TSTP Solution File: SWV727-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV727-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:18:04 EDT 2023
% Result : Unsatisfiable 10.19s 3.18s
% Output : Refutation 10.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 550
% Syntax : Number of formulae : 1042 ( 411 unt; 59 typ; 0 def)
% Number of atoms : 1811 ( 528 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12890 ( 848 ~; 828 |; 0 &;11214 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 59 usr; 16 con; 0-4 aty)
% Number of variables : 2842 ( 0 ^;2842 !; 0 ?;2842 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_K_type,type,
v_K: $i ).
thf(c_Message_OsymKeys_type,type,
c_Message_OsymKeys: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(v_evsf_type,type,
v_evsf: $i ).
thf(c_NS__Shared__Mirabelle_Ons__shared_type,type,
c_NS__Shared__Mirabelle_Ons__shared: $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
thf(v_X_type,type,
v_X: $i ).
thf(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
thf(c_Event_Oknows_type,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
thf(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
thf(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_Message_Omsg_OHash_type,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Message_OHPair_type,type,
c_Message_OHPair: $i > $i > $i ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Event_Oevent_OGets_type,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_Event_Oevent_ONotes_type,type,
c_Event_Oevent_ONotes: $i > $i > $i ).
thf(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
thf(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Public_OpublicKey_type,type,
c_Public_OpublicKey: $i > $i ).
thf(c_Event_Obad_type,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_Message_Osko__Message__Xanalz__insert__eq__I__1__1_type,type,
c_Message_Osko__Message__Xanalz__insert__eq__I__1__1: $i > $i > $i ).
thf(c_Event_OinitState_type,type,
c_Event_OinitState: $i > $i ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(c_Public_OshrK_type,type,
c_Public_OshrK: $i ).
thf(c_Public_Okeymode_OEncryption_type,type,
c_Public_Okeymode_OEncryption: $i ).
thf(c_Message_Osko__Message__Xparts__singleton__1__1_type,type,
c_Message_Osko__Message__Xparts__singleton__1__1: $i > $i > $i ).
thf(c_NS__Shared__Mirabelle_Ons__sharedp_type,type,
c_NS__Shared__Mirabelle_Ons__sharedp: $i > $o ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un_0) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(198,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(962,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(490,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ c_Public_OshrK @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__injective_0) ).
thf(1549,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ c_Public_OshrK @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(645,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(164,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(892,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__invKey__keysFor_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).
thf(909,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(477,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__parts_0) ).
thf(1522,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(438,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1443,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).
thf(655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(482,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1533,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(68,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(677,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(364,axiom,
! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).
thf(1305,plain,
! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(434,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1437,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(301,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__Un_0) ).
thf(1173,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(35,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).
thf(582,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cut_0) ).
thf(762,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Hash_0) ).
thf(1290,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(153,axiom,
! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).
thf(873,plain,
! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analzD_0) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__pubK_0) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).
thf(1260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_OFake_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( D = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_1) ).
thf(670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( D = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).
thf(538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth__analz_1) ).
thf(1354,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OHash_0) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(182,axiom,
! [A: $i] :
( ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat )
| ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_1) ).
thf(930,plain,
! [A: $i] :
( ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat )
| ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oused @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Gets_0) ).
thf(898,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oused @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1391,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(437,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_3) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_0) ).
thf(1359,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(59,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(651,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) @ tc_nat )
| ~ ( c_in @ D @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ C @ tc_Message_Omsg ) ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__parts__insert_0) ).
thf(829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) @ tc_nat )
| ~ ( c_in @ D @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ C @ tc_Message_Omsg ) ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Public_OshrK @ A )
!= ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__neq__shrK_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Public_OshrK @ A )
!= ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1046,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_2) ).
thf(565,plain,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(399,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__synth_0) ).
thf(1366,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_0) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(356,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1287,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(570,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1430,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat )
| ~ ( c_in @ B @ C @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_2) ).
thf(785,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat )
| ~ ( c_in @ B @ C @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oinsert @ A @ B @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Key__image_0) ).
thf(1323,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oinsert @ A @ B @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(471,axiom,
! [A: $i] :
( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
= ( c_Message_Osynth @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__idem_0) ).
thf(1511,plain,
! [A: $i] :
( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
= ( c_Message_Osynth @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__notin__image__publicKey_0) ).
thf(949,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(309,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1191,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).
thf(1462,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( hAPP @ c_Message_Omsg_OKey @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).
