TSTP Solution File: SWV770-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV770-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 12:18:25 EDT 2023
% Result : Unsatisfiable 60.81s 12.53s
% Output : Refutation 61.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 757
% Syntax : Number of formulae : 1431 ( 559 unt; 84 typ; 0 def)
% Number of atoms : 2607 ( 778 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 20828 (1286 ~;1260 |; 0 &;18282 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 84 usr; 24 con; 0-4 aty)
% Number of variables : 4046 ( 0 ^;4046 !; 0 ?;4046 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_in_type,type,
c_in: $i > $i > $i > $i ).
thf(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(v_K_type,type,
v_K: $i ).
thf(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(v_NB_type,type,
v_NB: $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(c_Event_Oknows_type,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
thf(v_evs_type,type,
v_evs: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Public_OshrK_type,type,
c_Public_OshrK: $i ).
thf(v_B_type,type,
v_B: $i ).
thf(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i ).
thf(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(v_A_type,type,
v_A: $i ).
thf(c_Event_Oevent_ONotes_type,type,
c_Event_Oevent_ONotes: $i > $i > $i ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i > $i ).
thf(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
thf(c_Event_Obad_type,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
thf(c_NS__Shared__Mirabelle_Ons__shared_type,type,
c_NS__Shared__Mirabelle_Ons__shared: $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_Event_Oevent_OGets_type,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(c_List_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
thf(class_HOL_Ouminus_type,type,
class_HOL_Ouminus: $i > $o ).
thf(c_Message_Omsg_OHash_type,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Message_OHPair_type,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_List_Olist__inter_type,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(c_Public_Okeymode_OEncryption_type,type,
c_Public_Okeymode_OEncryption: $i ).
thf(c_Public_Okeymode_OSignature_type,type,
c_Public_Okeymode_OSignature: $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
thf(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i ).
thf(c_Public_OpublicKey_type,type,
c_Public_OpublicKey: $i > $i ).
thf(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
thf(c_Event_OinitState_type,type,
c_Event_OinitState: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_Message_Oanalzp_type,type,
c_Message_Oanalzp: $i > $i > $o ).
thf(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
thf(c_Message_OsymKeys_type,type,
c_Message_OsymKeys: $i ).
thf(c_NS__Shared__Mirabelle_Ons__sharedp_type,type,
c_NS__Shared__Mirabelle_Ons__sharedp: $i > $i ).
thf(c_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1_type,type,
v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1: $i > $i > $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1_type,type,
c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1: $i > $i > $i ).
thf(c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2_type,type,
c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XrangeE__1__1_type,type,
c_ATP__Linkup_Osko__Set__XrangeE__1__1: $i > $i > $i > $i > $i ).
thf(c_List_Olength__unique_type,type,
c_List_Olength__unique: $i > $i > $i ).
thf(c_Public_Osko__Public__XNonce__supply1__1__1_type,type,
c_Public_Osko__Public__XNonce__supply1__1__1: $i > $i ).
thf(v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1_type,type,
v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1: $i > $i > $i > $i ).
thf(c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1_type,type,
c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1: $i > $i > $i > $i ).
thf(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1_type,type,
v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1: $i > $i > $i > $i ).
thf(v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1_type,type,
v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1: $i > $i > $i > $i ).
thf(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1_type,type,
v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1: $i > $i > $i > $i > $i ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(358,axiom,
hBOOL @ ( c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).
thf(1469,plain,
hBOOL @ ( c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(519,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1823,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(612,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).
thf(2031,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).
thf(1633,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(632,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist__inter @ B @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_1) ).
thf(2072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist__inter @ B @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__spies__pubK_0) ).
thf(1729,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(553,axiom,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remdups_0) ).
thf(1899,plain,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Nonce_0) ).
thf(1850,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).
thf(1295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(573,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cut_0) ).
thf(1950,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).
thf(1686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(672,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ c_Public_OshrK @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__injective_0) ).
thf(2163,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ c_Public_OshrK @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(892,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
| ( A = c_Message_Oagent_OSpy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).
thf(1586,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
| ( A = c_Message_Oagent_OSpy ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__see__shrK_0) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(545,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).
thf(1879,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_1) ).
thf(1337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__notin__image__privateKey_0) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ A )
!= ( c_Message_Oanalz @ B ) )
| ( ( c_Message_Oanalz @ C )
!= ( c_Message_Oanalz @ D ) )
| ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cong_0) ).
thf(846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ A )
!= ( c_Message_Oanalz @ B ) )
| ( ( c_Message_Oanalz @ C )
!= ( c_Message_Oanalz @ D ) )
| ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(909,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(159,axiom,
! [A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
thf(1031,plain,
! [A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(382,axiom,
! [A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).
thf(1522,plain,
! [A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(403,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(1569,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I57_J_0) ).
thf(1073,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(604,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).
thf(2014,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).
thf(1205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(651,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OHash @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I14_J_0) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OHash @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(505,axiom,
! [A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__shrK_0) ).
thf(1793,plain,
! [A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(2,negated_conjecture,
hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(677,plain,
hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(163,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Un_0) ).
thf(1041,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__keysFor_0) ).
thf(1486,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(652,axiom,
! [A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__emptyE_0) ).
thf(2117,plain,
! [A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).
thf(1596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Notes_0) ).
thf(2104,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(644,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__HPair_0) ).
thf(2099,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).
thf(1591,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(371,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OInj_0) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OHash_0) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(698,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(122,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__Un_0) ).
thf(945,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(618,axiom,
( ( c_Event_OinitState @ c_Message_Oagent_OSpy )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Public_OshrK @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__Spy_0) ).
thf(2042,plain,
( ( c_Event_OinitState @ c_Message_Oagent_OSpy )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Public_OshrK @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1078,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalzp @ A @ B )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OInj_0) ).
thf(1788,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalzp @ A @ B )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(487,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
= ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__Key_0) ).
thf(1756,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
= ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OFst_0) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
| ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
| ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ouminus @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).
thf(829,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ouminus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1746,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_OFake_0) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(620,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(2046,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(422,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ D ) ) ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cert__A__form_1) ).
thf(1613,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ D ) ) ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__notin__image__shrK_0) ).
thf(2010,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I16_J_0) ).
thf(1386,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Nonce_0) ).
thf(1803,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(2020,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).
thf(841,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(885,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(166,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
thf(1046,plain,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OBody_0) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(562,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_new__keys__not__used_0) ).
thf(1921,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(630,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__notin__image__publicKey_0) ).
thf(2067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).
thf(1529,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(661,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lists__conv__set_0) ).
thf(2136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(555,axiom,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_ONonce @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I31_J_0) ).
thf(1904,plain,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_ONonce @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_0) ).
thf(1265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(427,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ D @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ F ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ G ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__S__message__form_0) ).
thf(1623,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ D @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ F ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ G ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).
thf(1254,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing__imp__Un_0) ).
thf(1287,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(465,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ E ) ) ) ) ) @ ( c_List_Oset @ F @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ F @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ E ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ F ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__trusts__NS2_0) ).
thf(1709,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ E ) ) ) ) ) @ ( c_List_Oset @ F @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ F @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ E ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ F ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(591,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1 @ A @ B @ C ) @ A @ B ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ D @ ( c_Message_Omsg_ONonce @ E ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ F @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ F ) @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ B ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NS4__implies__NS3_0) ).
thf(1985,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1 @ A @ B @ C ) @ A @ B ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ D @ ( c_Message_Omsg_ONonce @ E ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ F @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ F ) @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ B ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(489,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_1) ).
