%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV732-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:20 AM UTC 2026
% Result : Unsatisfiable 17.39s 5.01s
% Output : Refutation 21.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 753
% Syntax : Number of formulae : 1507 ( 575 unt; 0 typ; 0 def)
% Number of atoms : 2951 ( 864 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 23064 (1452 ~;1444 |; 0 &;20168 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 94 usr; 26 con; 0-5 aty)
% Number of variables : 4862 ( 0 ^;4862 !; 0 ?;4862 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $i ).
thf(c_Event_Oevent_OSays_decl,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(v_S_decl,type,
v_S: $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(c_Message_Omsg_OCrypt_decl,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Public_OshrK_decl,type,
c_Public_OshrK: $i ).
thf(c_Message_Omsg_OMPair_decl,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_Message_Omsg_ONonce_decl,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(v_NA_decl,type,
v_NA: $i ).
thf(c_Message_Omsg_OAgent_decl,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(v_B_decl,type,
v_B: $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i ).
thf(v_K_decl,type,
v_K: $i ).
thf(v_X_decl,type,
v_X: $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(v_evs_decl,type,
v_evs: $i ).
thf(tc_Event_Oevent_decl,type,
tc_Event_Oevent: $i ).
thf(c_NS__Shared__Mirabelle_Ons__shared_decl,type,
c_NS__Shared__Mirabelle_Ons__shared: $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(c_Event_Oknows_decl,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_decl,type,
c_Message_Oagent_OSpy: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_Message_Oagent_decl,type,
tc_Message_Oagent: $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Event_Oevent_OGets_decl,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Event_Oevent_ONotes_decl,type,
c_Event_Oevent_ONotes: $i > $i > $i ).
thf(c_List_Oremdups_decl,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_Message_Omsg_OHash_decl,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Message_OHPair_decl,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_List_Olist__inter_decl,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(c_Public_Okeymode_OEncryption_decl,type,
c_Public_Okeymode_OEncryption: $i ).
thf(c_Public_Okeymode_OSignature_decl,type,
c_Public_Okeymode_OSignature: $i ).
thf(c_Fun_Ofun__upd_decl,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_Set_Ovimage_decl,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(c_Event_Obad_decl,type,
c_Event_Obad: $i ).
thf(c_Message_OinvKey_decl,type,
c_Message_OinvKey: $i ).
thf(c_Public_OpublicKey_decl,type,
c_Public_OpublicKey: $i > $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_Message_Oagent_OServer_decl,type,
c_Message_Oagent_OServer: $i ).
thf(c_Event_OinitState_decl,type,
c_Event_OinitState: $i > $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2_decl,type,
c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2: $i > $i > $i > $i > $i > $i ).
thf(class_Orderings_Otop_decl,type,
class_Orderings_Otop: $i > $o ).
thf(c_Message_OkeysFor_decl,type,
c_Message_OkeysFor: $i > $i ).
thf(c_Message_Oanalzp_decl,type,
c_Message_Oanalzp: $i > $i > $o ).
thf(c_Event_Oused_decl,type,
c_Event_Oused: $i > $i ).
thf(c_Fun_Othe__inv__into_decl,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1_decl,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1: $i > $i > $i > $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_Message_OsymKeys_decl,type,
c_Message_OsymKeys: $i ).
thf(c_Hilbert__Choice_Oinv__into_decl,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_NS__Shared__Mirabelle_Ons__sharedp_decl,type,
c_NS__Shared__Mirabelle_Ons__sharedp: $i > $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1_decl,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_decl,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_decl,type,
c_ATP__Linkup_Osko__Set__XrangeE__1__1: $i > $i > $i > $i > $i ).
thf(c_List_Olength__unique_decl,type,
c_List_Olength__unique: $i > $i > $i ).
thf(c_Public_Osko__Public__XNonce__supply1__1__1_decl,type,
c_Public_Osko__Public__XNonce__supply1__1__1: $i > $i ).
thf(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1_decl,type,
c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1: $i > $i > $i > $i > $i ).
thf(c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1_decl,type,
c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2_decl,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__List__Xin__lists__conv__set__1__1_decl,type,
c_List_Osko__List__Xin__lists__conv__set__1__1: $i > $i > $i > $i ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).
thf(892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__lists__conv_2) ).
thf(1665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(353,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(1586,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(297,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(1469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(374,axiom,
! [B: $i,A: $i] : ( A @ tc_List_Olist @ ( A @ ( B @ c_List_Olists ) @ ( A @ c_List_Olist_ONil @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lists_ONil_0) ).
thf(1633,plain,
! [B: $i,A: $i] : ( A @ tc_List_Olist @ ( A @ ( B @ c_List_Olists ) @ ( A @ c_List_Olist_ONil @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(663,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_lessequals ) ) )
| ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).
thf(2263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_lessequals ) ) )
| ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(228,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1315,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(741,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) @ hBOOL )
| ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lists__conv__set_0) ).
thf(2427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) @ hBOOL )
| ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(164,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
| ( A = c_Message_Oagent_OServer )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( E @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS3_0) ).
thf(1179,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
| ( A = c_Message_Oagent_OServer )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( E @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1956,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Osynth )
= ( A @ c_Message_Osynth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__idem_0) ).
thf(1110,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Osynth )
= ( A @ c_Message_Osynth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(485,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).
thf(1879,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_1) ).
thf(1718,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Hash__synth__analz_1) ).
thf(2094,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(270,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1411,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(699,axiom,
! [A: $i] :
( ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
= ( A @ ( c_Public_OshrK @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).
thf(2336,plain,
! [A: $i] :
( ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
= ( A @ ( c_Public_OshrK @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(603,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(2131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Oanalzp ) )
| ( B @ ( A @ c_Message_Oanalzp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analzp_OFst_0) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Oanalzp ) )
| ( B @ ( A @ c_Message_Oanalzp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(556,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(2031,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(735,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).
thf(2412,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(177,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1211,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(686,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(2309,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(96,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(1005,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(720,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Notes_0) ).
thf(2381,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(571,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__analz_0) ).
thf(2062,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(265,axiom,
tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).
thf(1401,plain,
tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(514,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Message_Oanalzp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analzp_OInj_0) ).
thf(1939,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Message_Oanalzp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(331,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(1544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(673,axiom,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).
thf(2282,plain,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I30_J_0) ).
thf(1692,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(1305,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(861,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(710,axiom,
tc_nat @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(2363,plain,
tc_nat @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).
thf(1855,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I2_J_0) ).
thf(1443,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(452,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I12_J_0) ).
thf(1808,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(595,axiom,
tc_nat @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(2114,plain,
tc_nat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(529,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1971,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(1793,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).
thf(1608,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(558,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__mono_0) ).
thf(2035,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS1_0) ).
thf(1735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(627,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(2184,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(749,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
| ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(2448,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
| ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(607,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(2141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(744,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Agent_0) ).
thf(2434,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(187,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) @ hBOOL )
| ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
thf(1233,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) @ hBOOL )
| ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(233,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( G @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__Server__message__form_0) ).
thf(1327,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( G @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(522,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Nonce_0) ).
thf(1954,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(632,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
!= ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__neq__publicKey_0) ).
thf(2195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
!= ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(407,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(428,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).
thf(1756,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__notin__image__privateKey_0) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(689,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).
thf(2316,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(618,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I57_J_0) ).
thf(2168,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__in__initState_0) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(430,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(1761,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_4) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1746,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(562,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(2046,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(502,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Event_OinitState @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).
thf(1914,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Event_OinitState @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__synth__analz_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(1046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(365,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1613,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).
thf(2010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( B @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_0) ).
thf(2082,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( B @ c_List_Oremdups ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(573,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_1) ).
thf(2067,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).
thf(1803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(489,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( A @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS2_0) ).
thf(1887,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( A @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(505,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).