thf(1059,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( hAPP @ c_Message_Omsg_OKey @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(281,axiom,
! [B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__shrK_0) ).
thf(1132,plain,
! [B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(456,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1479,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert2_0) ).
thf(969,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth_0) ).
thf(770,plain,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Notes_0) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__into__used_0) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__analz__shrK_1) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).
thf(817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__cut_0) ).
thf(902,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(881,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(461,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(5,negated_conjecture,
~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oused @ v_evsf ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(492,plain,
~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oused @ v_evsf ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_1) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(441,axiom,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__increasing_0) ).
thf(1450,plain,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(591,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(381,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__partsD_0) ).
thf(1334,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_0) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__into__used_0) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__spies__pubK_0) ).
thf(1283,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(102,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(766,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(156,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(877,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq__I_1) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ~ ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).
thf(1072,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I4_J_0) ).
thf(1394,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg )
| ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).
thf(1526,plain,
! [C: $i,B: $i,A: $i] :
( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg )
| ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_4) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).
thf(1119,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__MPair_0) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Crypt_0) ).
thf(920,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).
thf(1438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_1) ).
thf(925,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_0) ).
thf(1306,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__see__shrK_1) ).
thf(1199,plain,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oparts @ B ) )
| ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oparts @ B ) )
| ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ B @ C )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ B @ C )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(451,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ B @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(1470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ B @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(368,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1311,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
| ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
| ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I47_J_0) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) )
!= ( hAPP @ c_Public_OshrK @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priEK__noteq__shrK_0) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) )
!= ( hAPP @ c_Public_OshrK @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(798,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut_0) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_1) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OInj_0) ).
thf(825,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(475,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(1519,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat )
| ~ ( c_in @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_2) ).
thf(1255,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat )
| ~ ( c_in @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).
thf(1174,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).
thf(1502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(401,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1370,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Hash_0) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(277,axiom,
! [A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKey__neq__priEK_0) ).
thf(1123,plain,
! [A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(148,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(862,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1217,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_0) ).
thf(598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(176,axiom,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__emptyE_0) ).
thf(916,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(398,axiom,
c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).
thf(1365,plain,
c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).
thf(879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__HPair_0) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth_0) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(78,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).
thf(710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).
thf(1012,plain,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).
thf(1106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).
thf(1296,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1,negated_conjecture,
c_in @ v_K @ c_Message_OsymKeys @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(493,plain,
c_in @ v_K @ c_Message_OsymKeys @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).
thf(1210,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(24,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_ONotes @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).
thf(551,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_ONotes @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).
thf(1128,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).
thf(1350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(330,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).
thf(1234,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth__analz_0) ).
thf(1534,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(1328,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).
thf(1121,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Message_Osko__Message__Xparts__singleton__1__1 @ A @ B ) @ A @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__singleton_0) ).
thf(1227,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Message_Osko__Message__Xparts__singleton__1__1 @ A @ B ) @ A @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__def_0) ).
thf(725,plain,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).
thf(980,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(426,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert_0) ).
thf(1425,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__trans_0) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(212,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(989,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(154,axiom,
! [B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__in__initState_0) ).
thf(874,plain,
! [B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OHash @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I38_J_0) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OHash @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__notin__image__shrK_0) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(395,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__insert_0) ).
thf(1361,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1292,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( C
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_0) ).
thf(554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( C
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq__I_0) ).
thf(1182,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Says_0) ).
thf(1414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(226,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth_0) ).
thf(1016,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(71,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).
thf(686,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).
thf(1099,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma1_0) ).
thf(1451,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(491,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ B ) )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ B ) )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(240,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1050,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ c_Public_OshrK @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__pubK_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ c_Public_OshrK @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(219,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
= ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__image__Key_0) ).
thf(1002,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
= ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(108,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__symKeys__priK_0) ).
thf(779,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(837,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).
thf(997,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ B ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ B ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).
thf(1478,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(444,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).
thf(1456,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__neq__HPair_0) ).
thf(1382,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(380,axiom,
! [A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).
thf(1333,plain,
! [A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(334,axiom,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__increasing_0) ).
thf(1241,plain,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).
thf(1170,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_0) ).
thf(1035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).
thf(1466,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).
thf(1187,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(473,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1515,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__neq__publicKey_0) ).
thf(1026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ B @ tc_nat )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__image__eq_0) ).
thf(1086,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ B @ tc_nat )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing__imp__Un_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(953,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).