thf(1760,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(23,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(719,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insertI_0) ).
thf(1871,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth__analz_1) ).
thf(1907,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_0) ).
thf(1323,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__HPair_0) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(407,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth__eq_0) ).
thf(1577,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(232,axiom,
! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1191,plain,
! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(949,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(504,axiom,
hBOOL @ ( c_in @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONil_0) ).
thf(1792,plain,
hBOOL @ ( c_in @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(340,axiom,
! [A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__notin__used__empty_0) ).
thf(1430,plain,
! [A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__neq__HPair_0) ).
thf(917,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(393,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__neq__privateKey_0) ).
thf(1545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).
thf(1892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).
thf(1247,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oparts @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).
thf(1347,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oparts @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1773,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(515,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I56_J_0) ).
thf(1815,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1875,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(250,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__notin__initState_0) ).
thf(1232,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(530,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist__inter @ B @ D @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_0) ).
thf(1847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist__inter @ B @ D @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(817,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(902,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__image__eq_0) ).
thf(1319,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(462,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un_0) ).
thf(1704,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
thf(770,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(481,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1 @ C @ F @ E ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__trusts__NS4_0) ).
thf(1741,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1 @ C @ F @ E ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__def_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(924,plain,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(356,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OOops_0) ).
thf(1465,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1811,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).
thf(1911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(195,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert_0) ).
thf(1109,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(297,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_ONotes @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).
thf(1334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_ONotes @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(452,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).
thf(1682,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(538,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).
thf(1864,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(1020,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1051,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(1183,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__freshK_1) ).
thf(1283,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(222,axiom,
! [A: $i] :
( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
= ( c_Message_Osynth @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__idem_0) ).
thf(1169,plain,
! [A: $i] :
( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
= ( c_Message_Osynth @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(565,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).
thf(1928,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ B ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).
thf(1377,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ B ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(692,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__into__used_0) ).
thf(1447,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(323,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1394,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ B @ D @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).
thf(1405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ B @ D @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(669,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_5) ).
thf(2154,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(87,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth_0) ).
thf(866,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oremdups @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_0) ).
thf(1886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oremdups @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(599,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).
thf(2002,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(144,axiom,
c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Osimps_I2_J_0) ).
thf(998,plain,
c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_1) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(570,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__synth_0) ).
thf(1943,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(238,axiom,
! [A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty2_1) ).
thf(1201,plain,
! [A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(459,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).
thf(1697,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__MPair_0) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(78,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(849,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(586,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).
thf(1975,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Key_0) ).
thf(1564,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
thf(942,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(7,negated_conjecture,
~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(678,plain,
~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert2_0) ).
thf(1438,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(925,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(621,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty_0) ).
thf(2047,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(359,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).
thf(1470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).
thf(1708,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__privateKey_0) ).
thf(2093,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(177,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(1067,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).
thf(1736,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ C @ tc_Message_Omsg ) ) ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__parts__insert_0) ).
thf(1768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ C @ tc_Message_Omsg ) ) ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(714,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(627,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
= ( c_Message_OHPair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_2) ).
thf(2061,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
= ( c_Message_OHPair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Says_0) ).
thf(2000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).
thf(1730,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(798,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(172,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(1057,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut_0) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(471,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ B ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ I @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ J ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ A ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_3) ).
thf(1723,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ B ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ I @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ J ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ A ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oused @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Gets_0) ).
thf(1343,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oused @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OInj_0) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(224,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(1174,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(485,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ D @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS2_0) ).
thf(1751,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ D @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).
thf(1666,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(659,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).
thf(2132,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I37_J_0) ).
thf(2015,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I9_J_0) ).
thf(1560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
= A )
| ~ ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(862,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
= A )
| ~ ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__neq__HPair_0) ).
thf(1217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(666,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Agent_0) ).
thf(2147,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(520,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olength__unique @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_0) ).
thf(1619,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olength__unique @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).
thf(1370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(613,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OAgent_0) ).
thf(2032,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(815,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I1_J_0) ).
thf(1837,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(583,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).
thf(1968,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( hAPP @ c_Message_Omsg_OKey @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).
thf(1555,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( hAPP @ c_Message_Omsg_OKey @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(352,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__symKeys__priK_0) ).
thf(1457,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).
thf(1819,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(218,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(1159,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_1) ).
thf(1656,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).
thf(1407,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__in__initState_0) ).
thf(1281,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_List_Oappend @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__lists__conv_1) ).
thf(1392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_List_Oappend @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(480,axiom,
! [A: $i] : ( c_lessequals @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).
thf(1740,plain,
! [A: $i] : ( c_lessequals @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(650,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I8_J_0) ).
thf(2112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_0) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(405,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olists @ B @ A ) @ ( tc_List_Olist @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_ONil_0) ).
thf(1573,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olists @ B @ A ) @ ( tc_List_Olist @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(133,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(974,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__spies_0) ).
thf(1402,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(590,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth__eq_1) ).
thf(1983,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(490,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__analz__shrK_1) ).
thf(1762,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_ONonce @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I10_J_0) ).
thf(1328,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_ONonce @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1121,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(584,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing_0) ).
thf(1970,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(534,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).
thf(1856,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(136,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(980,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(338,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1425,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(189,axiom,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(1096,plain,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1138,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(783,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(82,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(309,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( A
= ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ E ) ) ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__S__message__form_1) ).
thf(1360,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( A
= ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ E ) ) ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).
thf(1350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(568,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).
thf(1936,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(13,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(697,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__neq__shrK_0) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(391,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1541,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(670,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).
thf(2157,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1143,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__invKey__keysFor_0) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(495,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).
thf(1772,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK_1) ).
thf(1259,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_0) ).
thf(1534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ B @ ( c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 @ B @ A @ C ) @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( B = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).
thf(1794,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ B @ ( c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 @ B @ A @ C ) @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( B = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ tc_Message_Oagent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_2) ).
thf(1953,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ tc_Message_Oagent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq_1) ).
thf(1160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ B @ tc_nat @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__image__eq_1) ).
thf(1461,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ B @ tc_nat @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I36_J_0) ).
thf(1889,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(3,negated_conjecture,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OMPair @ B @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(679,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OMPair @ B @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).
thf(1493,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(453,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).
thf(1683,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(157,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1028,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(609,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_ONonce @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I33_J_0) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_ONonce @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I4_J_0) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(103,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(901,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(180,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
thf(1075,plain,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I2_J_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(623,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__analz__shrK_0) ).
thf(2053,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__mono_0) ).
thf(1842,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).
thf(2108,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(616,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
thf(2038,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(72,axiom,
! [A: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(837,plain,
! [A: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( B = c_Message_Oagent_OSpy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).
thf(1297,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( B = c_Message_Oagent_OSpy ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(523,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1 @ A @ E @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ A ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ F @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ G ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__not__see__encrypted__key_0) ).
thf(1831,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1 @ A @ E @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ A ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ F @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ G ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(205,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__neq__HPair_0) ).
thf(1668,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(600,axiom,
! [A: $i] :
( ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty_1) ).
thf(2006,plain,
! [A: $i] :
( ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(508,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1799,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I18_J_0) ).
thf(1947,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1852,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(468,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1715,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OFst_0) ).
thf(1979,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(663,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_B__trusts__NS5__lemma_0) ).