thf(1921,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Otop )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1724,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Otop )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ c_in ) ) @ hBOOL )
| ~ ( D @ ( D @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( D @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_3) ).
thf(1475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ c_in ) ) @ hBOOL )
| ~ ( D @ ( D @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( D @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
!= ( C @ ( c_Public_OshrK @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__neq__priK_0) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
!= ( C @ ( c_Public_OshrK @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(497,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__analz__shrK_1) ).
thf(1904,plain,
! [B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).
thf(1518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(204,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__f_0) ).
thf(1265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
!= ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__inject_0) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
!= ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(198,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(1254,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(695,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( C @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__notin__image__publicKey_0) ).
thf(2328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( C @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(536,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ hAPP ) @ ( E @ ( C @ ( D @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A )
| ~ ( E @ ( C @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).
thf(1985,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ hAPP ) @ ( E @ ( C @ ( D @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A )
| ~ ( E @ ( C @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( D @ ( C @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS1_0) ).
thf(1660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( D @ ( C @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(838,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(1826,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(347,axiom,
! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).
thf(1577,plain,
! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(601,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(2126,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_List_Osko__List__Xin__lists__conv__set__1__1 ) ) @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lists__conv__set_1) ).
thf(2356,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_List_Osko__List__Xin__lists__conv__set__1__1 ) ) @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__eq_0) ).
thf(1055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__trans_0) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(701,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).
thf(2339,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(14,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(785,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(669,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(2274,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(917,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(294,axiom,
! [A: $i] :
~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__notin__used__empty_0) ).
thf(1462,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(144,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
thf(1132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(1800,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(491,axiom,
tc_nat @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(1892,plain,
tc_nat @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1087,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(1147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(613,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oparts )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__synth_0) ).
thf(2158,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oparts )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(308,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__symKeys__priK_0) ).
thf(1494,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__eq_1) ).
thf(1100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).
thf(1247,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).
thf(969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(249,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( D @ ( D @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) ) )
| ( ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_6) ).
thf(1362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( D @ ( D @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) ) )
| ( ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(525,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1963,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).
thf(1875,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(1778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(545,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(2007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(644,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert_0) ).
thf(2222,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(3,negated_conjecture,
~ ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_X @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(756,plain,
~ ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_X @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(693,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_2) ).
thf(2324,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(461,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(1828,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(557,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).
thf(2034,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(698,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).
thf(2335,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(551,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Hash_0) ).
thf(2017,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(307,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).
thf(1489,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I16_J_0) ).
thf(1415,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = D )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__ConsD_0) ).
thf(2105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = D )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).
thf(1811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).
thf(1418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(651,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(2236,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).
thf(1864,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).
thf(1283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(576,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).
thf(2073,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(766,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__neq__HPair_0) ).
thf(1169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(672,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__increasing_0) ).
thf(2281,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1072,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).
thf(1394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(543,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I56_J_0) ).
thf(2002,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( D @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( D @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__idem_0) ).
thf(849,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).
thf(1696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(531,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).
thf(1975,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(653,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(2242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(590,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(2103,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(1405,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(516,axiom,
tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_in ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONil_0) ).
thf(1943,plain,
tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_in ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(173,axiom,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(1201,plain,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__spies__pubK_0) ).
thf(1863,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I46_J_0) ).
thf(1206,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(636,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(2204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__Key_0) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Hash__neq__HPair_0) ).
thf(925,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(597,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__image__eq_0) ).
thf(2118,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(810,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_ONonce ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I10_J_0) ).
thf(1338,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_ONonce ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__Nonce_0) ).
thf(2047,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(542,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(2000,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( C @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__notin__image__privateKey_0) ).
thf(1199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( C @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(711,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).
thf(2364,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(649,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).
thf(2232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(679,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(2296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(685,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__analz__shrK_0) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(480,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1868,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_0) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(349,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ c_in ) ) @ hBOOL )
| ~ ( D @ ( D @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( D @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_1) ).
thf(1580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ c_in ) ) @ hBOOL )
| ~ ( D @ ( D @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( D @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__Agent_0) ).
thf(1487,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).
thf(815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(727,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).
thf(2396,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(550,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(2015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(260,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
| ( A
= ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__Server__message__form_2) ).
thf(1387,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
| ( A
= ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(495,axiom,
! [A: $i] :
( ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey_0) ).
thf(1900,plain,
! [A: $i] :
( ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_spies__pubK_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(240,axiom,
( ( ( v_x @ ( t_b @ ( t_a @ tc_fun ) @ ( v_B @ ( v_A @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
= ( t_b @ ( v_x @ ( v_B @ hAPP ) @ ( v_x @ ( v_A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( t_b @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def__raw_0) ).
thf(1343,plain,
( ( ( v_x @ ( t_b @ ( t_a @ tc_fun ) @ ( v_B @ ( v_A @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
= ( t_b @ ( v_x @ ( v_B @ hAPP ) @ ( v_x @ ( v_A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( t_b @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(655,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__partsD_0) ).
thf(2249,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1570,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(394,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1676,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(604,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( D @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) ) )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_1) ).
thf(2133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( D @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) ) )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(312,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( D @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_OOops_0) ).
thf(1502,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( D @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(426,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).
thf(1751,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(788,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I9_J_0) ).
thf(1619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(611,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).
thf(2150,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( B @ c_Message_Oparts ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).
thf(1370,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( B @ c_Message_Oparts ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(748,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(2445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(1365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I39_J_0) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).
thf(1555,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( B @ ( A @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).
thf(1296,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( B @ ( A @ c_List_Oset ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1624,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(2200,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(4,negated_conjecture,
( ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( v_K @ c_in ) ) @ hBOOL )
| ( v_X
!= ( v_A @ c_Message_Omsg_OAgent @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(757,plain,
( ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( v_K @ c_in ) ) @ hBOOL )
| ( v_X
!= ( v_A @ c_Message_Omsg_OAgent @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(974,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(513,axiom,
tc_bool @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(1938,plain,
tc_bool @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(847,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1032,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(360,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_0) ).
thf(1602,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(399,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( F @ c_in ) ) @ hBOOL )
| ( E = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
!= ( F @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).
thf(1687,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( F @ c_in ) ) @ hBOOL )
| ( E = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
!= ( F @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(624,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).
thf(2179,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth_1) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).
thf(1787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(1027,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(640,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__idem_0) ).
thf(2213,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(639,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( D @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__image__eq_1) ).
thf(2211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( D @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth_0) ).
thf(1407,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(703,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(2344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(688,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Public_OshrK @ hAPP ) )
!= ( C @ ( B @ c_Public_OpublicKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pubK__neq__shrK_0) ).
thf(2313,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Public_OshrK @ hAPP ) )
!= ( C @ ( B @ c_Public_OpublicKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
= ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__eq__MPair_2) ).
thf(1392,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
= ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(647,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth__eq_1) ).
thf(2228,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(594,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__remdups_0) ).
thf(2112,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(1291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__lists__conv_0) ).
thf(1740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_Message_Omsg @ ( C @ ( D @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( D @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__parts__insert_0) ).
thf(1910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_Message_Omsg @ ( C @ ( D @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( D @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( B @ c_Message_Oanalz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).
thf(1402,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( B @ c_Message_Oanalz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).
thf(1541,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).
thf(1983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(588,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(2100,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(948,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(474,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( C @ ( D @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__transfer_1) ).
thf(1856,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( C @ ( D @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1425,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(869,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__used_1) ).
thf(1360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Nonce_0) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(512,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).
thf(1936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).
thf(1592,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(681,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I11_J_0) ).
thf(2300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(596,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( B @ c_Message_Omsg_ONonce ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I31_J_0) ).
thf(2115,plain,
! [B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( B @ c_Message_Omsg_ONonce ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
thf(1851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I19_J_0) ).
thf(1794,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__image__eq_0) ).
