TSTP Solution File: SWV758-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV758-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 : 600s
% DateTime : Wed Jul 20 21:45:02 EDT 2022
% Result : Unsatisfiable 117.15s 117.37s
% Output : Refutation 117.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 105
% Syntax : Number of clauses : 389 ( 209 unt; 59 nHn; 389 RR)
% Number of literals : 607 ( 0 equ; 194 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 59 ( 59 usr; 29 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
~ hBOOL(c_in(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v)),
file('SWV758-1.p',unknown),
[] ).
cnf(19,axiom,
c_Fun_Oinj__on(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v,w),
file('SWV758-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ hBOOL(c_in(u,c_Set_Oinsert(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),w),w))
| equal(u,v) ),
file('SWV758-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ class_Orderings_Obot(u)
| equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x),c_Orderings_Obot__class_Obot(u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(27,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)),
file('SWV758-1.p',unknown),
[] ).
cnf(28,axiom,
( ~ class_Orderings_Obot(u)
| c_lessequals(c_Orderings_Obot__class_Obot(u),v,u) ),
file('SWV758-1.p',unknown),
[] ).
cnf(29,axiom,
~ equal(c_Set_Oinsert(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),
file('SWV758-1.p',unknown),
[] ).
cnf(33,axiom,
( ~ class_Lattices_Obounded__lattice(u)
| equal(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(u),v,u),v) ),
file('SWV758-1.p',unknown),
[] ).
cnf(34,axiom,
equal(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)),v),
file('SWV758-1.p',unknown),
[] ).
cnf(37,axiom,
equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),
file('SWV758-1.p',unknown),
[] ).
cnf(38,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v)),
file('SWV758-1.p',unknown),
[] ).
cnf(47,axiom,
~ equal(c_Set_Oinsert(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),
file('SWV758-1.p',unknown),
[] ).
cnf(50,axiom,
equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),
file('SWV758-1.p',unknown),
[] ).
cnf(51,axiom,
equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_List_Oset(c_List_Olist_ONil(u),u)),
file('SWV758-1.p',unknown),
[] ).
cnf(71,axiom,
equal(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(u,c_Lattices_Oupper__semilattice__class_Osup(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))),
file('SWV758-1.p',unknown),
[] ).
cnf(81,axiom,
c_lessequals(u,c_Lattices_Oupper__semilattice__class_Osup(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),
file('SWV758-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ class_Lattices_Oupper__semilattice(u)
| c_lessequals(v,c_Lattices_Oupper__semilattice__class_Osup(v,w,u),u) ),
file('SWV758-1.p',unknown),
[] ).
cnf(87,axiom,
equal(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),c_Set_Oinsert(v,c_Set_Oinsert(u,w,x),x)),
file('SWV758-1.p',unknown),
[] ).
cnf(106,axiom,
( ~ hBOOL(hAPP(u,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(u,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(u,v)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(117,axiom,
equal(c_List_Oappend(c_List_Olist_ONil(u),v,u),v),
file('SWV758-1.p',unknown),
[] ).
cnf(124,axiom,
equal(c_Lattices_Oupper__semilattice__class_Osup(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),
file('SWV758-1.p',unknown),
[] ).
cnf(125,axiom,
equal(c_Set_Oinsert(u,c_Set_Oinsert(u,v,w),w),c_Set_Oinsert(u,v,w)),
file('SWV758-1.p',unknown),
[] ).
cnf(126,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,v,w),x))
| hBOOL(hAPP(v,x))
| equal(u,x) ),
file('SWV758-1.p',unknown),
[] ).
cnf(129,axiom,
c_lessequals(u,c_Set_Oinsert(v,u,w),tc_fun(w,tc_bool)),
file('SWV758-1.p',unknown),
[] ).
cnf(136,axiom,
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,v,tc_fun(w,tc_bool)),x))
| hBOOL(hAPP(u,x))
| hBOOL(hAPP(v,x)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(157,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,v,u)
| equal(w,v) ),
file('SWV758-1.p',unknown),
[] ).
cnf(161,axiom,
( ~ c_lessequals(u,v,tc_fun(w,tc_bool))
| equal(c_Lattices_Oupper__semilattice__class_Osup(u,v,tc_fun(w,tc_bool)),v) ),
file('SWV758-1.p',unknown),
[] ).