thf(1185,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(794,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(586,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq_1) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(888,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(283,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).
thf(1135,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1146,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(856,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__see__shrK_0) ).
thf(1301,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).
thf(573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(200,axiom,
! [A: $i] : ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__shrK_0) ).
thf(965,plain,
! [A: $i] : ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1251,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).
thf(618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_0) ).
thf(819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(170,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).
thf(904,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__privateKey_0) ).
thf(772,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).
thf(743,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(415,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1403,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1520,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1226,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(138,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).
thf(843,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(428,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insertI_0) ).
thf(1428,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(936,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(333,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).
thf(1239,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1092,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing_0) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(325,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(392,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(1356,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ tc_Message_Oagent )
| ~ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_1) ).
thf(1271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ tc_Message_Oagent )
| ~ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(402,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I57_J_0) ).
thf(1371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(45,axiom,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey_0) ).
thf(611,plain,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(787,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(713,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(4,negated_conjecture,
~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ v_X @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(498,plain,
~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ v_X @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(704,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).
thf(1464,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ B @ C ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__knows__A_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ B @ C ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(132,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(831,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ A )
!= ( c_Message_Oanalz @ B ) )
| ( ( c_Message_Oanalz @ C )
!= ( c_Message_Oanalz @ D ) )
| ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cong_0) ).
thf(990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ A )
!= ( c_Message_Oanalz @ B ) )
| ( ( c_Message_Oanalz @ C )
!= ( c_Message_Oanalz @ D ) )
| ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(487,axiom,
! [B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).
thf(1542,plain,
! [B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).
thf(567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
= ( c_Message_OHPair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_2) ).
thf(737,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
= ( c_Message_OHPair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(764,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(681,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__trans_0) ).
thf(1408,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__neq__HPair_0) ).
thf(509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(237,axiom,
! [A: $i] :
( ( ( c_Message_OinvKey @ A )
= A )
| ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__K_0) ).
thf(1043,plain,
! [A: $i] :
( ( ( c_Message_OinvKey @ A )
= A )
| ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
!= ( hAPP @ c_Public_OshrK @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__priK_0) ).
thf(1376,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
!= ( hAPP @ c_Public_OshrK @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(436,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(858,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I45_J_0) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).
thf(1162,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(376,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1325,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(232,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1029,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(183,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(932,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(271,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(1112,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(6,negated_conjecture,
c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Set_Oinsert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(494,plain,
c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Set_Oinsert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ c_Message_OsymKeys @ tc_nat )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Decrypt_H_0) ).
thf(1080,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ c_Message_OsymKeys @ tc_nat )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I5_J_0) ).
thf(700,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ B @ tc_Message_Oagent )
| ~ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__image__eq_0) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ B @ tc_Message_Oagent )
| ~ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Key_0) ).
thf(959,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__neq__HPair_0) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(159,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(883,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(454,axiom,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__increasing_0) ).
thf(1477,plain,
! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(922,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(827,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(439,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(480,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).
thf(1113,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(563,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).
thf(1000,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).
thf(1435,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).
thf(722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__notin__image__shrK_0) ).
thf(1166,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_1) ).
thf(944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(424,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).
thf(1420,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insertI_0) ).
thf(1509,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(94,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(749,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__neq__privateKey_0) ).
thf(1472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
!= ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(663,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).
thf(548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
| ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).
thf(776,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
| ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(525,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(230,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1025,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OFst_0) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(292,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1156,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__parts__subset__parts_0) ).
thf(971,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__not__used_0) ).
thf(1531,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(263,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1098,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq_0) ).
thf(690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1516,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_5) ).
thf(1400,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(707,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(673,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__analz__shrK_0) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).
thf(502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(372,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(382,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__in__initState_0) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(344,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1262,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__notin__image__publicKey_0) ).
thf(1235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(485,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__into__used_0) ).
thf(1538,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(355,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1285,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_OinvKey @ A )
!= ( c_Message_OinvKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__eq_0) ).
thf(544,plain,
! [B: $i,A: $i] :
( ( ( c_Message_OinvKey @ A )
!= ( c_Message_OinvKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__trans_0) ).
thf(907,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono_0) ).
thf(1404,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).
thf(1543,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma2_0) ).
thf(1023,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_1) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(354,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1284,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_1) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OInj_0) ).
thf(978,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(3,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(497,plain,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_Message_Omsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(484,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1536,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( hAPP @ c_Message_Omsg_OKey @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).