thf(1329,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(1160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(554,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I1_J_0) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(526,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(933,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(351,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_priK__in__initState_0) ).
thf(1584,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1700,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Oanalzp ) )
| ( B @ ( A @ c_Message_Oanalzp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analzp_OSnd_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Oanalzp ) )
| ( B @ ( A @ c_Message_Oanalzp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(592,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(2108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(582,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I36_J_0) ).
thf(2085,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1889,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(109,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1039,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).
thf(1791,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
thf(2172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(690,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__f_0) ).
thf(2317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(1249,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_0) ).
thf(1297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(684,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( D @ ( B @ c_List_Olist__inter ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_1) ).
thf(2304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( D @ ( B @ c_List_Olist__inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(335,axiom,
tc_nat @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(1552,plain,
tc_nat @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(519,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1947,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
= ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__def_0) ).
thf(1429,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
= ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(1715,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(1979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(668,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).
thf(2272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).
thf(1825,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(232,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).
thf(1324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__synthD_0) ).
thf(1776,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(1263,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(997,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oanalz )
!= ( B @ c_Message_Oanalz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).
thf(2450,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oanalz )
!= ( B @ c_Message_Oanalz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(354,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oanalz )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__synth_0) ).
thf(1588,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oanalz )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__imp__keysFor_0) ).
thf(1530,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma2_0) ).
thf(1539,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__into__used_0) ).
thf(1456,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(257,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_OOops_0) ).
thf(1382,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(723,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Hash__synth__analz_0) ).
thf(2387,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(462,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( F @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( F @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( F @ c_List_Oset ) @ ( E @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A__trusts__NS2_0) ).
thf(1831,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( F @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( F @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( F @ c_List_Oset ) @ ( E @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).
thf(1231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__HPair_0) ).
thf(1668,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(530,axiom,
tc_bool @ class_Orderings_Otop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1974,plain,
tc_bool @ class_Orderings_Otop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(169,axiom,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__notin__initState_0) ).
thf(1192,plain,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_OInj_0) ).
thf(1932,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(1050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).
thf(2052,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__eq__HPair_1) ).
thf(1599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1627,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(714,axiom,
! [A: $i] :
( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
= ( A @ c_Event_OinitState ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Nil_0) ).
thf(2370,plain,
! [A: $i] :
( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
= ( A @ c_Event_OinitState ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth_0) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(454,axiom,
! [A: $i] :
~ ( tc_Message_Omsg @ ( A @ c_Event_Oused @ ( A @ c_Public_Osko__Public__XNonce__supply1__1__1 @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__supply1_0) ).
thf(1814,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( A @ c_Event_Oused @ ( A @ c_Public_Osko__Public__XNonce__supply1__1__1 @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__imp__invKey__keysFor_0) ).
thf(1241,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(561,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_0) ).
thf(2043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(402,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1695,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(341,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( B @ c_Message_Omsg_OHash ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I38_J_0) ).
thf(1563,plain,
! [B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( B @ c_Message_Omsg_OHash ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1846,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(578,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).
thf(2076,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(713,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__spies__bad__privateKey_0) ).
thf(2368,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(2402,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(733,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__parts_0) ).
thf(2408,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).
thf(1515,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Set_Oimage ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).
thf(1895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Set_Oimage ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(629,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono_0) ).
thf(2189,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(739,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).
thf(2423,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(538,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).
thf(1991,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(1318,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(700,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(2338,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(540,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1996,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(599,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(2121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_0) ).
thf(1906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(965,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(622,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(2176,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(677,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OAgent_0) ).
thf(2292,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(725,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OHash ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I14_J_0) ).
thf(2391,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OHash ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(657,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(2253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(304,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(1483,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(1548,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(555,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(2028,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(717,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(2376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist__inter ) ) @ c_List_Oset ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter__conv_0) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist__inter ) ) @ c_List_Oset ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(660,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).
thf(2260,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(463,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Osynth @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__Un_0) ).
thf(1833,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Osynth @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(488,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1884,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(140,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1125,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__image__eq_1) ).
thf(1535,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(728,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(2398,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_2) ).
thf(1520,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ c_Message_Oanalz @ ( B @ c_Message_Oanalz @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).
thf(1226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ c_Message_Oanalz @ ( B @ c_Message_Oanalz @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_usedI_0) ).
thf(1652,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(508,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__increasing_0) ).
thf(1929,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).
thf(1139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).
thf(2193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(694,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__trans_0) ).
thf(2326,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(226,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(1312,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OBody_0) ).
thf(1733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).
thf(1107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(747,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).
thf(2442,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(740,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(2425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__HPair_0) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= E )
| ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__eq_0) ).
thf(1464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= E )
| ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__Hash_0) ).
thf(1224,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(408,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1707,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(678,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ( A = c_Message_Oagent_OServer )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( E @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS3_0) ).
thf(2293,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ( A = c_Message_Oagent_OServer )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( E @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1997,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( A @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__image__eq_2) ).
thf(2166,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( A @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1090,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(753,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(2457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( A @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__image__eq_2) ).
thf(2148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( A @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(708,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OAgent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I15_J_0) ).
thf(2358,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OAgent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(1356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Public_OshrK @ hAPP ) )
!= ( C @ ( B @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_priK__neq__shrK_0) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Public_OshrK @ hAPP ) )
!= ( C @ ( B @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(176,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(472,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1853,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(211,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).
thf(1282,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(721,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).
thf(2383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(736,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(2415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__eq__HPair_0) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(435,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1771,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(139,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OInj_0) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(863,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(709,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS4_0) ).
thf(2361,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(687,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__synth__analz_2) ).
thf(2311,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(659,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_ONonce ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I33_J_0) ).
thf(2257,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_ONonce ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( B @ c_Message_Omsg_OAgent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I13_J_0) ).
thf(2284,plain,
! [B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( B @ c_Message_Omsg_OAgent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(718,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(2378,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__not__used_0) ).
thf(1690,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(626,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(2182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).
thf(1557,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(602,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_new__keys__not__used_0) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(666,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I37_J_0) ).
thf(2267,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(1162,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(256,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).
thf(1381,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1112,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(389,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__shrK_0) ).
thf(1667,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(625,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).
thf(2180,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__trans_0) ).
thf(1877,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 ) @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 ) @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( c_Message_Oagent_OSpy @ c_Event_OinitState @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__imp__Says__Notes__initState_0) ).
thf(1471,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 ) @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 ) @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( c_Message_Oagent_OSpy @ c_Event_OinitState @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(661,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(2261,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(457,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__Un_0) ).
thf(1821,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(417,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).
thf(1731,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(734,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(2410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(466,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( B @ hAPP ) @ ( A @ hAPP ) ) )
| ( ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( A @ hAPP ) )
= ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( D @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_5) ).
thf(1838,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( B @ hAPP ) @ ( A @ hAPP ) ) )
| ( ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( A @ hAPP ) )
= ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( D @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_Message_Oagent_OSpy )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).
thf(1293,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_Message_Oagent_OSpy )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(2278,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL )
| ( B = c_Message_Oagent_OSpy )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( A @ ( B @ c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 ) ) @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).
thf(1926,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL )
| ( B = c_Message_Oagent_OSpy )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( A @ ( B @ c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 ) ) @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(705,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_OAgent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I11_J_0) ).
thf(2350,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_OAgent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
!= ( D @ ( C @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__neq__privateKey_0) ).
thf(1594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
!= ( D @ ( C @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(163,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(1176,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
!= ( C @ ( c_Public_OshrK @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__neq__pubK_0) ).
thf(1477,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
!= ( C @ ( c_Public_OshrK @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(589,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( A @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Says_0) ).
thf(2101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( A @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(451,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( E @ c_lessequals ) ) )
| ( ( C @ ( D @ ( D @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).
thf(1805,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( E @ c_lessequals ) ) )
| ( ( C @ ( D @ ( D @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insertI_0) ).