cnf(168,axiom,
c_List_Odistinct(c_List_Olist_ONil(u),u),
file('SWV758-1.p',unknown),
[] ).
cnf(172,axiom,
equal(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(u,v,w,x),c_Set_Oimage(u,y,w,x),tc_fun(x,tc_bool)),c_Set_Oimage(u,c_Lattices_Oupper__semilattice__class_Osup(v,y,tc_fun(w,tc_bool)),w,x)),
file('SWV758-1.p',unknown),
[] ).
cnf(175,axiom,
c_lessequals(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),
file('SWV758-1.p',unknown),
[] ).
cnf(178,axiom,
( ~ class_HOL_Ouminus(u)
| equal(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(179,axiom,
hBOOL(hAPP(c_Set_Oinsert(u,v,w),u)),
file('SWV758-1.p',unknown),
[] ).
cnf(196,axiom,
equal(c_Lattices_Oupper__semilattice__class_Osup(u,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),
file('SWV758-1.p',unknown),
[] ).
cnf(200,axiom,
( ~ c_lessequals(c_Set_Oinsert(u,v,w),x,tc_fun(w,tc_bool))
| hBOOL(c_in(u,x,w)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(203,axiom,
equal(c_List_Olist_OCons(u,c_List_Oappend(v,w,x),x),c_List_Oappend(c_List_Olist_OCons(u,v,x),w,x)),
file('SWV758-1.p',unknown),
[] ).
cnf(211,axiom,
equal(c_Lattices_Oupper__semilattice__class_Osup(u,v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(v,u,tc_fun(w,tc_bool))),
file('SWV758-1.p',unknown),
[] ).
cnf(225,axiom,
( ~ c_Fun_Oinj__on(u,c_Lattices_Oupper__semilattice__class_Osup(v,w,tc_fun(x,tc_bool)),x,y)
| c_Fun_Oinj__on(u,v,x,y) ),
file('SWV758-1.p',unknown),
[] ).
cnf(228,axiom,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u),
file('SWV758-1.p',unknown),
[] ).
cnf(235,axiom,
( ~ class_HOL_Oord(u)
| ~ c_lessequals(v,w,tc_fun(x,u))
| c_lessequals(hAPP(v,y),hAPP(w,y),u) ),
file('SWV758-1.p',unknown),
[] ).
cnf(254,axiom,
hBOOL(c_in(u,c_Set_Oinsert(u,v,w),w)),
file('SWV758-1.p',unknown),
[] ).
cnf(260,axiom,
( ~ hBOOL(c_in(u,v,w))
| equal(c_Set_Oinsert(u,v,w),v) ),
file('SWV758-1.p',unknown),
[] ).
cnf(289,axiom,
equal(c_List_Oremdups(c_List_Olist_ONil(u),u),c_List_Olist_ONil(u)),
file('SWV758-1.p',unknown),
[] ).
cnf(290,axiom,
c_lessequals(u,c_Message_Osynth(u),tc_fun(tc_Message_Omsg,tc_bool)),
file('SWV758-1.p',unknown),
[] ).
cnf(295,axiom,
( ~ class_Lattices_Oupper__semilattice(u)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v,w,u),x,u)
| c_lessequals(w,x,u) ),
file('SWV758-1.p',unknown),
[] ).
cnf(300,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('SWV758-1.p',unknown),
[] ).
cnf(328,axiom,
equal(c_List_Oappend(c_List_Oappend(u,v,w),x,w),c_List_Oappend(u,c_List_Oappend(v,x,w),w)),
file('SWV758-1.p',unknown),
[] ).
cnf(334,axiom,
equal(c_Set_Oinsert(u,c_List_Oset(v,w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
file('SWV758-1.p',unknown),
[] ).
cnf(346,axiom,
( ~ equal(c_Set_Oimage(u,v,w,x),c_Set_Oimage(u,y,w,x))
| ~ c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)
| equal(v,y) ),
file('SWV758-1.p',unknown),
[] ).
cnf(350,axiom,
( ~ class_Orderings_Otop(u)
| equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x),c_Orderings_Otop__class_Otop(u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(384,axiom,
equal(c_Event_Oknows(u,c_List_Olist_ONil(tc_Event_Oevent)),c_Event_OinitState(u)),
file('SWV758-1.p',unknown),
[] ).
