ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ 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_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ D ) @ E ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conseq2) ).
thf(685,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ D ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ 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_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ D ) @ E ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(455,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)],[76]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ 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 ) ) ) ) @ D ) )
<=> ( ( ti @ A @ C )
= ( ti @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_fold1Set__sing) ).
thf(394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ 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 ) ) ) ) @ D ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ A @ C )
= ( ti @ A @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ 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 ) ) ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) ) ) @ ( finite_fold_graph @ A @ B ) )
= ( finite_fold_graph @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofold__graph_res) ).
thf(267,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ B ) ) @ ( fun @ B @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) ) ) @ ( finite_fold_graph @ A @ B ) )
= ( finite_fold_graph @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',fact_9_insertE) ).
thf(675,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)],[134]) ).
thf(136,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) ) @ ( hoare_122391849derivs @ A ) )
= ( hoare_122391849derivs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__derivs_res) ).
thf(680,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) ) @ ( hoare_122391849derivs @ A ) )
= ( hoare_122391849derivs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',fact_23_empty__def) ).
thf(342,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)],[48]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_28_insert__iff) ).
thf(355,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)],[53]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_65_folding__one_Osingleton) ).
thf(525,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)],[95]) ).
thf(147,axiom,
! [A: $i,B: $i] :
~ ! [C: $i,D: $i,E: $i] :
( B
!= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ C ) @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_triple_Oexhaust) ).
thf(712,plain,
! [A: $i,B: $i] :
~ ! [C: $i,D: $i,E: $i] :
( B
!= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ C ) @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ 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/sandbox/benchmark/theBenchmark.p',fact_55_the__eq__trivial) ).
thf(640,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ 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)],[129]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(705,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)],[143]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) @ D ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ F ) )
& ( ( ti @ A @ D )
= ( ti @ A @ G ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold_graph @ A @ A ) @ B ) @ E ) @ F ) @ G ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_fold1Set_Osimps) ).
thf(327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) @ D ) )
=> ? [E: $i,F: $i,G: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ F ) )
& ( ( ti @ A @ D )
= ( ti @ A @ G ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold_graph @ A @ A ) @ B ) @ E ) @ F ) @ G ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ F ) ) ) )
& ( ? [E: $i,F: $i,G: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ E ) @ F ) )
& ( ( ti @ A @ D )
= ( ti @ A @ G ) )
& ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold_graph @ A @ A ) @ B ) @ E ) @ F ) @ G ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ E ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_empty__fold1SetE) ).
thf(199,plain,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ ( bot_bot @ ( fun @ A @ bool ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(585,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)],[113]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ F ) @ G ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ 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_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ C ) @ F ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_conseq12) ).
thf(338,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ F ) @ G ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ 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_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ C ) @ F ) @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_the__sym__eq__trivial) ).
thf(643,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ A @ ( the @ A ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(544,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)],[102]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_20_empty__Collect__eq) ).
thf(470,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)],[82]) ).
thf(110,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( the @ A ) )
= ( the @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_OThe_res) ).
thf(576,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( the @ A ) )
= ( the @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(74,axiom,
! [A: $i] :
( ( bot @ A )
=> ( ( ti @ A @ ( bot_bot @ A ) )
= ( bot_bot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
thf(450,plain,
! [A: $i] :
( ( bot @ A )
=> ( ( ti @ A @ ( bot_bot @ A ) )
= ( bot_bot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(539,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)],[100]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(482,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)],[85]) ).
thf(139,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 @ A ) @ B )
= ( ti @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_the__equality) ).
thf(688,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 @ A ) @ B )
= ( ti @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',fact_98_folding__one__idem_Oidem) ).
thf(581,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)],[112]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',fact_26_insert__ident) ).
thf(495,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)],[88]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',fact_31_insert__Collect) ).
thf(759,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)],[163]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ D ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
thf(517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ D ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',fact_48_Set_Oset__insert) ).