thf(2069,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(983,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(577,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).
thf(2075,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(737,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
thf(2418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).
thf(1396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(746,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_5) ).
thf(2439,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( D @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( D @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__cut_0) ).
thf(1245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( D @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( D @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(324,axiom,
! [A: $i] :
( ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__image__Key_0) ).
thf(1528,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(606,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).
thf(2139,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(883,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(572,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).
thf(2064,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1015,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(654,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).
thf(2244,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).
thf(1435,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I3_J_0) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(1250,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__image__eq_1) ).
thf(1496,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(683,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__increasing_0) ).
thf(2303,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(1413,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__image__eq_0) ).
thf(2054,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(482,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1873,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(795,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(2037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I44_J_0) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz ) )
| ( ( C @ c_Message_Oanalz )
!= ( D @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oanalz )
!= ( B @ c_Message_Oanalz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__cong_0) ).
thf(1509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz ) )
| ( ( C @ c_Message_Oanalz )
!= ( D @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oanalz )
!= ( B @ c_Message_Oanalz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(635,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ ( I @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( H @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS5_0) ).
thf(2202,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ ( I @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( H @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(939,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).
thf(1958,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(1,negated_conjecture,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_X @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( v_A @ ( v_S @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(754,plain,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_X @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( v_A @ ( v_S @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(113,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(1049,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(108,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(1034,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(652,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Message_OinvKey @ hAPP ) )
!= ( B @ ( c_Message_OinvKey @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__eq_0) ).
thf(2239,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Message_OinvKey @ hAPP ) )
!= ( B @ ( c_Message_OinvKey @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).
thf(1662,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(586,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__transfer_0) ).
thf(2096,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(1758,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(1166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__image__eq_1) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oset ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__append_0) ).
thf(2234,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oset ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(697,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(2333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__notin__image__shrK_0) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(364,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__symKeys__pubK_0) ).
thf(1611,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(570,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).
thf(2060,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I17_J_0) ).
thf(1647,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(439,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
= ( B @ c_Message_Oanalz @ c_Message_Osynth ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).
thf(1780,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
= ( B @ c_Message_Oanalz @ c_Message_Osynth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I35_J_0) ).
thf(1753,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).
thf(2160,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(448,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(680,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
thf(2298,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(434,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1770,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__Decrypt_H_0) ).
thf(1566,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__cut_0) ).
thf(2143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(515,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Agent_0) ).
thf(1941,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(752,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Public_OshrK @ hAPP ) )
!= ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__injective_0) ).
thf(2454,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Public_OshrK @ hAPP ) )
!= ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(616,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(2165,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ c_Message_Omsg_OHash ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I47_J_0) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(441,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(742,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( F @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cert__A__form_0) ).
thf(2429,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( F @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(188,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( C @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( C @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_0) ).
thf(1235,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( C @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( C @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__neq__HPair_0) ).
thf(1763,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I1_J_0) ).
thf(1679,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I45_J_0) ).
thf(1300,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth__eq_0) ).
thf(1637,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(670,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(2276,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(643,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( E @ hAPP ) @ ( A @ hAPP ) ) )
| ( ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
| ~ ( C @ ( C @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( C @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_4) ).
thf(2219,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( E @ hAPP ) @ ( A @ hAPP ) ) )
| ( ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
| ~ ( C @ ( C @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( C @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).
thf(1658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(692,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
= ( B @ ( A @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__eq__HPair_2) ).
thf(2322,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
= ( B @ ( A @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(808,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__cut_0) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1218,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(511,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( E @ ( A @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS2_0) ).
thf(1934,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( E @ ( A @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(432,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OHash_0) ).
thf(1766,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(534,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(1221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(609,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(2145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_3) ).
thf(1504,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(352,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1585,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(97,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(1008,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(568,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_1) ).
thf(2056,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( C @ c_Event_Oused ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_used__Gets_0) ).
thf(1358,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( C @ c_Event_Oused ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(494,axiom,
! [A: $i] :
( ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__Key_0) ).
thf(1898,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(199,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).
thf(1257,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(406,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).
thf(1702,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(719,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).
thf(2379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).
thf(1485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(691,axiom,
( ( c_Message_Oagent_OSpy @ c_Event_OinitState )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_initState__Spy_0) ).
thf(2320,plain,
( ( c_Message_Oagent_OSpy @ c_Event_OinitState )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(314,axiom,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).
thf(1506,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ~ ( c_Public_Okeymode_OSignature @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Public_Okeymode_OEncryption @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keymode_Oinduct_0) ).
thf(1749,plain,
! [B: $i,A: $i] :
( ~ ( c_Public_Okeymode_OSignature @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Public_Okeymode_OEncryption @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__mono_0) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(391,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ( A
= ( D @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cert__A__form_1) ).
thf(1670,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ( A
= ( D @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(447,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).
thf(1797,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(487,axiom,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_OHash ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I32_J_0) ).
thf(1881,plain,
! [B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_OHash ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( C @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__image__Key_0) ).
thf(1272,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( C @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(2266,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(583,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__eq__MPair_1) ).
thf(2088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(293,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1459,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ ( B @ c_List_Osko__List__Xin__lists__conv__set__1__1 ) ) @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lists__conv__set_2) ).
thf(1966,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ ( B @ c_List_Osko__List__Xin__lists__conv__set__1__1 ) ) @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(398,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(336,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__see__shrK_0) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_3) ).
thf(1949,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(468,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).
thf(1844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Agent__neq__HPair_0) ).
thf(2215,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1126,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__lists__conv_1) ).
thf(1421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(549,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(2013,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(504,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B = C )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1918,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B = C )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( C @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( C @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_2) ).
thf(1316,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( C @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( C @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(579,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
thf(2078,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(231,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(1321,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(704,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
thf(2347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(383,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).
thf(1654,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).
thf(1216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OFst_0) ).
thf(2209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I4_J_0) ).
thf(2187,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( D @ ( D @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) ) )
| ( ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_7) ).
thf(1189,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( D @ ( D @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) ) )
| ( ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 ) ) ) ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 ) ) ) ) @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__see__shrK_1) ).
thf(2110,plain,
! [B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(1010,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(1390,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(702,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(2342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_OFst_0) ).
thf(1289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Oanalzp ) )
| ~ ( C @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ ( A @ c_Message_Oanalzp ) )
| ( B @ ( A @ c_Message_Oanalzp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analzp_ODecrypt_0) ).
thf(2226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Oanalzp ) )
| ~ ( C @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ ( A @ c_Message_Oanalzp ) )
| ( B @ ( A @ c_Message_Oanalzp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(479,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( F @ ( A @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Oops__parts__spies_0) ).
thf(1866,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( F @ ( A @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(575,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(2071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(732,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).
thf(2406,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(118,axiom,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keymode_Osimps_I1_J_0) ).
thf(1062,plain,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(303,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1481,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(74,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(946,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(743,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I34_J_0) ).
thf(2431,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(1523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(726,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(2394,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(414,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__the__inv__into__f_0) ).
thf(1721,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(621,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ ( I @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( H @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS5_0) ).
thf(2174,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ ( I @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( H @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(724,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I8_J_0) ).
thf(2389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(1341,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(587,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).
thf(2098,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__image__eq_0) ).
thf(1639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(676,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(2290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__notin__image__shrK_0) ).
thf(2251,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(372,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(1629,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(2004,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(662,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(2262,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(580,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(2081,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(729,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).
thf(2399,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).
thf(2198,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(615,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I18_J_0) ).
thf(2162,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(763,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(598,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__insert_0) ).
thf(2120,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(539,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1994,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(552,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).
thf(2019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(546,axiom,
tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Fun_Oinj__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__shrK_0) ).
thf(2009,plain,
tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Fun_Oinj__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(476,axiom,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Server__not__bad_0) ).