thf(1506,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ A @ B )
!= ( hAPP @ c_Message_Omsg_OKey @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(468,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OInj_0) ).
thf(1504,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(84,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).
thf(727,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ C @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__image__Key_0) ).
thf(976,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ C @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(99,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(759,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).
thf(1010,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(269,axiom,
! [A: $i] :
( ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ~ ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_0) ).
thf(1108,plain,
! [A: $i] :
( ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ~ ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1316,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__HPair_0) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(293,axiom,
( ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__empty_0) ).
thf(1157,plain,
( ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(2,negated_conjecture,
c_in @ v_evsf @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(495,plain,
c_in @ v_evsf @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(420,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__idem_0) ).
thf(1412,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(440,axiom,
! [A: $i] :
( ( c_Message_OinvKey @ ( hAPP @ c_Public_OshrK @ A ) )
= ( hAPP @ c_Public_OshrK @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).
thf(1448,plain,
! [A: $i] :
( ( c_Message_OinvKey @ ( hAPP @ c_Public_OshrK @ A ) )
= ( hAPP @ c_Public_OshrK @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Osko__Message__Xparts__singleton__1__1 @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__singleton_1) ).
thf(1189,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Osko__Message__Xparts__singleton__1__1 @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(139,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pubK__neq__shrK_0) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Public_OshrK @ A )
!= ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(350,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I56_J_0) ).
thf(1276,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(377,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__analz_0) ).
thf(1326,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(246,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1062,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1481,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(265,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(336,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(781,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).
thf(995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(37,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).
thf(588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(197,axiom,
! [B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).
thf(961,plain,
! [B: $i,A: $i] : ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__keysFor_0) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
thf(1385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(199,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__idem_0) ).
thf(963,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I46_J_0) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OCrypt @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).
thf(1491,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__mono_0) ).
thf(1308,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(310,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(1193,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
| ( A = c_Message_Oagent_OSpy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
| ( A = c_Message_Oagent_OSpy ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(319,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
= ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__Key_0) ).
thf(1212,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
= ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat )
| ~ ( c_in @ A @ B @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__image__eq_1) ).
thf(1513,plain,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat )
| ~ ( c_in @ A @ B @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(684,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(667,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(388,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert_0) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(96,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(752,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(328,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_in @ E @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_in @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(489,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ A )
!= ( c_Message_Oanalz @ B ) )
| ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).
thf(1546,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ A )
!= ( c_Message_Oanalz @ B ) )
| ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Key_0) ).
thf(833,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
| ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OFst_0) ).
thf(854,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(433,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1436,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__HPair_0) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I44_J_0) ).
thf(506,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OMPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(419,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__synthD_0) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(74,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).
thf(696,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__spies_0) ).
thf(955,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(116,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__symKeys__pubK_0) ).
thf(796,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(532,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(161,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).
thf(886,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_2) ).
thf(928,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).
thf(987,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(390,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1352,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(347,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I39_J_0) ).
thf(1268,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( hAPP @ c_Message_Omsg_OKey @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).
thf(528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Notes_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(822,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Hash_0) ).
thf(850,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(152,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__notin__image__Key_0) ).
thf(871,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).
thf(607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OBody_0) ).
thf(1093,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(839,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).
thf(982,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(220,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1004,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(803,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(373,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Un_0) ).
thf(1320,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__mono_0) ).
thf(940,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(222,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1009,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).
thf(659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(560,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(639,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(97,axiom,
( ( c_Message_Oanalz @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__empty_0) ).
thf(755,plain,
( ( c_Message_Oanalz @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1088,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I11_J_0) ).