cnf(399,axiom,
~ hBOOL(c_in(hAPP(c_Public_OshrK,u),c_Set_Oimage(c_Message_OinvKey,c_Set_Oimage(c_Public_OpublicKey(v),w,tc_Message_Oagent,tc_nat),tc_nat,tc_nat),tc_nat)),
file('SWV758-1.p',unknown),
[] ).
cnf(433,axiom,
~ hBOOL(c_in(c_Message_Omsg_ONonce(c_Public_Osko__Public__XNonce__supply1__1__1(u)),c_Event_Oused(u),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(434,axiom,
~ hBOOL(c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(438,axiom,
~ hBOOL(c_in(c_Message_Omsg_OCrypt(u,v),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(443,axiom,
( ~ hBOOL(c_in(u,c_Set_Oimage(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x),x))
| equal(hAPP(v,c_ATP__Linkup_Osko__Set__XrangeE__1__1(u,v,x,w)),u) ),
file('SWV758-1.p',unknown),
[] ).
cnf(444,axiom,
( ~ hBOOL(c_in(u,c_List_Oset(v,w),w))
| equal(c_List_Oremdups(c_List_Olist_OCons(u,v,w),w),c_List_Oremdups(v,w)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(451,axiom,
( ~ hBOOL(c_in(u,c_List_Oset(v,w),w))
| ~ c_List_Odistinct(c_List_Olist_OCons(u,v,w),w) ),
file('SWV758-1.p',unknown),
[] ).
cnf(452,axiom,
( hBOOL(c_in(u,c_List_Oset(v,w),w))
| equal(c_List_Olist_OCons(u,c_List_Oremdups(v,w),w),c_List_Oremdups(c_List_Olist_OCons(u,v,w),w)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(453,axiom,
( ~ c_List_Odistinct(u,v)
| hBOOL(c_in(w,c_List_Oset(u,v),v))
| c_List_Odistinct(c_List_Olist_OCons(w,u,v),v) ),
file('SWV758-1.p',unknown),
[] ).
cnf(454,axiom,
equal(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Message_Omsg_OKey,c_Set_Oimage(c_Message_OinvKey,c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OEncryption),c_Event_Obad,tc_Message_Oagent,tc_nat),tc_nat,tc_nat),tc_nat,tc_Message_Omsg),c_Set_Oimage(c_Message_Omsg_OKey,c_Set_Oimage(c_Message_OinvKey,c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OSignature),c_Event_Obad,tc_Message_Oagent,tc_nat),tc_nat,tc_nat),tc_nat,tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),c_Set_Oimage(c_Message_Omsg_OKey,c_Set_Oimage(c_Public_OshrK,c_Event_Obad,tc_Message_Oagent,tc_nat),tc_nat,tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),c_Set_Oimage(c_Message_Omsg_OKey,c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OEncryption),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat),tc_nat,tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),c_Set_Oimage(c_Message_Omsg_OKey,c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OSignature),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat),tc_nat,tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),c_Event_OinitState(c_Message_Oagent_OSpy)),
file('SWV758-1.p',unknown),
[] ).
cnf(466,axiom,
hBOOL(c_in(c_Message_Omsg_OAgent(u),c_Message_Osynth(v),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(487,axiom,
( ~ hBOOL(c_in(hAPP(c_Public_OshrK,u),c_Set_Oimage(c_Public_OshrK,v,tc_Message_Oagent,tc_nat),tc_nat))
| hBOOL(c_in(u,v,tc_Message_Oagent)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(520,axiom,
hBOOL(c_in(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v)),
file('SWV758-1.p',unknown),
[] ).
cnf(525,axiom,
~ equal(c_List_Olist_OCons(u,v,w),v),
file('SWV758-1.p',unknown),
[] ).
cnf(527,axiom,
equal(c_Message_Osynth(c_Message_Osynth(u)),c_Message_Osynth(u)),
file('SWV758-1.p',unknown),
[] ).
cnf(529,axiom,
hBOOL(c_in(hAPP(u,v),c_Set_Oimage(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x),x)),
file('SWV758-1.p',unknown),
[] ).
cnf(532,axiom,
~ hBOOL(c_in(hAPP(c_Public_OpublicKey(u),v),c_Set_Oimage(c_Public_OshrK,w,tc_Message_Oagent,tc_nat),tc_nat)),
file('SWV758-1.p',unknown),
[] ).
cnf(545,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v)),
file('SWV758-1.p',unknown),
[] ).