thf(1861,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(283,axiom,
tc_bool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1440,plain,
tc_bool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(696,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( B @ c_Message_Oanalz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).
thf(2330,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( B @ c_Message_Oanalz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(648,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
| ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(2230,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
| ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(224,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1309,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).
thf(1614,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(738,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(2421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(499,axiom,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__Key__image__eq_0) ).
thf(1908,plain,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(642,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(2218,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_Message_Oagent_OSpy )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Gets_0) ).
thf(1642,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_Message_Oagent_OSpy )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(682,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(2302,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(348,axiom,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Hash__notin__image__Key_0) ).
thf(1578,plain,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).
thf(2385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(1097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(332,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( H @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OCrypt ) @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).
thf(1546,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( H @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OCrypt ) @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).
thf(1625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(25,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(818,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(867,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(716,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__HPair_0) ).
thf(2374,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( D @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__image__eq_1) ).
thf(1348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( D @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(675,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(2287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(317,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).
thf(1512,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).
thf(1774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(612,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__neq__HPair_0) ).
thf(2155,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(658,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(2255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(1303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).
thf(1527,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(392,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Agent__synth_0) ).
thf(1673,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).
thf(790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(565,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(2050,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__into__used_0) ).
thf(1480,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(455,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
| ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(1816,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
| ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(1657,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__eq__MPair_0) ).
thf(1335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(340,axiom,
( ( v_x @ c_NS__Shared__Mirabelle_Ons__sharedp )
= ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_x @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp__ns__shared__eq_0) ).
thf(1561,plain,
( ( v_x @ c_NS__Shared__Mirabelle_Ons__sharedp )
= ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_x @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1789,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(712,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(2366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(171,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(1197,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(828,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I5_J_0) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(560,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).
thf(2040,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(584,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(2091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(731,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
| ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__into_0) ).
thf(2404,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
| ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(2223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(553,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_OFake_0) ).
thf(2021,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).
thf(1742,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(928,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(244,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symKey__neq__priEK_0) ).
thf(1352,plain,
! [A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(532,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(1261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Hash_0) ).
thf(1268,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XrangeE__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeE_0) ).
thf(1532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XrangeE__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(1378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OInj_0) ).
thf(1550,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(90,axiom,
c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keymode_Osimps_I2_J_0) ).
thf(992,plain,
c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Hash__synth_0) ).
thf(1713,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_OHPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_HPair__synth__analz_1) ).
thf(1902,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_OHPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(1120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(715,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__analzD_0) ).
thf(2372,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(509,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).
thf(1930,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
| ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(706,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ hAPP ) )
= ( B @ ( C @ ( D @ ( A @ ( D @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
| ( C @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_2) ).
thf(2353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ hAPP ) )
= ( B @ ( C @ ( D @ ( A @ ( D @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
| ( C @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).
thf(1537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).
thf(1582,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(664,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).
thf(2265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_initState__into__used_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(506,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ( A
= ( D @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__Server__message__form_1) ).
thf(1923,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
| ( A
= ( D @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma1_0) ).
thf(1597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(1880,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__used_0) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(667,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).
thf(2270,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
= ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Key_0) ).
thf(1621,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).
thf(803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(518,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).
thf(1945,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(745,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
!= ( B @ ( c_Public_OshrK @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_priEK__noteq__shrK_0) ).
thf(2436,plain,
! [B: $i,A: $i] :
( ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
!= ( B @ ( c_Public_OshrK @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_evs @ c_in ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(755,plain,
tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_evs @ c_in ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(751,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(2453,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(619,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(2170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(501,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insertI_0) ).
thf(1912,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(623,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(2177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(481,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
| ( ( A @ ( c_Message_OinvKey @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__K_0) ).
thf(1870,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
| ( ( A @ ( c_Message_OinvKey @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__notin__image__publicKey_0) ).
thf(1331,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(362,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS4_0) ).
thf(1606,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
| ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
| ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(517,axiom,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__shrK_0) ).
thf(1944,plain,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= D )
| ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).
thf(1367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= D )
| ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(637,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(2206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__image__eq_0) ).
thf(1737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olength__unique ) )
= ( C @ ( B @ c_List_Olength__unique ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_0) ).
thf(1681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olength__unique ) )
= ( C @ ( B @ c_List_Olength__unique ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).
thf(1848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(569,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__Un_0) ).
thf(2059,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(630,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__synth_0) ).
thf(2191,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
| ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__MPair_0) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
!= ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__inject_1) ).
thf(1449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
!= ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(2590,plain,
$false,
inference(e,[status(thm)],[892,1665,1586,1469,1823,1633,2263,1315,2427,1179,1818,1956,1110,1879,1718,2094,1411,2336,2131,1454,2031,1559,1105,2412,1237,977,1211,2309,1005,2381,2062,1401,1939,1544,2282,878,1692,1305,861,2363,1855,1443,1808,2114,1142,1971,1793,1078,1608,1137,2035,1735,2184,2448,2141,2434,1233,1327,1988,1954,1354,2195,1705,1756,1310,1164,2316,2168,1260,1761,913,1507,930,1095,1746,1001,2046,1914,1243,1441,841,1046,1613,2010,2082,2067,1803,1887,1650,1645,1921,1724,1475,2136,1904,1518,1265,1228,1254,1287,1709,2328,1985,1660,838,1826,1313,1577,2126,2356,1055,1409,2339,785,2274,917,1462,1132,1800,1892,1087,1147,1013,1115,1568,2158,1494,1100,1247,2049,969,1572,1362,1963,1875,1778,2007,2222,756,2324,1373,1828,1151,1020,2034,2335,821,2017,1489,1415,2105,1811,1418,2236,1858,1864,1283,2073,766,1169,2281,1447,1072,1394,2002,1433,849,1696,1975,2242,988,2103,1405,1943,1201,1863,1604,1206,942,2204,1438,925,2118,810,1338,2047,1915,1783,2000,798,1199,2364,1153,761,2232,2296,2307,1768,1868,1274,1042,1580,1487,815,2396,2015,1387,1900,910,957,1223,825,1343,2249,778,1570,1174,1676,2133,1502,1751,788,1619,2150,1370,1423,2445,1365,1968,1555,1296,1624,2200,757,974,1938,847,1032,1602,1687,1457,889,2179,1836,1787,1027,2213,2211,1407,2344,2313,1128,1634,1392,2228,2112,1291,1740,1910,1402,1541,1983,2100,948,1856,1425,869,1360,1350,1936,1592,2300,874,1143,2115,1270,1851,1794,1017,980,1498,783,1118,1329,1160,2023,1964,933,1182,1584,1700,1214,2108,2085,1889,1039,901,1075,1791,2172,2317,1155,1744,1249,1297,2304,1552,1947,1429,1715,1979,2272,1825,1324,1776,1263,997,2450,1588,1530,1539,1456,1382,2387,1831,1231,1668,1974,1192,1932,1060,1050,2052,1599,1627,2370,1525,1333,1814,1241,2043,1695,1563,1846,2076,2368,2402,2408,1515,1895,2189,2423,1991,1318,773,2338,1996,2121,1906,965,2176,2292,2391,1698,2253,1483,1548,2028,2376,1631,2260,904,1833,1884,1125,1535,2398,1520,1226,1652,1929,1139,2193,936,2326,1312,1733,1107,2442,1092,2425,1258,1464,1224,1707,2293,1239,1997,2166,1090,2457,919,2148,2358,1356,1194,1209,831,1853,1282,2383,2415,1574,1771,880,1122,1376,1307,863,2361,2311,2257,990,2284,2378,1690,2182,1557,2129,2267,1162,1149,915,1381,1952,1112,1667,2180,1877,1471,2261,1821,1731,2410,1838,1293,2278,1926,2350,1594,768,1176,986,1477,2101,851,922,1805,2069,983,2075,2418,1841,1396,2439,1044,1245,1445,1528,2139,883,2064,1015,2244,1435,1726,1250,1496,2303,1413,2054,1873,944,1467,795,2037,1684,1134,1509,1081,2202,939,1958,754,823,836,1049,1034,2239,1662,2096,1758,1166,1277,2124,2234,2333,1145,1025,1070,1611,2060,1647,1780,1753,2160,1798,2298,1003,1770,1566,2143,2012,1941,954,1252,2454,2165,1186,1785,2429,1235,1763,1679,1130,907,1711,1053,1300,1452,1637,2276,2219,1658,2322,951,808,1285,1218,1934,1766,1981,1023,1221,2145,1504,1585,1008,859,2056,1358,1898,1257,1702,2379,1485,2320,1506,1749,1427,1670,1797,1881,1272,2266,876,2088,1459,1966,1685,1553,1949,1844,2215,1126,771,1421,2013,1918,1316,1084,2078,1321,1834,2347,1654,1216,2209,2187,1189,2110,1010,1390,2342,1289,844,2226,1866,2071,1590,2406,1062,1481,946,2431,1523,2394,813,1385,1721,2174,2389,1341,2098,1674,1639,2290,2251,1629,2004,995,2262,1030,2081,2399,2198,2162,763,899,2120,1994,2019,2009,1861,1440,2330,2230,1893,1309,1614,2421,800,1908,2218,1642,2302,1280,1578,2385,1097,1546,1625,818,867,2374,1348,999,2287,1512,1774,2155,2255,833,967,854,1303,1527,1673,790,2050,865,1480,1816,1657,1335,1561,1789,2366,1197,828,1065,2040,1172,897,2091,2404,2223,960,1473,2021,1346,886,1742,928,1352,1977,1261,1268,1532,1378,1550,992,1713,1902,871,1120,2372,1930,2353,1384,1537,1582,2265,1500,1923,1597,1880,1431,2270,1621,803,1945,2436,775,755,2453,2170,1912,2177,1870,1331,1606,1944,1367,2206,1737,1681,1184,1848,2059,2191,1204,1449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV732-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/0.42 % Computer : n026.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 14:54:40 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.67/0.74 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.01 % [INFO] Parsing done (271ms).