thf(2140,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(497,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1776,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(263,axiom,
( ( c_Event_OinitState @ c_Message_Oagent_OServer )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ c_Message_Oagent_OServer ) ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ c_Message_Oagent_OServer ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__Server_0) ).
thf(1263,plain,
( ( c_Event_OinitState @ c_Message_Oagent_OServer )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ c_Message_Oagent_OServer ) ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ c_Message_Oagent_OServer ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(143,axiom,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__increasing_0) ).
thf(997,plain,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).
thf(2125,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(985,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_2) ).
thf(1478,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(257,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1249,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(350,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1451,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_2) ).
thf(1382,plain,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oremdups @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(1060,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oremdups @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(168,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__insert_0) ).
thf(1050,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I30_J_0) ).
thf(1627,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalzp @ A @ B )
| ~ ( c_Message_Oanalzp @ A @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) )
| ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OCrypt @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_ODecrypt_0) ).
thf(1991,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalzp @ A @ B )
| ~ ( c_Message_Oanalzp @ A @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) )
| ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OCrypt @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(498,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).
thf(1779,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).
thf(1695,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(634,axiom,
! [A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ c_Public_OshrK @ A ) )
= ( hAPP @ c_Public_OshrK @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).
thf(2076,plain,
! [A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ c_Public_OshrK @ A ) )
= ( hAPP @ c_Public_OshrK @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(5,negated_conjecture,
~ ( hBOOL @ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(674,plain,
~ ( hBOOL @ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I35_J_0) ).
thf(1663,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(379,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ ( c_Message_Omsg_OCrypt @ E @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ H @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).
thf(1515,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ ( c_Message_Omsg_OCrypt @ E @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ H @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(551,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(423,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Agent__synth_0) ).
thf(1616,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(230,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(476,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ A @ F ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Oops__parts__spies_0) ).
thf(1732,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ A @ F ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__parts__subset__parts_0) ).
thf(1434,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(535,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__image__eq_0) ).
thf(1857,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(184,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1086,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(938,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pubK__neq__shrK_0) ).
thf(2057,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).
thf(765,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).
thf(773,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).
thf(1996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(654,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1 @ A @ B @ C @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_B__trusts__NS3_0) ).
thf(2121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1 @ A @ B @ C @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1135,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_0) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(451,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__synthD_0) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(824,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).
thf(1483,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma1_0) ).
thf(1548,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(745,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(473,axiom,
~ ( hBOOL @ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Server__not__bad_0) ).
thf(1727,plain,
~ ( hBOOL @ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(377,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ I @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_2) ).
thf(1510,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ I @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(578,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ H ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ I @ A @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS5_0) ).
thf(1959,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ H ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ I @ A @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(614,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( A = c_Message_Oagent_OServer )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS3_0) ).
thf(2033,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( A = c_Message_Oagent_OServer )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(667,axiom,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) )
!= ( hAPP @ c_Public_OshrK @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priEK__noteq__shrK_0) ).
thf(2149,plain,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) )
!= ( hAPP @ c_Public_OshrK @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(611,axiom,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OAgent @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I13_J_0) ).
thf(2028,plain,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OAgent @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I45_J_0) ).
thf(1301,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(64,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(819,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).
thf(1833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(560,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__image__eq_1) ).
thf(1916,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(547,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert_0) ).
thf(1884,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_List_Oappend @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__lists__conv_0) ).
thf(1652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_List_Oappend @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(958,plain,
! [B: $i,A: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I19_J_0) ).
thf(1701,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Decrypt_H_0) ).
thf(1520,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(660,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(2134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(500,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ E @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ D @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS2_0) ).
thf(1784,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ E @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ D @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).
thf(1389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).
thf(843,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(248,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( A = c_Message_Oagent_OServer )
| ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS3_0) ).
thf(1226,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( A = c_Message_Oagent_OServer )
| ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ B @ ( c_ATP__Linkup_Osko__Set__XrangeE__1__1 @ A @ B @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeE_0) ).
thf(1488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ B @ ( c_ATP__Linkup_Osko__Set__XrangeE__1__1 @ A @ B @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).
thf(1503,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).
thf(1786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
thf(787,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(713,plain,
class_Lattices_Oboolean__algebra @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(432,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth_0) ).
thf(1635,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(253,axiom,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(1239,plain,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(2166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(552,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__see__shrK_1) ).
thf(1897,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(704,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(449,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1675,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).
thf(1058,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(624,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_2) ).
thf(2055,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono_0) ).
thf(1092,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(533,axiom,
! [B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_List_Oset @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty2_0) ).
thf(1853,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_List_Oset @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(273,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).
thf(1282,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(637,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS4_0) ).
thf(2084,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I5_J_0) ).
thf(1117,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(30,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(736,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(643,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analzD_0) ).
thf(2097,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Oappend @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__lists__conv_2) ).
thf(1603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Oappend @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(456,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I12_J_0) ).
thf(1690,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(629,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__trans_0) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I44_J_0) ).
thf(1209,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(653,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).
thf(2119,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1011,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(567,axiom,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1933,plain,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(93,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(880,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(509,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(404,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ E @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS4_0) ).
thf(1571,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ E @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(315,axiom,
hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).
thf(1376,plain,
hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(890,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).
thf(1877,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Nonce_0) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(658,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( hAPP @ c_Message_Omsg_OKey @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).
thf(2129,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( hAPP @ c_Message_Omsg_OKey @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(518,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).
thf(1821,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(537,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__analz_0) ).
thf(1862,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( C
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_0) ).
thf(1325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( C
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(430,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).
thf(1630,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Agent__neq__HPair_0) ).
thf(1993,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(557,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ B @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__image__eq_0) ).
thf(1909,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ B @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(1029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(895,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1149,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(574,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1952,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(197,axiom,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Osimps_I1_J_0) ).
thf(1112,plain,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(455,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1688,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(460,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1699,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(868,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(638,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).
thf(2086,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(225,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(1176,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(608,axiom,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__increasing_0) ).
thf(2022,plain,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).
thf(2101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(511,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(631,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).
thf(2069,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ B ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ B @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__freshK_2) ).
thf(1562,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ B ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ B @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(685,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(633,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).
thf(2075,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(527,axiom,
! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).
thf(1841,plain,
! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth_0) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1044,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(695,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(780,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).
thf(1643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).
thf(1726,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ouminus @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ B @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
thf(1364,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ouminus @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ B @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(722,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_3) ).
thf(1467,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(927,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(206,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1134,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(593,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1990,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(754,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(167,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1049,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1,negated_conjecture,
hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(675,plain,
hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_0) ).
thf(1583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).
thf(1304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).
thf(1873,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(488,axiom,
! [A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ c_Message_OinvKey @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey_0) ).
thf(1758,plain,
! [A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ c_Message_OinvKey @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(4,negated_conjecture,
~ ( hBOOL @ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(680,plain,
~ ( hBOOL @ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(182,axiom,
! [A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
thf(1081,plain,
! [A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).
thf(749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(484,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_0) ).
thf(1748,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(855,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS1_0) ).
thf(1598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(579,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).
thf(1961,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1025,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__HPair_0) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(971,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(418,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1605,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS1_0) ).
thf(1647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(486,axiom,
! [A: $i] :
( ( ( hAPP @ c_Message_OinvKey @ A )
= A )
| ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__K_0) ).
thf(1753,plain,
! [A: $i] :
( ( ( hAPP @ c_Message_OinvKey @ A )
= A )
| ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(386,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__in__initState_0) ).