thf(1468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
= ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(7,negated_conjecture,
( ~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_nat )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oused @ v_evsf ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(496,plain,
( ~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_nat )
| ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oused @ v_evsf ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__image__eq_1) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg )
| ~ ( c_in @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1597,plain,
$false,
inference(cvc4,[status(thm)],[809,1337,1168,893,962,1179,1549,1110,645,892,1237,846,909,628,1406,1522,1443,741,655,1533,677,1305,1437,1173,582,762,730,1290,873,1205,1497,1426,1137,1310,1164,715,1260,1063,670,538,1354,1222,930,898,1391,1441,841,1359,1475,1265,1482,651,829,1095,973,1046,565,1366,1055,1287,570,1430,1298,785,1330,1323,1511,949,542,934,1191,1462,1059,1132,1379,1479,969,770,1115,1362,1232,817,902,1398,881,1489,492,789,1450,591,1373,1040,1418,1334,1020,966,1283,905,766,877,866,1072,1394,1526,998,1433,1201,1119,774,1104,1242,920,1438,925,1306,1199,1153,1338,1470,1311,1067,512,942,1047,798,1057,1387,957,746,825,1519,1255,1174,1502,1487,1370,815,1123,862,1217,598,1423,916,1032,1365,625,879,852,1457,522,1159,757,1281,710,1012,1106,1296,665,493,1210,551,1128,1350,1234,1534,1328,1121,1227,725,980,1425,869,783,989,874,1143,1540,1006,1493,884,1082,1361,1292,554,1182,642,1414,1214,1016,686,1075,1099,1451,1552,1050,984,1002,1246,779,622,837,1263,997,515,1150,1478,1456,1382,1333,1241,633,805,1170,1035,1466,1187,1515,1026,1086,938,953,1185,794,586,718,888,1278,1135,1146,1103,1273,856,1301,573,733,601,965,750,1251,618,819,904,694,1389,772,743,1403,1520,1226,843,1125,875,577,1428,1139,936,1312,1239,1092,1090,1224,1356,1271,1371,611,787,713,498,1258,704,1464,947,1194,900,831,1117,1524,990,1542,567,737,616,764,604,681,1408,509,1043,1376,1439,890,811,631,858,535,594,1162,1325,1029,1344,1460,932,1112,494,1080,848,700,520,1396,959,636,883,1176,1477,922,912,1171,768,827,1445,1528,1113,563,1000,1435,722,675,1166,944,1420,648,1509,749,1472,1018,836,1203,1208,663,548,776,525,557,580,1025,1070,1156,971,739,1368,1531,1484,1098,993,690,1516,1400,707,1053,673,791,1038,502,1317,1130,1336,1220,1262,1235,1538,951,1285,1218,544,907,1404,744,1543,1023,613,1284,864,978,497,1141,1536,1052,1506,1504,727,976,759,1010,1108,1316,1084,1157,1321,495,1412,1448,1189,844,1453,1276,1326,1062,1481,1101,1244,781,995,588,1253,961,813,1385,963,517,1341,896,1491,914,1308,1193,1077,1212,1513,684,800,667,1294,1133,1348,752,1229,1546,1148,1248,735,833,967,854,1303,1436,918,1495,506,807,1410,1197,696,955,1346,796,1363,1314,532,1065,886,928,987,1352,1268,860,596,528,1357,1500,822,850,871,607,1093,839,982,1431,1004,803,1320,940,1009,659,560,1416,639,755,1088,1468,496,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV727-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 03:06:43 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.90/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/1.12 % [INFO] Parsing done (224ms).
% 1.77/1.13 % [INFO] Running in sequential loop mode.
% 2.19/1.33 % [INFO] eprover registered as external prover.
% 2.19/1.33 % [INFO] cvc4 registered as external prover.
% 2.19/1.33 % [INFO] Scanning for conjecture ...
% 2.72/1.45 % [INFO] Found a conjecture and 486 axioms. Running axiom selection ...
% 3.09/1.57 % [INFO] Axiom selection finished. Selected 484 axioms (removed 2 axioms).
% 3.73/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 3.73/1.71 % [INFO] Type checking passed.
% 3.73/1.71 % [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 ...
% 10.19/3.18 % External prover 'cvc4' found a proof!
% 10.19/3.18 % [INFO] Killing All external provers ...