% 1.26/1.02 % [INFO] Running in sequential loop mode.
% 2.45/1.26 % [INFO] eprover registered as external prover.
% 2.45/1.27 % [INFO] Scanning for conjecture ...
% 3.16/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 751 axioms. Running axiom selection ...
% 4.12/1.66 % [INFO] Axiom selection finished. Selected 749 axioms (removed 2 axioms).
% 5.34/1.96 % [INFO] Problem is propositional (TPTP CNF).
% 5.34/1.99 % [INFO] Type checking passed.
% 5.34/1.99 % [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 ...
% 17.39/5.00 % External prover 'e' found a proof!
% 17.39/5.00 % [INFO] Killing All external provers ...
% 17.39/5.01 % Time passed: 4492ms (effective reasoning time: 3980ms)
% 17.39/5.01 % Axioms used in derivation (749): cls_Key__image__eq_0, cls_synth_OHash_0, cls_shrK__in__initState_0, cls_Int__absorb2_0, cls_subset__insert_1, cls_Diff__iff_2, cls_append__in__lists__conv_2, 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_inf__sup__absorb_0, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_inf__sup__aci_I2_J_0, cls_Crypt__notin__initState_0, cls_parts_OBody_0, cls_msg_Osimps_I47_J_0, cls_MPair__synth__analz_0, cls_symKeys__invKey__iff_0, cls_sup__ge1_0, cls_Un__subset__iff_0, cls_order__eq__iff_0, cls_A__trusts__NS2_0, cls_parts__partsD_0, cls_equalityI_0, cls_fun__diff__def__raw_0, cls_insert__inter__insert_0, cls_sup__top__left_0, cls_insertE_0, cls_knows__Spy__Gets_0, cls_parts_OInj_0, cls_parts_OFst_0, cls_Un__Diff_0, cls_privateKey__image__eq_1, cls_MPair__used_0, cls_Cons__eq__append__conv_5, cls_fun__upd__image_1, cls_pushes_I9_J_0, cls_subset__image__iff_2, cls_the__inv__f__f_0, cls_initState__subset__knows_0, cls_inj__image__eq__iff_0, cls_range__ex1__eq_3, cls_image__mono_0, cls_insert__code_1, cls_le__funD_0, cls_inj__on__image__iff_4, cls_knows__Notes_0, cls_range__ex1__eq_0, cls_set__ConsD_0, cls_synth__analz__mono_0, cls_append__self__conv_0, cls_HPair__eq_0, cls_inj__on__image__Int_0, cls_fun__upd__apply_1, clsarity_nat__Lattices_Odistrib__lattice, cls_list_Oinject_0, cls_parts__image__Key_0, cls_analz__subset__iff_1, clsarity_bool__Lattices_Olower__semilattice, cls_knows__Says_0, cls_le__iff__inf_1, 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, clsarity_fun__Orderings_Oorder, cls_analz__cong_0, cls_image__Int_0, cls_UnCI_1, cls_Says__imp__used_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_vimage__Diff_0, cls_analz__image__freshK__simps_I56_J_0, cls_Diff__Un_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_not__Cons__self2_0, cls_Int__subset__iff_2, cls_le__inf__iff_1, clsarity_bool__HOL_Ominus, cls_cert__A__form_0, cls_ns__sharedp_ONS4_0, cls_the__inv__into__onto_0, cls_Diff__subset__conv_0, cls_msg_Osimps_I34_J_0, cls_Int__Un__distrib2_0, cls_mem__def_1, cls_msg_Osimps_I49_J_0, clsarity_nat__Orderings_Olinorder, cls_msg_Osimps_I6_J_1, cls_Says__imp__parts__knows__Spy_0, cls_analz__subset__parts_0, cls_HPair__def_0, cls_Fake__parts__insert_0, cls_ns__shared_OOops_0, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_inf1E_1, 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_sup__inf__distrib2_0, cls_Gets__imp__knows__agents_0, cls_le__sup__iff_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_inf__sup__distrib1_0, cls_vimage__UNIV_0, cls_self__append__conv_0, cls_inj__transfer_1, cls_Crypt__synth__analz_0, cls_Int__absorb1_0, cls_knows__subset__knows__Says_0, cls_same__append__eq_0, clsarity_fun__Lattices_Oupper__semilattice, cls_inj__image__subset__iff_0, cls_Nonce__supply1_0, cls_HPair__eq__MPair_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_msg_Osimps_I3_J_0, cls_append__Cons_0, cls_distinct_Osimps_I2_J_0, cls_ns__sharedp_ONS2_0, cls_inj__image__mem__iff_0, cls_subset__insert__iff_2, cls_publicKey__into__used_0, cls_Key__synth__eq_1, cls_inj__on__image__iff_5, 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_analz__image__freshK__lemma_4, cls_inf__commute_0, cls_lists_ONil_0, cls_ns__sharedp_OOops_0, cls_analz__image__freshK__simps_I61_J_0, clsarity_fun__Orderings_Otop, cls_ns__sharedp_OFake_0, cls_f__inv__into__f_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_le__iff__sup_1, cls_pushes_I11_J_0, cls_le__supI_0, cls_Un__subset__iff_1, cls_append1__eq__conv_1, cls_parts__increasing_0, cls_Un__Int__distrib2_0, cls_append__eq__append__conv2_4, cls_inf__fun__eq_0, cls_analz__Crypt__if_1, cls_knows__Spy__Notes_1, cls_Hash__notin__image__Key_0, cls_invKey__image__eq_1, cls_HPair__eq__MPair_2, cls_synth__synthD_0, cls_order__eq__refl_0, cls_msg_Osimps_I7_J_0, cls_rangeI_0, cls_parts__subset__iff_1, cls_rev__image__eqI_0, cls_inj__on__insert_0, cls_privateKey__notin__image__publicKey_0, cls_distinct_Osimps_I2_J_1, cls_f__the__inv__into__f_0, cls_ns__shared_ONS4_0, cls_shrK__notin__image__publicKey_0, cls_analz__cut_0, cls_in__parts__UnE_0, cls_keymode_Oinduct_0, cls_le__supE_1, cls_fun__upd__other_0, cls_le__iff__sup_0, cls_publicKey__inject_0, cls_distinct_Osimps_I1_J_0, cls_HPair__eq_1, cls_the__inv__into__into_0, cls_insert__ident_0, cls_in__set__conv__decomp__last_2, cls_inv__f__eq_0, cls_Un__UNIV__right_0, cls_Un__absorb2_0, cls_used__nil__subset_0, cls_inv__image__comp_0, clsarity_bool__Orderings_Oorder, cls_inf__sup__aci_I8_J_0, cls_lemma1_0, cls_Key__not__used_0, cls_parts__mono_0, cls_synth_OMPair_0, cls_vimageI_0, cls_parts__insert__MPair_0, cls_symKeys__invKey__iff_1, cls_Nil__is__append__conv_0, cls_pushes_I4_J_0, cls_append__Nil2_0, cls_Un__upper2_0, cls_remdups_Osimps_I2_J_0, cls_parts__knows__Spy__subset__used_0, cls_UnCI_0, cls_Int__insert__right_1, cls_msg_Osimps_I44_J_0, cls_analz__subset__iff_0, cls_append__self__conv2_0, cls_remdups__id__iff__distinct_0, cls_inf__top__right_0, cls_privateKey__notin__image__shrK_0, cls_self__append__conv2_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_Diff__idemp_0, cls_inj__shrK_0, cls_event_Osimps_I6_J_0, cls_pushes_I5_J_0, cls_self__append__conv2_1, cls_analz__mono__contra_I3_J_0, cls_event_Osimps_I9_J_0, cls_Spy__spies__bad__privateKey_0, cls_ns__shared_ONil_0, cls_rangeE_0, cls_inf__eq__top__eq1_0, cls_inv__into__image__cancel_0, cls_msg_Osimps_I40_J_0, cls_range__ex1__eq_2, cls_Spy__spies__bad__shrK_0, cls_symKey__neq__priEK_0, cls_distinct__append_0, cls_parts__Un_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_pushes_I8_J_0, cls_inv__into__f__f_0, cls_append__Nil_0, cls_in__lists__conv__set_0, clsarity_bool__Lattices_Oupper__semilattice, cls_msg_Osimps_I43_J_0, cls_event_Osimps_I3_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_vimage__Un_0, cls_msg_Osimps_I14_J_0, cls_append__is__Nil__conv_2, cls_synth__analz__insert__eq_0, cls_analz__conj__parts_0, cls_inf__absorb2_0, cls_keysFor__insert__MPair_0, 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_inf__sup__ord_I2_J_0, cls_cert__A__form_1, cls_fun__upd__triv_0, cls_Fake__analz__insert_0, cls_sup__commute_0, cls_sym__shrK_0, cls_inj__on__image__iff_2, cls_knows__Gets_0, cls_agent_Osimps_I4_J_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Spy__see__shrK_0, cls_new__keys__not__used_0, clsarity_nat__Lattices_Olower__semilattice, cls_inj__image__subset__iff_1, cls_msg_Osimps_I7_J_1, cls_list__inter__conv_0, cls_inf__sup__aci_I3_J_0, cls_Says__Server__message__form_2, cls_analz_OFst_0, cls_set__eq__subset_2, cls_parts__insert__subset__Un_0, cls_Un__mono_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_analz_OInj_0, cls_linorder__linear_0, cls_parts__insertI_0, cls_inj__on__inv__into_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_inj__on__the__inv__into_0, cls_Nonce__synth__eq_1, clsarity_fun__Lattices_Olattice, cls_HPair__synth__analz_0, cls_Int__assoc_0, cls_analz__parts_0, cls_inj__on__image__iff_6, cls_order__antisym_0, cls_order__trans_0, cls_ns__sharedp__ns__shared__eq_0, cls_pushes_I12_J_0, cls_subset__trans_0, cls_double__diff_0, cls_msg_Osimps_I4_J_0, cls_self__append__conv_1, cls_keysFor__insert__HPair_0, cls_MPair__eq__HPair_0, cls_pushes_I2_J_0, cls_not__Cons__self_0, cls_inf__le2_0, cls_analz__image__freshK__lemma_3, cls_insertI1_0, cls_DiffI_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_sup__assoc_0, cls_list__inter_Osimps_I1_J_0, cls_Diff__Int__distrib2_0, cls_analz__Crypt__if_0, cls_le__sup__iff_1, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, 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_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_insert__Diff1_0, cls_Nil__is__append__conv_1, cls_msg_Osimps_I16_J_0, cls_msg_Osimps_I35_J_0, cls_fun__upd__twist_0, cls_event_Osimps_I2_J_1, cls_append__assoc_0, cls_ns__shared_OFake_0, cls_inf__sup__aci_I1_J_0, cls_Un__absorb1_0, cls_synth__Un_0, cls_parts__cut_0, cls_analz__image__freshK__simps_I57_J_0, cls_sup__least_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_top__greatest_0, cls_sup__top__right_0, cls_shrK__notin__image__privateKey_0, cls_sup1E_0, cls_distrib__inf__le_0, cls_Int__commute_0, cls_Un__UNIV__left_0, cls_subset__refl_0, cls_vimage__subsetI_0, cls_analz__Un_0, cls_append__in__lists__conv_0, cls_not__symKeys__priK_0, cls_Spy__in__bad_0, cls_image__Un_0, cls_image__diff__subset_0, cls_publicKey__notin__image__shrK_0, cls_Int__Diff_0, cls_sup1CI_1, cls_insertCI_0, cls_msg_Osimps_I42_J_0, cls_fun__upd__apply_0, cls_image__Int__subset_0, cls_le__inf__iff_2, cls_vimage__Int_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_Crypt__synth__analz_1, clsarity_nat__Lattices_Olattice, cls_UNIV__I_0, cls_DiffE_0, cls_HPair__synth__analz_1, cls_msg_Osimps_I13_J_0, cls_image__iff_2, cls_Notes__imp__knows__Spy_0, cls_le__infE_0, cls_image__set__diff_0, cls_Crypt__synth__eq_0, cls_spies__pubK_0, cls_analzp_OSnd_0, cls_invKey__K_0, cls_Un__Diff__cancel_0, cls_analz__spies__pubK_0, cls_order__eq__iff_2, cls_le__infI1_0, cls_Fake__analz__eq_0, cls_inf__assoc_0, cls_event_Osimps_I1_J_1, cls_analz__mono__contra_I2_J_0, cls_inj__vimage__image__eq_0, cls_analz__insert__HPair_0, cls_Int__UNIV__right_0, cls_priK__in__initState_0, cls_Un__Diff__cancel2_0, cls_list__inter_Osimps_I2_J_0, cls_distinct__append_1, cls_top1I_0, cls_event_Osimps_I7_J_0, cls_Int__absorb_0, cls_parts__insert__Hash_0, cls_Int__lower2_0, cls_Notes__imp__used_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_publicKey__neq__privateKey_0, cls_in__lists__conv__set_1, 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_inj__on__fun__updI_0, cls_Diff__Int__distrib_0, cls_Diff__mono_0, cls_publicKey__image__eq_2, cls_inf__eq__top__eq2_0, cls_UnE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_vimage__mono_0, cls_Int__left__absorb_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_order__antisym__conv_0, cls_msg_Osimps_I18_J_0, cls_distinct_Osimps_I2_J_2, cls_parts__analz_0, cls_event_Osimps_I2_J_0, cls_neq__shrK_0, cls_usedI_0, cls_analz__analzD_0, cls_invKey__eq_0, cls_Un__Int__distrib_0, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_Int__lower1_0, cls_parts__trans_0, cls_set__remdups_0, clsarity_bool__Lattices_Olattice, cls_keysFor__insert__Agent_0, cls_event_Osimps_I4_J_0, cls_Spy__see__shrK_1, cls_Int__subset__iff_0, 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_analz__insert__MPair_0, cls_eq__eqI_0, cls_msg_Osimps_I30_J_0, cls_parts__insert__Key_0, cls_vimage__eq_1, 