thf(1531,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).
thf(993,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(146,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1003,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insertI_0) ).
thf(1770,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(626,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).
thf(2060,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_OHash @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I32_J_0) ).
thf(1743,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_OHash @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_0) ).
thf(1400,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(17,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(707,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(126,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(954,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalzp @ A @ B )
| ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OMPair @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OSnd_0) ).
thf(1252,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalzp @ A @ B )
| ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OMPair @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(365,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
= ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__image__Key_0) ).
thf(1484,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
= ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ A )
!= ( c_Message_Oanalz @ B ) )
| ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).
thf(2160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ A )
!= ( c_Message_Oanalz @ B ) )
| ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(341,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__idem_0) ).
thf(1432,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(162,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1038,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(22,axiom,
( ( c_Message_Oanalz @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__empty_0) ).
thf(717,plain,
( ( c_Message_Oanalz @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(540,axiom,
! [A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_1) ).
thf(1869,plain,
! [A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(290,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OCrypt @ D @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ G ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_0) ).
thf(1317,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OCrypt @ D @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ G ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(554,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( D = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_1) ).
thf(1901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( D = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(619,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I11_J_0) ).
thf(2044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).
thf(1579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(907,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_1) ).
thf(1711,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_4) ).
thf(1499,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(503,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Agent_0) ).
thf(1790,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(592,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Message_OinvKey @ A )
!= ( hAPP @ c_Message_OinvKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__eq_0) ).
thf(1987,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Message_OinvKey @ A )
!= ( hAPP @ c_Message_OinvKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).
thf(1300,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Notes_0) ).
thf(1637,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Hash_0) ).
thf(1285,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__trans_0) ).
thf(1738,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).
thf(1023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(585,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__neq__publicKey_0) ).
thf(1972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(507,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OInj_0) ).
thf(1797,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).
thf(1372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(83,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(859,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__into__used_0) ).
thf(1404,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(308,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_OOops_0) ).
thf(1358,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).
thf(1543,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(492,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__Key__image__eq_0) ).
thf(1766,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ ( tc_fun @ tc_nat @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__mono_0) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ ( tc_fun @ tc_nat @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(589,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_1) ).
thf(1981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ B @ C ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__knows__A_0) ).
thf(1353,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ B @ C ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(576,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ tc_Message_Oagent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_2) ).
thf(1955,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ tc_Message_Oagent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
thf(2145,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(546,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_injD_0) ).
thf(1881,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_0) ).
thf(1272,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I1_J_0) ).
thf(1617,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__neq__HPair_0) ).
thf(1940,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(76,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(845,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalzp @ A @ B )
| ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OMPair @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OFst_0) ).
thf(1421,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalzp @ A @ B )
| ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OMPair @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(639,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_OAgent @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I11_J_0) ).
thf(2088,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_OAgent @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(353,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_OinitState @ c_Message_Oagent_OSpy ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 @ A @ B ) @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 @ A @ B ) @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 @ A @ B ) @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__imp__Says__Notes__initState_0) ).
thf(1459,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_OinitState @ c_Message_Oagent_OSpy ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 @ A @ B ) @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 @ A @ B ) @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 @ A @ B ) @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(582,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth_0) ).
thf(1966,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(396,axiom,
! [A: $i] :
( ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_0) ).
thf(1553,plain,
! [A: $i] :
( ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(516,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OHash @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I38_J_0) ).
thf(1517,plain,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OHash @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(499,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ D ) ) ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_1) ).
thf(1781,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ D ) ) ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).
thf(1126,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(349,axiom,
( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def__raw_0) ).
thf(1448,plain,
( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth__analz_0) ).
thf(2110,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(539,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).
thf(1866,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(597,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__append_0) ).
thf(1998,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(561,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1918,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(289,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(1316,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_0) ).
thf(1649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(217,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1157,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(635,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).
thf(2078,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__notin__image__publicKey_0) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(559,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_1) ).
thf(1913,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(976,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(529,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).
thf(1844,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(688,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).
thf(1654,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ C @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__image__Key_0) ).
thf(1289,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ C @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(351,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).
thf(1453,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(477,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1734,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(512,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).
thf(1807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__pubK_0) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).
thf(1476,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(300,axiom,
! [A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) ) @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKey__neq__priEK_0) ).
thf(1341,plain,
! [A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) ) @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I3_J_0) ).
thf(1639,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(610,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).
thf(2026,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I46_J_0) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(383,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__notin__image__Key_0) ).
thf(1523,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).
thf(1721,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(191,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__idem_0) ).
thf(1101,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(995,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(398,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__symKeys__pubK_0) ).
thf(1558,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK_2) ).
thf(2152,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__image__eq_1) ).
thf(1491,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(636,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OAgent @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I15_J_0) ).
thf(2081,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OAgent @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(279,axiom,
! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).
thf(1294,plain,
! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Agent_0) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__cut_0) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(378,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1513,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(642,axiom,
! [A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
= ( c_Event_OinitState @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Nil_0) ).
thf(2095,plain,
! [A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
= ( c_Event_OinitState @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(615,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(2036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I17_J_0) ).
thf(1607,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(41,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(763,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(102,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(899,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ c_Public_Okeymode_OEncryption ) )
| ~ ( hBOOL @ ( hAPP @ A @ c_Public_Okeymode_OSignature ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Oinduct_0) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ c_Public_Okeymode_OEncryption ) )
| ~ ( hBOOL @ ( hAPP @ A @ c_Public_Okeymode_OSignature ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ c_Public_OshrK @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__pubK_0) ).
thf(1444,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ c_Public_OshrK @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(346,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1 @ A @ C @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ A ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ E @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ D ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OAgent @ E ) ) ) ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_secrecy__lemma_0) ).
thf(1442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1 @ A @ C @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ A ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
| ( hBOOL @ ( c_in @ E @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ D ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OAgent @ E ) ) ) ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I34_J_0) ).
thf(2142,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(655,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).
thf(2123,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(577,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
thf(1957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).
thf(1678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I47_J_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__not__used_0) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(601,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__partsD_0) ).
thf(2008,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(622,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(2050,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(86,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(865,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq_0) ).
thf(1097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(413,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).
thf(1593,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__trans_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(212,axiom,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__increasing_0) ).
thf(1148,plain,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(448,axiom,
( ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__empty_0) ).
thf(1673,plain,
( ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma2_0) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(457,axiom,
! [A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ ( c_Public_Osko__Public__XNonce__supply1__1__1 @ A ) ) @ ( c_Event_Oused @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__supply1_0) ).
thf(1693,plain,
! [A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ ( c_Public_Osko__Public__XNonce__supply1__1__1 @ A ) ) @ ( c_Event_Oused @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(171,axiom,
class_HOL_Ouminus @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
thf(1056,plain,
class_HOL_Ouminus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(640,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(2091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(68,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(828,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(176,axiom,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1065,plain,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ C @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ C @ tc_nat @ tc_Message_Omsg ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK_0) ).
thf(2040,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ C @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ C @ tc_nat @ tc_Message_Omsg ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).
thf(1436,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(536,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oremdups @ B @ C ) @ C ) )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_1) ).
thf(1859,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oremdups @ B @ C ) @ C ) )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__notin__image__privateKey_0) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(897,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Key_0) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(43,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(767,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__notin__image__shrK_0) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(128,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_2) ).
thf(2063,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C )
| ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(420,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__shrK_0) ).
thf(1610,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(657,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__parts_0) ).