thf(748,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)],[159]) ).
thf(62,axiom,
! [A: $i] :
( ( hBOOL @ ( ti @ bool @ A ) )
<=> ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(401,plain,
! [A: $i] :
( ( ( hBOOL @ ( ti @ bool @ A ) )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ ( ti @ bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hoare_509422987triple @ A ) @ B @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_509422987triple @ A ) @ B ) @ ( hoare_728318379le_rec @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ 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/sandbox/benchmark/theBenchmark.p',fact_16_triple_Orecs) ).
thf(588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hoare_509422987triple @ A ) @ B @ ( hAPP @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ B ) ) ) @ ( fun @ ( hoare_509422987triple @ A ) @ B ) @ ( hoare_728318379le_rec @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ 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)],[114]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_finite__Collect__disjI) ).
thf(699,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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)],[142]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_34_insert__compr__raw) ).
thf(731,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)],[153]) ).
thf(68,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_1 @ 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/sandbox/benchmark/theBenchmark.p',fact_70_folding__one_Oinsert) ).
thf(418,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_1 @ 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)],[68]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_41_the__elem__eq) ).
thf(378,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)],[57]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',fact_52_mk__disjoint__insert) ).
thf(207,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)],[15]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(549,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)],[103]) ).
thf(99,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_1 @ 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/sandbox/benchmark/theBenchmark.p',fact_99_folding__one__idem_Oin__idem) ).
thf(536,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_1 @ 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)],[99]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_finite_OinsertI) ).
thf(716,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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)],[148]) ).
thf(39,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 @ A ) @ C )
= ( ti @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_the1__equality) ).
thf(300,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 @ A ) @ C )
= ( ti @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_11_emptyE) ).
thf(752,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)],[160]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( finite_fold1 @ A ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ 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 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_fold1__singleton__def) ).
thf(315,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ A ) @ ( finite_fold1 @ A ) @ D ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ A @ 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 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ E ) @ F ) )
<=> ( ( ( ( ti @ ( fun @ B @ bool ) @ E )
= ( bot_bot @ ( fun @ B @ bool ) ) )
& ( ( ti @ A @ F )
= ( ti @ A @ D ) ) )
| ? [G: $i,H: $i,I: $i] :
( ( ( ti @ ( fun @ B @ bool ) @ E )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ G ) @ H ) )
& ( ( ti @ A @ F )
= ( hAPP @ A @ A @ ( hAPP @ B @ ( fun @ A @ A ) @ C @ G ) @ I ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ G ) @ H ) )
& ( 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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ H ) @ I ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_fold__graph_Osimps) ).
thf(432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ E ) @ F ) )
=> ( ( ( ( ti @ ( fun @ B @ bool ) @ E )
= ( bot_bot @ ( fun @ B @ bool ) ) )
& ( ( ti @ A @ F )
= ( ti @ A @ D ) ) )
| ? [G: $i,H: $i,I: $i] :
( ( ( ti @ ( fun @ B @ bool ) @ E )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ G ) @ H ) )
& ( ( ti @ A @ F )
= ( hAPP @ A @ A @ ( hAPP @ B @ ( fun @ A @ A ) @ C @ G ) @ I ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ G ) @ H ) )
& ( 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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ H ) @ I ) ) ) ) )
& ( ( ( ( ( ti @ ( fun @ B @ bool ) @ E )
= ( bot_bot @ ( fun @ B @ bool ) ) )
& ( ( ti @ A @ F )
= ( ti @ A @ D ) ) )
| ? [G: $i,H: $i,I: $i] :
( ( ( ti @ ( fun @ B @ bool ) @ E )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ G ) @ H ) )
& ( ( ti @ A @ F )
= ( hAPP @ A @ A @ ( hAPP @ B @ ( fun @ A @ A ) @ C @ G ) @ I ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ G ) @ H ) )
& ( 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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ H ) @ 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 ) ) ) @ ( finite_fold_graph @ B @ A ) @ C ) @ D ) @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ A ) @ B )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_com_Osimps_I13_J) ).