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_vimageE_0, cls_parts__Un__subset2_0, cls_insert__subset_2, cls_inf1I_0, cls_le__supI1_0, cls_le__eqI_0, cls_sup__left__idem_0, cls_inj__on__image__iff_7, cls_keymode_Osimps_I2_J_0, cls_inf__idem_0, clsarity_fun__Lattices_Obounded__lattice, cls_Spy__analz__shrK_0, cls_subsetD_0, cls_Key__synth_0, cls_Int__left__commute_0, cls_le__sup__iff_2, 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_fun__upd__idem_0, cls_fun__diff__def_0, cls_set__append_0, cls_sup__inf__absorb_0, cls_xt1_I6_J_0, cls_event_Osimps_I8_J_0, cls_Un__Int__assoc__eq_1, cls_analz__mono__contra_I1_J_0, cls_fun__upd__idem__iff_0, cls_insert__absorb2_0, cls_inj__on__image__iff_1, cls_analz__mono_0, cls_Crypt__synth_0, cls_inf__sup__aci_I4_J_0, cls_analz_OSnd_0, cls_Crypt__imp__keysFor_0, cls_append__is__Nil__conv_1, cls_Nonce__synth__eq_0, cls_Int__iff_2, cls_vimage__code_1, cls_priEK__noteq__shrK_0, cls_analz__synth_0, cls_event_Osimps_I1_J_2, cls_the__inv__into__f__eq_0, cls_Nonce__synth_0, cls_inf__greatest_0, cls_analz__insert__eq_0, cls_parts__insert__Nonce_0, cls_synth__subset__iff_0, cls_Un__left__absorb_0, cls_msg_Osimps_I5_J_0, cls_Crypt__notin__image__Key_0, cls_inv__into__injective_0, cls_analz__analz__Un_0, cls_keymode_Osimps_I1_J_0, cls_Cons__eq__appendI_0, cls_event_Osimps_I1_J_0, cls_IntI_0, cls_inj__transfer_0, cls_Crypt__synth_1, cls_ns__shared_ONS3_0, cls_le__iff__inf_0, cls_Hash__synth_0, clsarity_nat__Lattices_Oupper__semilattice, cls_MPair__synth_0, cls_append__is__Nil__conv_0, cls_msg_Osimps_I17_J_0, cls_eq__eqI_1, cls_knows__subset__knows__Notes_0, cls_Diff__Int_0, cls_append__eq__appendI_0, cls_subset__inj__on_0, cls_initState__into__used_0, cls_parts__Un__subset1_0, cls_subset__insert_0, cls_sup__idem_0, cls_msg_Osimps_I41_J_0, cls_Cons__eq__append__conv_4, cls_inf__sup__ord_I3_J_0, cls_msg_Osimps_I32_J_0, cls_fun__upd__same_0, cls_append__in__lists__conv_1, cls_inf__sup__aci_I5_J_0, cls_keysFor__parts__insert_0, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_HPair__synth__analz_2, cls_privateKey__image__eq_0, cls_msg_Osimps_I31_J_0, cls_analz__increasing_0, cls_distinct__remdups_0, cls_vimageI2_0, clsarity_fun__Orderings_Opreorder, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_inj__on__image__iff_3, cls_IntE_1, cls_analz__image__Key_0, cls_IntE_0, cls_Un__least_0, cls_ns__shared_ONS2_0, cls_inj__on__contraD_0, cls_sup1CI_0, cls_Int__greatest_0, cls_inj__onD_0, cls_Oops__parts__spies_0, cls_shrK__neq__pubK_0, cls_not__symKeys__pubK_0, cls_sup__ge2_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_Nil__is__append__conv_2, clsarity_bool__Lattices_Odistrib__lattice, cls_ns__shared_ONS5_0, cls_le__infE_1, cls_parts__idem_0, cls_in__lists__conv__set_2, cls_ns__sharedp_ONS5_0, cls_image__eqI_0, cls_the__inv__into__f__f_0, cls_subset__UNIV_0, cls_analz__insertI_0, cls_image__subset__iff_0, cls_inf__le1_0, cls_inf__left__idem_0, cls_knows__Spy__subset__knows__Spy__Says_0, cls_lemma2_0, cls_Int__UNIV__left_0, cls_inj__on__diff_0, cls_inv__into__into_0, cls_insertCI_1, cls_range__ex1__eq_1, cls_invKey_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_Diff__subset__conv_1, cls_insert__code_0, cls_le__eqI_1, cls_vimageD_0, cls_analz__trans_0, cls_used__Gets_0, cls_Diff__Int2_0, cls_Nonce__notin__initState_0, cls_DiffE_1, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_inj__on__image__iff_0, cls_inv__f__f_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_Diff__partition_0, cls_le__infI2_0, cls_insert__image_0, cls_shrK__image__eq_0, cls_msg_Osimps_I10_J_0, cls_inj__on__Un_1, cls_sup__inf__distrib1_0, cls_Un__Int__assoc__eq_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_fun__upd__upd_0, cls_Hash__synth__analz_1, cls_list__inter_Osimps_I2_J_1, cls_image__vimage__eq_0, cls_analz__Decrypt_H_0, cls_inf__top__left_0, 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_Says__Server__message__form_0, cls_Agent__neq__HPair_0, clsarity_fun__Lattices_Odistrib__lattice, clsarity_fun__HOL_Ominus, cls_event_Osimps_I5_J_0, cls_sup__absorb1_0, cls_privateKey__into__used_0, cls_MPair__synth__analz_1, clsarity_nat__Orderings_Oorder, cls_remdups__eq__nil__iff_0, cls_Nonce__Key__image__eq_0, cls_knows__Spy__Notes_0, cls_priK__neq__shrK_0, cls_parts__synth_0, cls_invKey__image__eq_0, cls_analz__image__freshK__lemma_1, cls_equalityE_0, cls_msg_Osimps_I37_J_0, cls_publicKey__inject_1, cls_inf__sup__distrib2_0, cls_MPair__eq__HPair_2, cls_imageI_0, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_parts__insert__Crypt_0, cls_Hash__neq__HPair_0, cls_ns__sharedp_ONS1_0, cls_msg_Osimps_I33_J_0, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_synth__cut_0, cls_analz__insert__Nonce_0, cls_Notes__imp__knows_0, cls_msg_Osimps_I11_J_0, cls_image__inv__f__f_0, cls_subset__insert__iff_1, cls_Crypt__imp__invKey__keysFor_0, cls_pushes_I6_J_0, clsarity_bool__Orderings_Otop, cls_publicKey__in__initState_0, cls_publicKey__image__eq_1, cls_synth__mono_0, cls_inv__into__f__eq_0, cls_remdups_Osimps_I2_J_1, cls_Int__insert__right_0, cls_Diff__subset_0, cls_analz__into__parts_0, cls_predicate1D_0, cls_inf1E_0, cls_synth_OAgent_0, cls_fun__upd__idem__iff_1, cls_analz__insert_0, clsarity_nat__HOL_Ominus
% 17.39/5.01 % No. of inferences in proof: 1507
% 17.39/5.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4492 ms resp. 3980 ms w/o parsing
% 21.68/5.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.68/5.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------