thf(2127,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Hash_0) ).
thf(1261,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).
thf(1268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(153,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1019,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_1) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(307,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).
thf(1357,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__mono_0) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
!= ( hAPP @ c_Public_OshrK @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__priK_0) ).
thf(1925,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
!= ( hAPP @ c_Public_OshrK @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(467,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__trusts__NS4__lemma_0) ).
thf(1713,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(10,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(691,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(375,axiom,
( ( c_NS__Shared__Mirabelle_Ons__sharedp @ v_x )
= ( c_in @ v_x @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp__ns__shared__eq_0) ).
thf(1505,plain,
( ( c_NS__Shared__Mirabelle_Ons__sharedp @ v_x )
= ( c_in @ v_x @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(662,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ F ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cert__A__form_0) ).
thf(2138,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ F ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( A = C )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__freshK_0) ).
thf(1930,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( A = C )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
| ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(839,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(728,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(522,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Hash_0) ).
thf(1829,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(587,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ E @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ H ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ I @ A @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS5_0) ).
thf(1977,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ E @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ H ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ I @ A @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
| ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
| ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(387,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1532,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(860,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(319,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1384,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(1537,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).
thf(1331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(580,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).
thf(1962,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__into__used_0) ).
thf(1463,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).
thf(2018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_1) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(6,negated_conjecture,
hBOOL @ ( c_in @ v_evs @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(676,plain,
hBOOL @ ( c_in @ v_evs @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(185,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1088,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(514,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I39_J_0) ).
thf(1812,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(647,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).
thf(2106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(882,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(312,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ c_Public_OshrK @ B ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ A @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_2) ).
thf(1367,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ c_Public_OshrK @ B ) )
| ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ A @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(120,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(940,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(935,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(571,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).
thf(1945,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
| ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
| ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1009,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(14979,plain,
$false,
inference(e,[status(thm)],[1036,1469,1823,2031,1633,2072,1105,1729,1899,1850,1179,777,1295,1950,1110,1686,2163,892,1586,1501,809,1879,1337,1718,1237,846,909,1031,1083,962,1522,1569,1073,2014,1205,2114,878,1793,677,1041,1486,2117,1596,2104,2099,1591,1497,1671,1164,698,747,945,1063,2042,1078,1788,1756,1310,1507,1222,930,829,1196,1746,1835,1001,2046,1613,2010,1386,1803,2020,841,885,1046,1645,1921,2067,1529,2136,1904,1265,1623,1254,724,1287,1709,1985,1760,719,785,1871,1907,1323,1826,1279,1577,1191,949,1792,1430,917,751,1545,853,1892,1247,1347,1115,1773,1815,1875,1232,1847,817,902,1319,1704,1013,770,1741,1398,924,1465,789,1811,1911,1109,1334,1682,1864,1020,806,1051,1183,1283,1169,1928,1377,692,1447,1622,1394,1405,1600,2154,866,1886,2002,998,1345,988,1943,1201,1697,1242,849,1975,1564,920,942,678,1438,793,925,1199,2047,1153,761,1470,1708,2093,1067,1736,1768,714,2061,2000,1730,798,1057,1274,1723,1343,1355,1174,1751,1666,2132,2015,1560,1042,952,1123,862,1217,2147,1824,1619,1370,2032,815,1423,1837,1968,1555,1457,1819,1159,1656,757,1407,1128,1281,1392,1740,2112,1291,710,1573,974,1402,742,1983,1762,1328,1121,1970,1856,980,1425,1096,1006,1138,783,857,1360,1350,1936,697,1089,1234,1541,874,2157,1143,1270,1772,1259,1534,1794,1953,1567,1160,1461,1214,1016,1889,679,1155,1419,1493,1683,1028,2023,1964,1659,901,1075,1414,2053,1842,2108,2038,837,701,1297,1831,1131,1668,1192,2006,1799,1947,1852,1715,1979,2140,1776,1263,997,2125,985,1150,1478,1249,1451,738,1539,1382,1060,1050,1627,1525,1991,1779,1695,2076,1071,674,1663,1515,1895,1616,1185,1732,1434,1857,1086,938,1054,2057,765,773,1996,2121,1135,1764,1146,1680,824,1483,1548,745,733,1727,1510,1959,1103,2033,2149,2028,1301,819,904,1833,1916,1884,1652,826,958,1701,1520,2134,1784,1389,843,1125,1256,1226,1488,1428,1503,1786,1312,787,713,1635,1239,2166,1897,704,1224,1675,1058,1107,2055,1092,1194,831,1853,1282,2084,1117,736,2097,1603,1690,2065,1209,2119,1574,1011,1589,1933,880,1801,1571,1376,890,811,1877,1339,2129,1821,1862,1325,1177,1630,1993,1909,726,1029,895,1149,964,932,1952,1112,1688,1699,868,2086,883,1176,2022,2101,851,922,1805,2069,1562,912,685,1171,983,2075,1841,1396,1044,695,780,1643,1726,1364,722,1203,1467,927,1277,1134,1990,754,1181,1049,675,1583,1304,1873,1758,1166,795,680,1081,749,1748,855,1598,1961,1025,1611,887,971,2012,1605,1647,1753,1531,993,1003,1770,2060,1743,1400,707,954,1252,1484,2160,1432,791,1188,1038,717,1869,1317,1901,2044,1579,1220,907,1711,1499,1790,1987,1300,1637,1285,1738,1023,1972,1797,1372,876,859,1404,1358,1543,1766,1141,1981,1353,1955,2145,1094,978,1881,1272,991,1617,1940,845,1421,2088,1459,1966,1553,1817,1517,1781,1126,1448,2110,1866,1998,1918,1316,1649,1157,2078,1321,1913,976,1844,688,1654,1412,1289,1453,1734,1807,1276,1476,1341,1639,1481,2026,1244,1523,731,813,1721,946,1101,995,1558,2152,1491,2081,914,1294,1440,1308,1706,1212,1513,2095,2036,800,1607,763,899,1661,1444,1442,2142,2123,1957,1678,967,1229,1625,2008,2050,865,1097,835,1593,1380,1148,1673,1495,1693,1056,2091,828,1065,2040,1436,1859,1363,1314,897,1410,767,1033,1197,960,1473,2063,1610,2127,1261,1268,1019,1550,1357,1923,822,1925,1713,1004,691,871,1505,2138,1930,839,728,740,1829,1977,1532,860,1384,1537,1331,803,1962,1463,2018,1416,676,1088,1812,2106,708,882,1367,940,935,1945,1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV770-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 02:30:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.81/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.52/1.06 % [INFO] Parsing done (230ms).
% 1.52/1.07 % [INFO] Running in sequential loop mode.
% 2.27/1.27 % [INFO] eprover registered as external prover.
% 2.27/1.27 % [INFO] cvc4 registered as external prover.
% 2.27/1.28 % [INFO] Scanning for conjecture ...
% 2.74/1.43 % [INFO] Found a conjecture and 686 axioms. Running axiom selection ...
% 3.43/1.59 % [INFO] Axiom selection finished. Selected 666 axioms (removed 20 axioms).
% 4.10/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 4.10/1.77 % [INFO] Type checking passed.
% 4.10/1.77 % [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 ...
% 60.81/12.53 % External prover 'e' found a proof!
% 60.81/12.53 % [INFO] Killing All external provers ...