cnf(547,axiom,
equal(hAPP(c_Message_OinvKey,hAPP(c_Message_OinvKey,u)),u),
file('SWV758-1.p',unknown),
[] ).
cnf(548,axiom,
~ hBOOL(c_in(hAPP(c_Message_OinvKey,hAPP(c_Public_OpublicKey(u),v)),c_Message_OsymKeys,tc_nat)),
file('SWV758-1.p',unknown),
[] ).
cnf(553,axiom,
equal(c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(u,v),w,tc_Event_Oevent)),c_Event_Oused(w)),
file('SWV758-1.p',unknown),
[] ).
cnf(559,axiom,
~ hBOOL(c_in(c_Message_Omsg_OCrypt(u,v),c_Set_Oimage(c_Message_Omsg_OKey,w,tc_nat,tc_Message_Omsg),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(566,axiom,
hBOOL(c_in(hAPP(c_Message_Omsg_OKey,hAPP(c_Public_OshrK,u)),c_Event_OinitState(u),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(568,axiom,
hBOOL(c_in(hAPP(c_Message_Omsg_OKey,hAPP(c_Public_OshrK,u)),c_Event_Oused(v),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(576,axiom,
( ~ hBOOL(c_in(u,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v)),tc_Message_Omsg))
| hBOOL(c_in(u,c_Event_Oused(v),tc_Message_Omsg)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(579,axiom,
( ~ hBOOL(c_in(c_Event_Oevent_ONotes(u,v),c_List_Oset(w,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(v,c_Event_Oused(w),tc_Message_Omsg)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(625,axiom,
( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(u,v),c_Message_Oparts(w),tc_Message_Omsg))
| hBOOL(c_in(v,c_Message_Oparts(w),tc_Message_Omsg)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(629,axiom,
( ~ hBOOL(c_in(u,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v),c_Message_Omsg_OMPair(w,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(x),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,y),z)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,u)),tc_Message_Omsg))
| hBOOL(c_in(v,c_Event_Obad,tc_Message_Oagent))
| equal(z,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,x),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,y),c_Message_Omsg_OAgent(v)))) ),
file('SWV758-1.p',unknown),
[] ).
cnf(641,axiom,
( ~ hBOOL(hAPP(u,v))
| hBOOL(c_in(v,u,w)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(642,axiom,
( ~ hBOOL(c_in(u,v,w))
| hBOOL(hAPP(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(657,axiom,
( ~ class_Lattices_Olattice(u)
| class_Lattices_Oupper__semilattice(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(658,axiom,
( ~ class_Lattices_Obounded__lattice(u)
| class_Lattices_Obounded__lattice(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(659,axiom,
( ~ class_Lattices_Oboolean__algebra(u)
| class_Lattices_Oboolean__algebra(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(660,axiom,
( ~ class_Orderings_Opreorder(u)
| class_Orderings_Opreorder(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(661,axiom,
( ~ class_Lattices_Olattice(u)
| class_Lattices_Olattice(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(662,axiom,
( ~ class_Orderings_Oorder(u)
| class_Orderings_Oorder(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(663,axiom,
( ~ class_Orderings_Otop(u)
| class_Orderings_Otop(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(664,axiom,
( ~ class_Orderings_Obot(u)
| class_Orderings_Obot(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(665,axiom,
( ~ class_HOL_Ouminus(u)
| class_HOL_Ouminus(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(666,axiom,
( ~ class_HOL_Oord(u)
| class_HOL_Oord(tc_fun(v,u)) ),
file('SWV758-1.p',unknown),
[] ).
cnf(674,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(675,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(676,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(677,axiom,
class_Orderings_Opreorder(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(678,axiom,
class_Lattices_Olattice(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(679,axiom,
class_Orderings_Oorder(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(680,axiom,
class_Orderings_Otop(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(681,axiom,
class_Orderings_Obot(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(682,axiom,
class_HOL_Ouminus(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(683,axiom,
class_HOL_Oord(tc_bool),
file('SWV758-1.p',unknown),
[] ).
cnf(686,axiom,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(687,axiom,
hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
file('SWV758-1.p',unknown),
[] ).
cnf(689,axiom,
~ hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)),
file('SWV758-1.p',unknown),
[] ).
cnf(691,axiom,
hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
file('SWV758-1.p',unknown),
[] ).
cnf(692,axiom,
~ hBOOL(c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
file('SWV758-1.p',unknown),
[] ).