thf(273,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)],[30]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_29_insert__commute) ).
thf(373,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)],[55]) ).
thf(40,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_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ 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_509422987triple @ A ) @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ C ) @ D ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).
thf(305,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_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ 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_509422987triple @ A ) @ bool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ B ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ C ) @ D ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_finite__nonempty__imp__fold1Set) ).
thf(294,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ C ) )
=> ( ( ( ti @ ( fun @ A @ bool ) @ C )
!= ( bot_bot @ ( fun @ A @ bool ) ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ 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/sandbox/benchmark/theBenchmark.p',fact_97_finite__ne__induct) ).
thf(506,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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_1 @ 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)],[91]) ).
thf(10,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fdisj )
= fdisj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
thf(195,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fdisj )
= fdisj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ F ) @ G ) )
<=> ( ( B = E )
& ( C = F )
& ( D = G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_triple_Oinject) ).
thf(664,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ F ) @ G ) )
=> ( ( B = E )
& ( C = F )
& ( D = G ) ) )
& ( ( ( B = E )
& ( C = F )
& ( D = G ) )
=> ( ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ F ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(141,axiom,
! [A: $i] :
( ( ( ti @ bool @ A )
= fTrue )
| ( ( ti @ bool @ A )
= fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(696,plain,
! [A: $i] :
( ( ( ti @ bool @ A )
= fTrue )
| ( ( ti @ bool @ A )
= fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(126,axiom,
( ( ti @ bool @ fTrue )
= fTrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
thf(624,plain,
( ( ti @ bool @ fTrue )
= fTrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_13_singleton__conv) ).
thf(728,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)],[152]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ D ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ 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_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ B ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_conseq1) ).
thf(464,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ D ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ 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_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ C ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ B ) @ E ) @ F ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
thf(427,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)],[71]) ).
thf(96,axiom,
( ( ti @ ( fun @ com @ ( fun @ com @ com ) ) @ semi )
= semi ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Com_Ocom_OSemi_res) ).
thf(528,plain,
( ( ti @ ( fun @ com @ ( fun @ com @ com ) ) @ semi )
= semi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold_graph @ A @ A ) @ B ) @ C ) @ D ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fold1Set_Ointros) ).
thf(459,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( finite_fold_graph @ A @ A ) @ B ) @ C ) @ D ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ A ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( finite_fold1Set @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(7,axiom,
! [A: $i] :
( ( finite_finite @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_finite) ).
thf(178,plain,
! [A: $i] :
( ( finite_finite @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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/sandbox/benchmark/theBenchmark.p',fact_72_finite__Collect__conjI) ).
thf(277,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite_1 @ 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)],[31]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',fact_27_insert__code) ).
thf(486,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)],[87]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',fact_53_com_Osimps_I3_J) ).
thf(215,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)],[17]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',fact_14_Collect__conv__if2) ).
thf(560,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)],[106]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ F ) @ G ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ G ) @ B ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ F ) @ B ) ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Comp) ).
thf(755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ F ) @ G ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ G ) @ B ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ bool ) @ ( hoare_122391849derivs @ A ) @ D ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) @ ( insert @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) @ ( hAPP @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) @ ( hAPP @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ A @ ( fun @ state @ bool ) ) @ ( hoare_509422987triple @ A ) ) ) @ ( hoare_1008221573triple @ A ) @ E ) @ ( hAPP @ com @ com @ ( hAPP @ com @ ( fun @ com @ com ) @ semi @ F ) @ B ) ) @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_63_nonempty__iff) ).
thf(364,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)],[54]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(708,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)],[144]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_36_singletonE) ).
thf(254,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)],[25]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_38_singleton__iff) ).
thf(227,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)],[19]) ).