% 60.81/12.53 % Time passed: 12014ms (effective reasoning time: 11453ms)
% 60.81/12.53 % 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)>
% 60.81/12.53 % Axioms used in derivation (666): clsarity_nat__HOL_Oord, cls_Key__image__eq_0, cls_Crypt__notin__initState_0, cls_NS4__implies__NS3_0, cls_synth_OHash_0, cls_shrK__in__initState_0, cls_minus__le__iff_0, cls_subset__insert_1, cls_Compl__subset__Compl__iff_1, cls_analz__image__freshK__lemma_5, cls_not__parts__not__analz_0, cls_inj__image__mem__iff_1, cls_top__fun__eq_0, cls_set__subset__Cons_0, cls_parts_OBody_0, cls_msg_Osimps_I47_J_0, cls_MPair__synth__analz_0, cls_symKeys__invKey__iff_0, cls_append__in__lists__conv_2, cls_bot__fun__eq_0, cls_sup__ge1_0, cls_privateKey__image__eq_1, cls_Says__S__message__form_0, cls_Un__subset__iff_0, cls_parts__partsD_0, cls_equalityI_0, cls_sup__top__left_0, cls_insertE_0, cls_knows__Spy__Gets_0, cls_parts_OInj_0, cls_parts_OFst_0, cls_A__trusts__NS2_0, cls_B__trusts__NS5__lemma_0, cls_MPair__used_0, cls_Cons__eq__append__conv_5, cls_knows__Notes_0, cls_subset__image__iff_2, cls_set__ConsD_0, cls_set__empty2_1, cls_initState__subset__knows_0, cls_HPair__eq_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_subset__empty_1, cls_pushes_I9_J_0, cls_synth__analz__mono_0, cls_append__self__conv_0, cls_secrecy__lemma_0, cls_used__Says_0, cls_sup__bot__right_0, cls_insert__code_1, cls_list_Oinject_0, cls_analz__subset__iff_1, cls_Says__imp__used_0, cls_knows__Says_0, cls_analz__image__freshK__simps_I56_J_0, cls_Agent__synth_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_in__set__conv__decomp_1, cls_Un__commute_0, cls_ns__sharedp_ONS3_0, cls_fun__Compl__def_0, cls_analz__cong_0, cls_UnCI_1, cls_set__empty_1, cls_parts__image__Key_0, cls_insert__absorb_0, cls_used__Notes_0, cls_cert__A__form_0, cls_ns__sharedp_ONS4_0, cls_unique__session__keys_0, cls_msg_Osimps_I34_J_0, cls_compl__eq__compl__iff_0, cls_mem__def_1, cls_msg_Osimps_I49_J_0, clsarity_nat__Orderings_Olinorder, cls_analz__insert__freshK_0, cls_msg_Osimps_I6_J_1, cls_Says__imp__parts__knows__Spy_0, cls_analz__subset__parts_0, cls_HPair__def_0, cls_empty__iff_0, cls_not__Cons__self2_0, cls_Fake__parts__insert_0, cls_ns__shared_OOops_0, cls_MPair__eq__HPair_1, cls_msg_Osimps_I45_J_0, cls_msg_Osimps_I12_J_0, cls_insert__iff_1, cls_eq__Nil__appendI_0, cls_knows__subset__knows__Says_0, cls_Gets__imp__knows__agents_0, cls_inj__on__Un__image__eq__iff_0, cls_knows__subset__knows__Cons_0, cls_append__eq__Cons__conv_4, cls_Crypt__synth__eq_1, cls_analz__idem_0, cls_insert__subset_0, cls_self__append__conv_0, cls_Crypt__synth__analz_0, cls_same__append__eq_0, clsarity_fun__Lattices_Oupper__semilattice, cls_inj__image__subset__iff_0, cls_Nonce__supply1_0, cls_le__sup__iff_0, cls_ComplD_0, cls_HPair__eq__MPair_0, cls_set__rev__mp_0, cls_msg_Osimps_I3_J_0, cls_append__Cons_0, cls_ns__sharedp_ONS2_0, cls_analz__image__freshK__lemma_4, cls_inj__image__mem__iff_0, cls_subset__insert__iff_2, cls_parts__empty_0, cls_NS3__msg__in__parts__spies_0, cls_shrK__in__knows_0, cls_shrK__image__eq_1, cls_agent_Osimps_I5_J_0, cls_analz__image__freshK__lemma_2, cls_Compl__partition_0, cls_distinct_Osimps_I2_J_0, cls_lists_ONil_0, cls_ns__sharedp_OOops_0, cls_publicKey__into__used_0, cls_inj__image__Compl__subset_0, cls_sup__compl__top_0, cls_Key__synth__eq_1, cls_analz__image__freshK__simps_I61_J_0, clsarity_fun__Orderings_Otop, cls_ns__sharedp_OFake_0, cls_initState__Spy_0, cls_synth__insert_0, cls_Un__left__commute_0, cls_Key__image__eq_1, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_privateKey__image__eq_2, cls_keysFor__insert__Hash_0, cls_synth_OCrypt_0, cls_knows__Nil_0, cls_analz__insert__Hash_0, cls_Says__imp__spies_0, cls_in__set__conv__decomp__first_2, cls_Server__not__bad_0, cls_analz__image__freshK__simps_I65_J_0, cls_parts__insert__HPair_0, cls_analz__Crypt__if_1, cls_le__supI_0, cls_Un__subset__iff_1, cls_append1__eq__conv_1, cls_parts__increasing_0, cls_append__eq__append__conv2_4, cls_Un__empty_2, cls_le__iff__sup_1, cls_knows__Spy__Notes_1, cls_Hash__notin__image__Key_0, cls_pushes_I11_J_0, cls_analz__image__freshK_2, cls_invKey__image__eq_1, cls_compl__bot__eq_0, cls_HPair__eq__MPair_2, cls_msg_Osimps_I7_J_0, cls_rangeI_0, cls_parts__subset__iff_1, cls_initState__Server_0, cls_rev__image__eqI_0, cls_inj__on__insert_0, cls_privateKey__notin__image__publicKey_0, cls_distinct_Osimps_I2_J_1, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_ns__shared_ONS4_0, cls_empty__is__image_0, cls_synth__synthD_0, cls_shrK__notin__image__publicKey_0, cls_analz__cut_0, cls_in__parts__UnE_0, cls_keymode_Oinduct_0, cls_le__iff__sup_0, cls_publicKey__inject_0, cls_distinct_Osimps_I1_J_0, cls_HPair__eq_1, cls_Fake__parts__sing__imp__Un_0, cls_in__set__conv__decomp__last_2, cls_synth_OMPair_0, cls_fun__Compl__def__raw_0, cls_Un__UNIV__right_0, cls_Un__absorb2_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_lemma1_0, cls_Key__not__used_0, cls_parts__mono_0, cls_parts__emptyE_0, cls_used__nil__subset_0, cls_parts__insert__MPair_0, cls_symKeys__invKey__iff_1, cls_pushes_I4_J_0, cls_sup__eq__bot__eq2_0, cls_append__Nil2_0, cls_Un__upper2_0, cls_msg_Osimps_I44_J_0, cls_remdups_Osimps_I2_J_0, cls_remdups__id__iff__distinct_0, cls_analz__empty_0, cls_Nil__is__append__conv_0, cls_le__minus__iff_0, cls_parts__knows__Spy__subset__used_0, cls_UnCI_0, cls_analz__subset__iff_0, cls_append__self__conv2_0, cls_self__append__conv2_0, cls_msg_Osimps_I40_J_0, cls_subset__iff_0, cls_insert__code_2, cls_msg_Osimps_I38_J_0, cls_parts_OSnd_0