% 10.19/3.18 % Time passed: 2639ms (effective reasoning time: 2044ms)
% 10.19/3.18 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.19/3.18 % Axioms used in derivation (484): clsarity_nat__HOL_Oord, cls_Key__image__eq_0, cls_Crypt__notin__initState_0, cls_Diff__cancel_0, cls_synth_OHash_0, cls_shrK__in__initState_0, cls_subset__insert_1, cls_Diff__iff_2, cls_analz__image__freshK__lemma_5, cls_not__parts__not__analz_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_image__constant_0, cls_Un__Diff_0, cls_Un__subset__iff_0, cls_order__eq__iff_0, cls_parts__partsD_0, cls_MPair__used_0, cls_equalityI_0, cls_sup__top__left_0, cls_insertE_0, cls_knows__Spy__Gets_0, cls_parts_OInj_0, cls_parts_OFst_0, cls_knows__Notes_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_synth__analz__mono_0, cls_initState__subset__knows_0, cls_HPair__eq_0, cls_used__Says_0, cls_empty__is__image_1, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_sup__bot__right_0, cls_insert__code_1, cls_list_Oinject_0, cls_parts__image__Key_0, cls_analz__subset__iff_1, cls_knows__Says_0, cls_analz__image__freshK__simps_I56_J_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_analz__cong_0, cls_UnCI_1, cls_msg_Osimps_I6_J_1, cls_insert__absorb_0, cls_used__Notes_0, cls_Diff__subset__conv_0, cls_Fake__parts__insert_0, cls_mem__def_1, cls_msg_Osimps_I49_J_0, clsarity_nat__Orderings_Olinorder, cls_analz__subset__parts_0, cls_HPair__def_0, cls_empty__iff_0, cls_not__Cons__self2_0, cls_MPair__eq__HPair_1, cls_msg_Osimps_I45_J_0, cls_insert__iff_1, cls_Crypt__synth__eq_1, cls_Crypt__synth__analz_0, cls_knows__subset__knows__Says_0, clsarity_fun__Lattices_Oupper__semilattice, cls_le__sup__iff_0, cls_knows__subset__knows__Cons_0, cls_analz__idem_0, cls_insert__subset_0, cls_HPair__eq__MPair_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_analz__image__freshK__lemma_4, cls_subset__insert__iff_2, cls_publicKey__into__used_0, cls_Key__synth__eq_1, cls_parts__empty_0, cls_synth__insert_0, cls_shrK__in__knows_0, cls_shrK__image__eq_1, cls_analz__image__freshK__lemma_2, cls_analz__insert__Hash_0, cls_analz__image__freshK__simps_I61_J_0, clsarity_fun__Orderings_Otop, cls_ns__sharedp_OFake_0, cls_Un__left__commute_0, cls_Key__image__eq_1, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_keysFor__insert__Hash_0, cls_synth_OCrypt_0, cls_parts__increasing_0, cls_analz__image__freshK__simps_I65_J_0, cls_parts__insert__HPair_0, cls_analz__Crypt__if_1, cls_pushes_I11_J_0, cls_HPair__eq__MPair_2, cls_le__supI_0, cls_Un__subset__iff_1, cls_Un__empty_2, cls_le__iff__sup_1, cls_knows__Spy__Notes_1, cls_Hash__notin__image__Key_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_privateKey__notin__image__publicKey_0, clsarity_fun__Orderings_Obot, cls_Diff__UNIV_0, cls_le__supE_1, cls_empty__is__image_0, cls_synth__synthD_0, cls_shrK__notin__image__publicKey_0, cls_analz__cut_0, cls_in__parts__UnE_0, cls_le__iff__sup_0, cls_publicKey__inject_0, cls_HPair__eq_1, cls_Fake__parts__sing__imp__Un_0, cls_Un__UNIV__right_0, cls_Un__absorb2_0, cls_parts__emptyE_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_lemma1_0, cls_Key__not__used_0, cls_parts__mono_0, cls_synth_OMPair_0, cls_image__constant__conv_1, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_parts__insert__MPair_0, cls_symKeys__invKey__iff_1, cls_pushes_I4_J_0, cls_sup__eq__bot__eq2_0, cls_Un__upper2_0, cls_msg_Osimps_I44_J_0, cls_analz__subset__iff_0, cls_analz__empty_0, cls_parts__knows__Spy__subset__used_0, cls_UnCI_0, cls_msg_Osimps_I40_J_0, cls_subset__iff_0, cls_insert__code_2, cls_msg_Osimps_I38_J_0, cls_parts__Un_0, cls_parts_OSnd_0, clsarity_fun__HOL_Oord, cls_Diff__idemp_0, cls_pushes_I5_J_0, cls_analz__mono__contra_I3_J_0, cls_rev__predicate1D_0, cls_event_Osimps_I9_J_0, cls