thf(1429,plain,
$false,
inference(cvc4,[status(thm)],[350,613,234,555,352,408,762,683,308,741,202,597,385,533,500,320,257,389,724,570,619,542,421,606,284,416,325,289,591,376,238,348,480,211,646,602,280,734,453,411,248,678,270,381,297,424,165,192,693,467,484,197,522,461,757,710,224,519,169,622,738,457,721,503,633,311,530,662,718,430,166,264,745,573,180,176,286,711,204,413,579,291,604,406,172,736,567,245,616,599,477,594,251,626,345,552,685,455,394,267,675,680,342,355,525,712,640,705,327,199,585,338,643,544,470,576,450,539,482,688,581,495,759,517,748,401,588,699,731,418,378,207,549,536,716,300,752,315,432,273,373,305,294,506,195,664,696,624,728,464,427,528,459,178,277,486,215,560,755,364,708,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW470+5 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n001.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 22:39:06 EDT 2023
% 0.16/0.36 % CPUTime :
% 1.00/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.80/1.10 % [INFO] Parsing done (231ms).
% 1.80/1.11 % [INFO] Running in sequential loop mode.
% 2.47/1.32 % [INFO] eprover registered as external prover.
% 2.47/1.32 % [INFO] cvc4 registered as external prover.
% 2.47/1.32 % [INFO] Scanning for conjecture ...
% 3.10/1.48 % [INFO] Found a conjecture and 162 axioms. Running axiom selection ...
% 3.36/1.58 % [INFO] Axiom selection finished. Selected 162 axioms (removed 0 axioms).
% 4.33/1.82 % [INFO] Problem is first-order (TPTP FOF).
% 4.33/1.84 % [INFO] Type checking passed.
% 4.33/1.84 % [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 ...
% 90.97/39.96 % External prover 'cvc4' found a proof!
% 90.97/39.96 % [INFO] Killing All external provers ...
% 90.97/39.96 % Time passed: 39427ms (effective reasoning time: 38847ms)
% 90.97/39.96 % 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)>
% 90.97/39.96 % Axioms used in derivation (162): fact_77_Collect__def, help_fimplies_2_1_U, fact_87_fold1__singleton, arity_HOL_Obool___Finite__Set_Ofinite, fact_4_constant, tsy_c_fconj_res, tsy_c_Finite__Set_Ofold__graph_res, help_COMBS_1_1_U, fact_19_empty__iff, tsy_c_Orderings_Obot__class_Obot_res, fact_73_finite_OemptyI, fact_17_equals0D, arity_fun___Orderings_Obot, fact_88_folding__one_Oclosed, tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__derivs_res, fact_6_conseq2, tsy_c_COMBK_res, help_fconj_3_1_U, tsy_c_fimplies_res, fact_31_insert__Collect, fact_81_fold__graph_OinsertI, fact_61_theI_H, tsy_c_member_res, fact_40_empty__not__insert, fact_62_conseq, fact_54_the__sym__eq__trivial, fact_3_hoare__derivs_Oinsert, fact_66_bot__empty__eq, fact_60_the1__equality, fact_5_escape, fact_50_com_Osimps_I12_J, fact_28_insert__iff, fact_0_empty, fact_58_the__equality, tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rec_res, fact_41_the__elem__eq, fact_44_bot__fun__def, fact_10_insertCI, fact_92_finite_Osimps, fact_48_Set_Oset__insert, fact_43_bot__apply, fact_33_insertI1, tsy_c_hAPP_res, fact_95_fold__graph_Osimps, tsy_c_Set_OCollect_res, tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