, clsarity_fun__HOL_Oord, cls_remdups__eq__nil__iff_1, cls_pushes_I5_J_0, cls_self__append__conv2_1, cls_analz__mono__contra_I3_J_0, cls_event_Osimps_I9_J_0, cls_ns__shared_ONil_0, cls_rangeE_0, cls_privateKey__notin__image__shrK_0, cls_singleton__iff_1, cls_Spy__spies__bad__shrK_0, cls_symKey__neq__priEK_0, cls_distinct__append_0, cls_parts__Un_0, cls_event_Osimps_I6_J_0, cls_subset__empty_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_A__trusts__NS4_0, cls_subset__Compl__self__eq_1, cls_Spy__spies__bad__privateKey_0, cls_pushes_I8_J_0, cls_parts__insert_0, cls_msg_Osimps_I14_J_0, cls_compl__top__eq_0, cls_analz__conj__parts_0, cls_append__Nil_0, cls_in__lists__conv__set_0, clsarity_bool__Lattices_Oupper__semilattice, cls_msg_Osimps_I43_J_0, cls_ns__shared_ONS1_0, cls_append__eq__append__conv2_5, cls_append__eq__Cons__conv_5, cls_Spy__analz__shrK_1, cls_image__insert_0, cls_shrK__in__used_0, cls_append__is__Nil__conv_2, cls_synth__analz__insert__eq_0, cls_event_Osimps_I3_J_0, cls_UNIV__not__empty_0, cls_keysFor__insert__MPair_0, cls_le__minus__iff_1, cls_Nonce__notin__used__empty_0, cls_parts__insert__Agent_0, cls_synth__trans_0, cls_Un__insert__left_0, cls_Says__imp__analz__Spy_0, cls_doubleton__eq__iff_2, cls_Compl__partition2_0, cls_keysFor__mono_0, cls_set__empty2_0, cls_cert__A__form_1, clsarity_nat__Orderings_Obot, cls_Fake__analz__insert_0, cls_inj__image__subset__iff_1, cls_sym__shrK_0, cls_msg_Osimps_I7_J_1, cls_Says__Server__message__form_2, cls_agent_Osimps_I4_J_0, cls_insert__subset_1, cls_Spy__see__shrK_0, cls_new__keys__not__used_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_Compl__anti__mono_0, cls_analz_OFst_0, cls_set__eq__subset_2, cls_parts__insert__subset__Un_0, cls_Un__mono_0, cls_knows__Gets_0, cls_Compl__UNIV__eq_0, cls_analz_OInj_0, cls_Nonce__synth__eq_1, cls_parts__insertI_0, cls_Key__neq__HPair_0, cls_msg_Osimps_I46_J_0, cls_shrK__neq__priK_0, cls_synth__increasing_0, cls_ns__sharedp_ONil_0, cls_Un__subset__iff_2, cls_msg_Osimps_I19_J_0, cls_analzp_OFst_0, cls_msg_Osimps_I1_J_0, cls_Nonce__neq__HPair_0, cls_publicKey__notin__image__privateKey_0, cls_privateKey__neq__publicKey_0, cls_linorder__linear_0, cls_Un__empty_0, clsarity_fun__Lattices_Olattice, cls_HPair__synth__analz_0, cls_analz__parts_0, cls_ns__sharedp__ns__shared__eq_0, cls_pushes_I12_J_0, cls_subset__trans_0, cls_analz__image__freshK__lemma_3, cls_Compl__eq__Compl__iff_0, cls_insert__is__Un_0, cls_msg_Osimps_I4_J_0, cls_self__append__conv_1, cls_image__empty_0, cls_Compl__subset__Compl__iff_0, clsarity_bool__HOL_Ouminus, cls_keysFor__insert__HPair_0, cls_MPair__eq__HPair_0, cls_pushes_I2_J_0, cls_not__Cons__self_0, cls_insertI1_0, cls_msg_Osimps_I36_J_0, cls_append__same__eq_0, cls_analz__insert__Crypt__subset_0, cls_analzp_ODecrypt_0, cls_MPair__synth_1, cls_subset__Compl__self__eq_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_list__inter_Osimps_I1_J_0, cls_analz__Crypt__if_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_le__supE_0, cls_analz__insert__cong_0, cls_msg_Osimps_I48_J_0, cls_msg_Osimps_I39_J_0, cls_parts__cut__eq_0, cls_analz__image__freshK_0, cls_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_msg_Osimps_I16_J_0, cls_msg_Osimps_I35_J_0, cls_event_Osimps_I2_J_1, cls_append__assoc_0, cls_ns__shared_OFake_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup1E_0, cls_synth__Un_0, cls_Un__UNIV__left_0, cls_parts__cut_0, cls_analz__image__freshK__simps_I57_J_0, cls_sup__least_0, cls_subset__refl_0, cls_analz__shrK__Decrypt_0, cls_analz__insert__Agent_0, cls_parts__subset__iff_0, cls_synth__subset__iff_1, cls_analz_ODecrypt_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_sup__top__right_0, cls_shrK__notin__image__privateKey_0, cls_analz__Un_0, cls_append__in__lists__conv_0, cls_not__symKeys__priK_0, cls_inj__on__iff_0, cls_image__Un_0, cls_publicKey__notin__image__shrK_0, cls_inj__on__empty_0, cls_sup1CI_1, cls_insertCI_0, cls_Notes__imp__knows__Spy_0, cls_msg_Osimps_I42_J_0, clsarity_fun__Lattices_Oboolean__algebra, cls_Spy__not__see__encrypted__key_0, cls_Crypt__synth__eq_0, cls_invKey__K_0, cls_Spy__in__bad_0, cls_singletonE_0, cls_parts__insert__knows__A_0, cls_Crypt__synth__analz_1, clsarity_nat__Lattices_Olattice, cls_UNIV__I_0, cls_HPair__synth__analz_1, cls_msg_Osimps_I13_J_0, cls_image__iff_2, cls_spies__pubK_0, cls_analzp_OSnd_0, cls_analz__spies__pubK_0, cls_bot1E_0, cls_Fake__analz__eq_0, cls_parts__insert__Hash_0, cls_event_Osimps_I1_J_1, cls_Notes__imp__used_0, cls_analz__mono__contra_I2_J_0, cls_analz__insert__HPair_0, cls_priK__in__initState_0, cls_bex__empty_0, cls_distinct__append_1, cls_unique__session__keys_3, cls_top1I_0, cls_event_Osimps_I7_J_0, cls_insert__mono_0, cls_analzp_OInj_0, cls_le__supI2_0, cls_synth__analz__insert__eq_1, cls_analz__image__freshK__lemma_0, cls_Un__assoc_0, cls_A__trusts__NS4__lemma_0, cls_publicKey__neq__privateKey_0, cls_list__inter_Osimps_I2_J_0, cls_parts__insert2_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_distinct__remdups__id_0, cls_synth_OInj_0, cls_synth__idem_0, cls_msg_Osimps_I15_J_0, cls_publicKey__image__eq_2, cls_msg_Osimps_I18_J_0, cls_UnE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_shrK__injective_0, cls_remdups__eq__nil__right__iff_1, cls_inj__on__def_0, cls_Un__absorb_0, cls_MPair__used_1, cls_distinct_Osimps_I2_J_2, cls_event_Osimps_I2_J_0, cls_neq__shrK_0, cls_usedI_0, cls_parts__insert__Key_0, cls_analz__analzD_0, cls_invKey__eq_0, cls_parts__trans_0, cls_set__remdups_0, clsarity_bool__Lattices_Olattice, cls_keysFor__insert__Agent