_Spy__spies__bad__privateKey_0, cls_insert__Diff__single_0, cls_privateKey__notin__image__shrK_0, cls_singleton__iff_1, cls_Spy__spies__bad__shrK_0, cls_symKey__neq__priEK_0, cls_event_Osimps_I6_J_0, cls_subset__empty_0, cls_parts__insert_0, cls_analz__conj__parts_0, clsarity_bool__Lattices_Oupper__semilattice, cls_msg_Osimps_I43_J_0, cls_keysFor__insert__MPair_0, cls_synth__trans_0, cls_Un__insert__left_0, cls_doubleton__eq__iff_2, cls_subset__insert__iff_3, cls_Spy__analz__shrK_1, cls_image__insert_0, cls_shrK__in__used_0, cls_diff__single__insert_0, cls_synth__analz__insert__eq_0, cls_event_Osimps_I3_J_0, cls_UNIV__not__empty_0, clsarity_nat__Orderings_Obot, cls_Fake__analz__insert_0, cls_sym__shrK_0, cls_msg_Osimps_I7_J_1, cls_knows__Gets_0, cls_insert__subset_1, cls_Spy__see__shrK_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_analz_OFst_0, cls_set__eq__subset_2, cls_parts__insert__subset__Un_0, cls_Un__mono_0, cls_privateKey__neq__publicKey_0, cls_analz_OInj_0, cls_parts__insertI_0, cls_Key__neq__HPair_0, cls_msg_Osimps_I46_J_0, cls_shrK__neq__priK_0, cls_synth__increasing_0, cls_Un__subset__iff_2, cls_linorder__linear_0, cls_Un__empty_0, clsarity_fun__Lattices_Olattice, cls_HPair__synth__analz_0, cls_msg_Osimps_I4_J_0, cls_analz__parts_0, cls_order__antisym_0, cls_order__trans_0, cls_pushes_I12_J_0, cls_image__empty_0, cls_subset__trans_0, cls_double__diff_0, cls_not__Cons__self_0, cls_analz__image__freshK__lemma_3, cls_insert__is__Un_0, cls_parts__singleton_0, cls_keysFor__insert__HPair_0, cls_MPair__eq__HPair_0, cls_insertI1_0, cls_DiffI_0, cls_analz__insert__Crypt__subset_0, clsarity_bool__Orderings_Opreorder, cls_MPair__synth_1, cls_empty__not__insert_0, cls_knows__Spy__Says_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_image__constant__conv_0, cls_analz__Crypt__if_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_le__supE_0, cls_analz__insert__cong_0, cls_msg_Osimps_I48_J_0, cls_msg_Osimps_I39_J_0, cls_parts__cut__eq_0, cls_event_Osimps_I2_J_1, cls_ns__shared_OFake_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup__top__right_0, cls_sup1E_0, cls_Un__UNIV__left_0, cls_parts__cut_0, cls_analz__image__freshK__simps_I57_J_0, cls_sup__least_0, cls_subset__refl_0, cls_analz__shrK__Decrypt_0, cls_parts__subset__iff_0, cls_synth__subset__iff_1, cls_analz__Un_0, cls_analz_ODecrypt_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_Diff__insert2_0, cls_synth__Un_0, cls_not__symKeys__priK_0, clsarity_nat__Orderings_Opreorder, cls_image__diff__subset_0, cls_publicKey__notin__image__shrK_0, cls_sup1CI_1, cls_image__iff_2, cls_insertCI_0, cls_msg_Osimps_I42_J_0, cls_Crypt__synth__eq_0, cls_spies__pubK_0, cls_Spy__in__bad_0, cls_singletonE_0, cls_insert__Key__image_0, cls_image__Un_0, cls_insert__Diff_0, cls_parts__insert__knows__A_0, cls_Crypt__synth__analz_1, clsarity_nat__Lattices_Olattice, cls_UNIV__I_0, cls_DiffE_0, cls_HPair__synth__analz_1, cls_invKey__K_0, cls_Un__Diff__cancel_0, cls_analz__spies__pubK_0, cls_order__eq__iff_2, cls_bot1E_0, cls_Fake__analz__eq_0, cls_parts__insert__Hash_0, cls_event_Osimps_I1_J_1, cls_analz__mono__contra_I2_J_0, cls_insert__mono_0, cls_analz__insert__HPair_0, cls_priK__in__initState_0, cls_publicKey__neq__privateKey_0, cls_Un__Diff__cancel2_0, cls_parts__insert2_0, cls_bex__empty_0, cls_top1I_0, cls_event_Osimps_I7_J_0, cls_le__supI2_0, cls_synth__analz__insert__eq_1, cls_analz__image__freshK__lemma_0, cls_Un__assoc_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_shrK__injective_0, cls_synth_OInj_0, cls_synth__idem_0, cls_Diff__mono_0, cls_publicKey__image__eq_2, cls_order__antisym__conv_0, cls_UnE_0, cls_subset__insertI2_0, cls_Un__absorb_0, cls_MPair__used_1, cls_parts__trans_0, clsarity_bool__Lattices_Olattice, cls_parts__analz_0, cls_event_Osimps_I2_J_0, cls_neq__shrK_0, cls_usedI_0, cls_parts__insert__Key_0, cls_analz__analzD_0, cls_invKey__eq_0, clsarity_bool__Lattices_Obounded__lattice, cls_event_Osimps_I4_J_0, cls_subset__insert__iff_4, cls_Spy__see__shrK_1, 