__case_res, tsy_c_hAPP_arg1, fact_49_com_Osimps_I13_J, fact_15_Collect__conv__if, help_fNot_2_1_U, fact_96_folding__one__idem_Oinsert__idem, tsy_v_c_res, tsy_c_COMBC_res, fact_46_Comp, fact_74_finite_OinsertI, help_fNot_1_1_U, fact_35_singleton__inject, tsy_c_COMBS_res, help_fFalse_1_1_T, fact_68_fold1Set__nonempty, fact_64_fold1Set__sing, tsy_c_fFalse_res, tsy_c_Com_Ocom_OSKIP_res, fact_69_fold1Set_Ointros, fact_86_fold1__singleton__def, fact_8_conseq12, fact_2_cut, fact_98_folding__one__idem_Oidem, tsy_c_hBOOL_arg1, fact_91_finite__induct, tsy_c_Finite__Set_Ofold1_res, tsy_c_Com_Ocom_OSemi_res, fact_21_ex__in__conv, tsy_c_Finite__Set_Ofinite_res, help_COMBB_1_1_U, fact_53_com_Osimps_I3_J, fact_34_insert__compr__raw, fact_23_empty__def, fact_27_insert__code, help_fdisj_1_1_U, fact_51_the__elem__def, fact_16_triple_Orecs, tsy_c_hAPP_arg2, fact_38_singleton__iff, fact_20_empty__Collect__eq, tsy_c_Set_Othe__elem_res, tsy_c_HOL_OThe_res, tsy_v_b_res, fact_83_finite__code, help_fconj_2_1_U, fact_72_finite__Collect__conjI, tsy_c_Finite__Set_Ofolding__one__idem_res, tsy_c_COMBB_res, tsy_c_fNot_res, fact_12_singleton__conv2, tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple_res, fact_65_folding__one_Osingleton, fact_24_insert__absorb, fact_26_insert__ident, fact_82_finite, tsy_c_HOL_Oundefined_res, tsy_c_Finite__Set_Ofolding__one_res, fact_59_theI, help_ti_idem, help_fequal_1_1_T, arity_fun___Finite__Set_Ofinite, fact_14_Collect__conv__if2, fact_84_finite__Collect__disjI, fact_29_insert__commute, tsy_c_fequal_res, fact_32_insert__compr, fact_30_insert__absorb2, fact_71_fold1__def, fact_76_mem__def, tsy_v_P_res, fact_57_equals0I, fact_55_the__eq__trivial, fact_99_folding__one__idem_Oin__idem, fact_97_finite__ne__induct, fact_78_folding__one_Oeq__fold, help_fdisj_2_1_U, help_COMBK_1_1_U, tsy_c_Set_Oinsert_res, fact_90_finite__nonempty__imp__fold1Set, fact_85_finite__insert, fact_1_triple_Oinject, fact_56_If__def, fact_63_nonempty__iff, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, fact_13_singleton__conv, help_fequal_2_1_T, fact_37_doubleton__eq__iff, fact_89_insert__fold1SetE, fact_45_hoare__derivs_OSkip, help_fconj_1_1_U, help_fdisj_3_1_U, fact_70_folding__one_Oinsert, tsy_v_G_res, help_fFalse_1_1_U, fact_47_triple_Oexhaust, fact_11_emptyE, fact_52_mk__disjoint__insert, fact_25_insertI2, fact_36_singletonE, fact_93_finite__imp__fold__graph, fact_80_empty__fold__graphE, help_fimplies_1_1_U, tsy_c_Finite__Set_Ofold1Set_res, fact_75_ext, fact_67_empty__fold1SetE, fact_79_fold__graph_OemptyI, help_fimplies_3_1_U, fact_39_insert__not__empty, fact_94_fold1Set_Osimps, fact_9_insertE, tsy_c_fdisj_res, fact_18_Collect__empty__eq, fact_22_all__not__in__conv, fact_42_triple_Osimps_I2_J, tsy_c_fTrue_res, fact_7_conseq1
% 90.97/39.96 % No. of inferences in proof: 328
% 90.97/39.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 39427 ms resp. 38847 ms w/o parsing
% 91.92/40.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 91.92/40.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------