cnf(731,plain,
equal(c_Set_Oimage(c_Message_Omsg_OKey,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OshrK,c_Event_Obad,tc_Message_Oagent,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OEncryption),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OSignature),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat),c_Set_Oimage(c_Message_OinvKey,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OEncryption),c_Event_Obad,tc_Message_Oagent,tc_nat),c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OSignature),c_Event_Obad,tc_Message_Oagent,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,tc_nat),tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_bool)),tc_nat,tc_Message_Omsg),c_Event_OinitState(c_Message_Oagent_OSpy)),
inference(rew,[status(thm),theory(equality)],[211,454,71,172]),
[iquote('0:Rew:211.0,454.0,71.0,454.0,71.0,454.0,172.0,454.0,211.0,454.0,71.0,454.0,172.0,454.0,211.0,454.0,172.0,454.0,172.0,454.0,172.0,454.0')] ).
cnf(821,plain,
~ hBOOL(c_in(hAPP(c_Public_OshrK,v_A),c_Set_Oimage(c_Public_OshrK,c_Event_Obad,tc_Message_Oagent,tc_nat),tc_nat)),
inference(res,[status(thm),theory(equality)],[487,689]),
[iquote('0:Res:487.1,689.0')] ).
cnf(828,plain,
hBOOL(c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[686,625]),
[iquote('0:Res:686.0,625.0')] ).
cnf(850,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Event_Oused(v_evs),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[686,576]),
[iquote('0:Res:686.0,576.0')] ).
cnf(864,plain,
~ hBOOL(hAPP(c_List_Oset(v_evs,tc_Event_Oevent),c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB))))),
inference(res,[status(thm),theory(equality)],[641,692]),
[iquote('0:Res:641.1,692.0')] ).
cnf(895,plain,
( ~ hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| equal(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))),v_X)
| hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)) ),
inference(res,[status(thm),theory(equality)],[687,629]),
[iquote('0:Res:687.0,629.1')] ).
cnf(921,plain,
equal(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))),v_X),
inference(mrr,[status(thm)],[895,691,689]),
[iquote('0:MRR:895.0,895.2,691.0,689.0')] ).
cnf(1097,plain,
( ~ class_Orderings_Obot(tc_fun(u,tc_bool))
| c_lessequals(c_List_Oset(c_List_Olist_ONil(u),u),v,tc_fun(u,tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[51,28]),
[iquote('0:SpR:51.0,28.1')] ).
cnf(1100,plain,
c_lessequals(c_List_Oset(c_List_Olist_ONil(u),u),v,tc_fun(u,tc_bool)),
inference(ssi,[status(thm)],[1097,666,683,682,680,681,677,679,676,675,678,674,665,663,664,660,662,659,658,661,657]),
[iquote('0:SSi:1097.0,666.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,665.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,663.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,664.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,660.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,662.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,659.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,658.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,661.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,657.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1')] ).
cnf(1108,plain,
~ hBOOL(c_in(u,c_List_Oset(c_List_Olist_ONil(v),v),v)),
inference(spl,[status(thm),theory(equality)],[51,10]),
[iquote('0:SpL:51.0,10.0')] ).
cnf(1211,plain,
~ hBOOL(hAPP(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),c_Message_Omsg_OCrypt(u,v))),
inference(res,[status(thm),theory(equality)],[641,438]),
[iquote('0:Res:641.1,438.0')] ).
cnf(1214,plain,
~ hBOOL(hAPP(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),c_Message_Omsg_ONonce(u))),
inference(res,[status(thm),theory(equality)],[641,434]),
[iquote('0:Res:641.1,434.0')] ).
cnf(1215,plain,
~ hBOOL(hAPP(c_Event_Oused(u),c_Message_Omsg_ONonce(c_Public_Osko__Public__XNonce__supply1__1__1(u)))),
inference(res,[status(thm),theory(equality)],[641,433]),
[iquote('0:Res:641.1,433.0')] ).
cnf(1228,plain,
hBOOL(hAPP(c_Event_Oused(v_evs),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),
inference(res,[status(thm),theory(equality)],[850,642]),
[iquote('0:Res:850.0,642.0')] ).
cnf(1285,plain,
~ hBOOL(hAPP(c_Message_OsymKeys,hAPP(c_Message_OinvKey,hAPP(c_Public_OpublicKey(u),v)))),
inference(res,[status(thm),theory(equality)],[641,548]),
[iquote('0:Res:641.1,548.0')] ).