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_invKey__shrK_0, cls_Crypt__Spy__analz__bad_0, cls_parts__singleton_1, cls_parts__Un__subset2_0, cls_insert__subset_2, cls_le__supI1_0, cls_le__eqI_0, cls_sup__left__idem_0, cls_insert__not__empty_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_Spy__analz__shrK_0, cls_subsetD_0, cls_Key__synth_0, cls_Hash__synth__analz_0, cls_analz__synth__Un_0, cls_Crypt__synth_0, cls_subset__singletonD_0, cls_event_Osimps_I8_J_0, cls_priEK__noteq__shrK_0, cls_insert__absorb2_0, cls_analz__mono_0, cls_analz_OSnd_0, cls_Crypt__imp__keysFor_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_doubleton__eq__iff_1, cls_analz__mono__contra_I1_J_0, cls_analz__synth_0, cls_event_Osimps_I1_J_2, cls_analz__insert__eq_0, cls_analz__analz__Un_0, cls_synth__subset__iff_0, cls_Diff__empty_0, cls_Un__left__absorb_0, cls_msg_Osimps_I5_J_0, cls_event_Osimps_I1_J_0, cls_Crypt__notin__image__Key_0, cls_Crypt__synth_1, cls_Hash__synth_0, cls_inf__sup__ord_I3_J_0, cls_MPair__synth_0, cls_inf__sup__aci_I5_J_0, cls_eq__eqI_1, cls_singleton__inject_0, cls_HPair__synth__analz_2, cls_initState__into__used_0, cls_analz__increasing_0, cls_subset__insert_0, cls_sup__idem_0, cls_msg_Osimps_I41_J_0, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_knows__subset__knows__Notes_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_keysFor__parts__insert_0, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_Un__empty_1, cls_parts__Un__subset1_0, clsarity_fun__Orderings_Opreorder, cls_Fake__parts__sing_0, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_analz__image__Key_0, cls_analz__insert__eq__I_1, cls_Un__least_0, cls_sup1CI_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_parts__idem_0, cls_lemma2_0, cls_image__eqI_0, cls_subset__UNIV_0, cls_analz__insertI_0, cls_image__subset__iff_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_knows__Spy__subset__knows__Spy__Says_0, cls_invKey_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_analz__insert__eq__I_0, cls_Diff__subset__conv_1, cls_insert__code_0, cls_le__eqI_1, cls_subset__insertI_0, cls_analz__trans_0, cls_used__Gets_0, cls_msg_Osimps_I6_J_0, cls_DiffE_1, cls_analz__subset__cong_0, cls_Diff__insert__absorb_0, cls_Diff__partition_0, cls_sup__bot__left_0, cls_insert__image_0, cls_shrK__image__eq_0, cls_analz__Decrypt_H_0, cls_used__parts__subset__parts_0, cls_insert__commute_0, cls_insert__iff_2, cls_keysFor__insert__Key_0, cls_Crypt__neq__HPair_0, cls_gen__analz__insert__eq_0, cls_HPair__eq__MPair_1, cls_Hash__synth__analz_1, cls_Fake__parts__insert__in__Un_0, cls_analz__insert__Key_0, cls_Un__insert__right_0, cls_publicKey__inject_1, 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_knows__Spy__Notes_0, cls_priK__neq__shrK_0, cls_parts__synth_0, cls_image__is__empty_0, cls_analz__image__freshK__lemma_1, cls_equalityE_0, cls_keysFor__insert__Crypt_0, cls_MPair__eq__HPair_2, cls_imageI_0, cls_parts__insert__Crypt_0, cls_Hash__neq__HPair_0, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_ball__empty_0, cls_synth__mono_0, cls_synth__cut_0, cls_empty__Diff_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_Diff__subset_0, cls_analz__into__parts_0, cls_predicate1D_0, cls_analz__insert_0, cls_parts__insert__spies_0
% 10.19/3.18 % No. of inferences in proof: 983
% 10.19/3.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2639 ms resp. 2044 ms w/o parsing
% 10.89/3.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.89/3.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------