_0, cls_parts__analz_0, cls_le__imp__neg__le_0, cls_event_Osimps_I4_J_0, cls_Spy__see__shrK_1, cls_injD_0, cls_Crypt__notin__used__empty_0, cls_publicKey__image__eq_0, cls_pubK__neq__shrK_0, cls_MPair__synth__analz_2, cls_bot__empty__eq_0, cls_analz__insert__MPair_0, cls_msg_Osimps_I30_J_0, cls_list_Osimps_I3_J_0, clsarity_bool__Lattices_Obounded__lattice, cls_knows__Spy__imp__Says__Notes__initState_0, cls_Says__Server__message__form_1, cls_invKey__shrK_0, cls_Crypt__Spy__analz__bad_0, cls_parts__Un__subset2_0, cls_insert__subset_2, cls_le__supI1_0, cls_sup__left__idem_0, cls_insert__not__empty_0, cls_keymode_Osimps_I2_J_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_Spy__analz__shrK_0, cls_subsetD_0, cls_Key__synth_0, cls_Hash__synth__analz_0, cls_keysFor__insert__Nonce_0, cls_analz__synth__Un_0, cls_sup__fun__eq_0, cls_pushes_I1_J_0, cls_Crypt__synth_0, cls_set__append_0, cls_double__compl_0, cls_subset__singletonD_0, cls_event_Osimps_I8_J_0, cls_insert__absorb2_0, cls_analz__mono_0, cls_analz_OSnd_0, cls_Crypt__imp__keysFor_0, cls_append__is__Nil__conv_1, cls_Nonce__synth__eq_0, cls_priEK__noteq__shrK_0, cls_ComplI_0, cls_doubleton__eq__iff_1, cls_analz__mono__contra_I1_J_0, cls_analz__synth_0, cls_event_Osimps_I1_J_2, cls_minus__le__iff_1, cls_Nonce__synth_0, cls_analz__insert__eq_0, cls_parts__insert__Nonce_0, cls_analz__analz__Un_0, cls_synth__subset__iff_0, cls_Un__left__absorb_0, cls_msg_Osimps_I5_J_0, cls_event_Osimps_I1_J_0, cls_Crypt__notin__image__Key_0, cls_keymode_Osimps_I1_J_0, cls_Cons__eq__appendI_0, cls_Crypt__synth_1, cls_ns__shared_ONS3_0, clsarity_bool__Lattices_Oboolean__algebra, cls_Hash__synth_0, cls_MPair__synth_0, cls_append__is__Nil__conv_0, cls_msg_Osimps_I17_J_0, cls_append__eq__appendI_0, cls_neg__le__iff__le_0, cls_initState__into__used_0, cls_subset__insert_0, cls_sup__idem_0, cls_msg_Osimps_I41_J_0, cls_Cons__eq__append__conv_4, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_msg_Osimps_I32_J_0, cls_append__in__lists__conv_1, cls_inf__sup__aci_I5_J_0, cls_knows__subset__knows__Notes_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_keysFor__parts__insert_0, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_subset__inj__on_0, cls_singleton__inject_0, cls_HPair__synth__analz_2, cls_privateKey__image__eq_0, cls_msg_Osimps_I31_J_0, cls_analz__increasing_0, cls_Un__empty_1, cls_parts__Un__subset1_0, cls_distinct__remdups_0, cls_unique__session__keys_1, cls_Fake__parts__sing_0, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_analz__image__Key_0, cls_B__trusts__NS3_0, cls_Un__least_0, cls_double__complement_0, cls_set__empty_0, cls_ns__shared_ONS2_0, cls_inj__on__contraD_0, cls_sup1CI_0, cls_inj__onD_0, cls_shrK__neq__pubK_0, cls_not__symKeys__pubK_0, cls_sup__ge2_0, cls_Says__S__message__form_1, cls_Oops__parts__spies_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_Nil__is__append__conv_2, cls_ns__shared_ONS5_0, cls_parts__idem_0, cls_lemma2_0, cls_ns__sharedp_ONS5_0, cls_image__eqI_0, cls_subset__UNIV_0, cls_analz__insert__freshK_1, cls_unique__session__keys_2, cls_analz__insertI_0, cls_image__subset__iff_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_knows__Spy__subset__knows__Spy__Says_0, cls_invKey_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_insert__code_0, cls_subset__insertI_0, cls_analz__trans_0, cls_used__Gets_0, cls_Nonce__notin__initState_0, cls_msg_Osimps_I6_J_0, cls_length__unique_Osimps_I2_J_0, cls_Says__imp__knows_0, cls_analz__subset__cong_0, cls_analz__insert__freshK_2, cls_sup__bot__left_0, cls_insert__image_0, cls_shrK__image__eq_0, cls_list__inter_Osimps_I2_J_1, cls_msg_Osimps_I10_J_0, cls_inj__on__Un_1, cls_analz__Decrypt_H_0, cls_insert__commute_0, cls_insert__iff_2, cls_keysFor__insert__Key_0, cls_Crypt__neq__HPair_0, cls_gen__analz__insert__eq_0, cls_HPair__eq__MPair_1, cls_Hash__synth__analz_1, cls_compl__sup__top_0, cls_used__parts__subset__parts_0, cls_MPair__synth__analz_1, cls_knows__imp__Says__Gets__Notes__initState_0, cls_Fake__parts__insert__in__Un_0, cls_append1__eq__conv_0, cls_analz__insert__Key_0, cls_Un__insert__right_0, cls_publicKey__inject_1, cls_Says__Server__message__form_0, cls_Agent__neq__HPair_0, cls_event_Osimps_I5_J_0, cls_privateKey__into__used_0, cls_remdups__eq__nil__iff_0, cls_Nonce__Key__image__eq_0, cls_knows__Spy__Notes_0, cls_priK__neq__shrK_0, clsarity_fun__HOL_Ouminus, cls_parts__synth_0, cls_invKey__image__eq_0, cls_image__is__empty_0, cls_analz__image__freshK__lemma_1, cls_equalityE_0, cls_msg_Osimps_I37_J_0, cls_MPair__eq__HPair_2, cls_imageI_0, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_Compl__empty__eq_0, cls_sup__absorb1_0, cls_parts__insert__Crypt_0, cls_Hash__neq__HPair_0, cls_ns__sharedp_ONS1_0, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_ball__empty_0, cls_synth__cut_0, cls_analz__insert__Nonce_0, cls_synth_OAgent_0, cls_Notes__imp__knows_0, cls_msg_Osimps_I11_J_0, cls_subset__insert__iff_1, cls_Crypt__imp__invKey__keysFor_0, cls_pushes_I6_J_0, cls_msg_Osimps_I33_J_0, cls_analz__image__freshK_1, clsarity_bool__Orderings_Otop, cls_publicKey__in__initState_0, cls_publicKey__image__eq_1, cls_synth__mono_0, cls_remdups_Osimps_I2_J_1, cls_analz__into__parts_0, cls_predicate1D_0, cls_analz__insert_0, cls_parts__insert__spies_0
% 60.81/12.53 % No. of inferences in proof: 1347
% 60.81/12.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12014 ms resp. 11453 ms w/o parsing
% 61.35/12.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 61.35/12.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------