cnf(1501,plain,
~ hBOOL(hAPP(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),v_X)),
inference(spl,[status(thm),theory(equality)],[921,1211]),
[iquote('0:SpL:921.0,1211.0')] ).
cnf(1637,plain,
~ hBOOL(hAPP(c_Set_Oimage(c_Public_OshrK,c_Event_Obad,tc_Message_Oagent,tc_nat),hAPP(c_Public_OshrK,v_A))),
inference(res,[status(thm),theory(equality)],[641,821]),
[iquote('0:Res:641.1,821.0')] ).
cnf(1639,plain,
( ~ class_Orderings_Obot(tc_bool)
| equal(hAPP(c_List_Oset(c_List_Olist_ONil(t_a),t_a),v_x),c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[51,25]),
[iquote('0:SpR:51.0,25.1')] ).
cnf(1640,plain,
( ~ class_Orderings_Obot(tc_bool)
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(spl,[status(thm),theory(equality)],[25,38]),
[iquote('0:SpL:25.1,38.0')] ).
cnf(1642,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(ssi,[status(thm)],[1640,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:1640.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(1643,plain,
equal(hAPP(c_List_Oset(c_List_Olist_ONil(t_a),t_a),v_x),c_Orderings_Obot__class_Obot(tc_bool)),
inference(ssi,[status(thm)],[1639,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:1639.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(1658,plain,
~ hBOOL(c_in(v_X,c_Set_Oimage(c_Message_Omsg_OKey,u,tc_nat,tc_Message_Omsg),tc_Message_Omsg)),
inference(spl,[status(thm),theory(equality)],[921,559]),
[iquote('0:SpL:921.0,559.0')] ).
cnf(1660,plain,
~ hBOOL(hAPP(c_Set_Oimage(c_Message_Omsg_OKey,u,tc_nat,tc_Message_Omsg),v_X)),
inference(res,[status(thm),theory(equality)],[641,1658]),
[iquote('0:Res:641.1,1658.0')] ).
cnf(2014,plain,
equal(c_Set_Oinsert(c_Message_Omsg_OAgent(u),c_Message_Osynth(v),tc_Message_Omsg),c_Message_Osynth(v)),
inference(res,[status(thm),theory(equality)],[466,260]),
[iquote('0:Res:466.0,260.0')] ).
cnf(2018,plain,
equal(c_Set_Oinsert(hAPP(c_Message_Omsg_OKey,hAPP(c_Public_OshrK,u)),c_Event_OinitState(u),tc_Message_Omsg),c_Event_OinitState(u)),
inference(res,[status(thm),theory(equality)],[566,260]),
[iquote('0:Res:566.0,260.0')] ).
cnf(2019,plain,
equal(c_Set_Oinsert(hAPP(c_Message_Omsg_OKey,hAPP(c_Public_OshrK,u)),c_Event_Oused(v),tc_Message_Omsg),c_Event_Oused(v)),
inference(res,[status(thm),theory(equality)],[568,260]),
[iquote('0:Res:568.0,260.0')] ).
cnf(2024,plain,
equal(c_Set_Oinsert(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),
inference(res,[status(thm),theory(equality)],[520,260]),
[iquote('0:Res:520.0,260.0')] ).
cnf(2109,plain,
~ equal(c_Message_Osynth(u),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool))),
inference(spl,[status(thm),theory(equality)],[2014,47]),
[iquote('0:SpL:2014.0,47.0')] ).
cnf(2110,plain,
~ equal(c_Message_Osynth(u),c_List_Oset(c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg)),
inference(rew,[status(thm),theory(equality)],[51,2109]),
[iquote('0:Rew:51.0,2109.0')] ).
cnf(2276,plain,
~ hBOOL(hAPP(c_Set_Oimage(c_Public_OshrK,u,tc_Message_Oagent,tc_nat),hAPP(c_Public_OpublicKey(v),w))),
inference(res,[status(thm),theory(equality)],[641,532]),
[iquote('0:Res:641.1,532.0')] ).
cnf(3040,plain,
hBOOL(hAPP(c_List_Oset(c_List_Olist_OCons(u,v,w),w),u)),
inference(spr,[status(thm),theory(equality)],[334,179]),
[iquote('0:SpR:334.0,179.0')] ).
cnf(3042,plain,
hBOOL(c_in(u,c_List_Oset(c_List_Olist_OCons(u,v,w),w),w)),
inference(spr,[status(thm),theory(equality)],[334,254]),
[iquote('0:SpR:334.0,254.0')] ).
cnf(3043,plain,
equal(c_Set_Oinsert(u,c_List_Oset(c_List_Olist_OCons(u,v,w),w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
inference(spr,[status(thm),theory(equality)],[334,125]),
[iquote('0:SpR:334.0,125.0')] ).
cnf(3114,plain,
equal(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),c_List_Oset(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),v)),
inference(spr,[status(thm),theory(equality)],[51,334]),
[iquote('0:SpR:51.0,334.0')] ).
cnf(3121,plain,
equal(c_List_Oset(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
inference(rew,[status(thm),theory(equality)],[334,3043]),
[iquote('0:Rew:334.0,3043.0')] ).
cnf(3661,plain,
~ equal(c_Event_OinitState(u),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool))),
inference(spl,[status(thm),theory(equality)],[2018,47]),
[iquote('0:SpL:2018.0,47.0')] ).
cnf(3662,plain,
~ equal(c_Event_OinitState(u),c_List_Oset(c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg)),
inference(rew,[status(thm),theory(equality)],[51,3661]),
[iquote('0:Rew:51.0,3661.0')] ).
cnf(3682,plain,
~ equal(c_Event_Oused(u),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool))),
inference(spl,[status(thm),theory(equality)],[2019,47]),
[iquote('0:SpL:2019.0,47.0')] ).
cnf(3683,plain,
~ equal(c_Event_Oused(u),c_List_Oset(c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg)),
inference(rew,[status(thm),theory(equality)],[51,3682]),
[iquote('0:Rew:51.0,3682.0')] ).
cnf(3703,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),w)) ),
inference(res,[status(thm),theory(equality)],[179,106]),
[iquote('0:Res:179.0,106.0')] ).
cnf(4642,plain,
hBOOL(c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[828,576]),
[iquote('0:Res:828.0,576.0')] ).
cnf(4649,plain,
hBOOL(hAPP(c_Event_Oused(v_evs),c_Message_Omsg_ONonce(v_NB))),
inference(res,[status(thm),theory(equality)],[4642,642]),
[iquote('0:Res:4642.0,642.0')] ).
cnf(5449,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),w))
| equal(w,u) ),
inference(res,[status(thm),theory(equality)],[641,24]),
[iquote('0:Res:641.1,24.0')] ).
cnf(5607,plain,
~ c_List_Odistinct(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),w),
inference(res,[status(thm),theory(equality)],[3042,451]),
[iquote('0:Res:3042.0,451.0')] ).
cnf(5674,plain,
( ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))
| hBOOL(c_in(w,v,u)) ),
inference(spl,[status(thm),theory(equality)],[2024,200]),
[iquote('0:SpL:2024.0,200.0')] ).
cnf(5690,plain,
hBOOL(c_in(u,c_Message_Osynth(c_Set_Oinsert(u,v,tc_Message_Omsg)),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[290,200]),
[iquote('0:Res:290.0,200.0')] ).
cnf(5746,plain,
hBOOL(hAPP(c_Message_Osynth(c_Set_Oinsert(u,v,tc_Message_Omsg)),u)),
inference(res,[status(thm),theory(equality)],[5690,642]),
[iquote('0:Res:5690.0,642.0')] ).
cnf(5793,plain,
hBOOL(hAPP(c_Message_Osynth(c_List_Oset(c_List_Olist_OCons(u,v,tc_Message_Omsg),tc_Message_Omsg)),u)),
inference(spr,[status(thm),theory(equality)],[334,5746]),
[iquote('0:SpR:334.0,5746.0')] ).
cnf(6697,plain,
equal(c_List_Oappend(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),w,v),c_List_Olist_OCons(u,w,v)),
inference(spr,[status(thm),theory(equality)],[117,203]),
[iquote('0:SpR:117.0,203.0')] ).
cnf(6755,plain,
hBOOL(hAPP(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),v)),
inference(spr,[status(thm),theory(equality)],[87,179]),
[iquote('0:SpR:87.0,179.0')] ).
cnf(7830,plain,
( ~ class_HOL_Ouminus(tc_bool)
| equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x),tc_bool),hAPP(u,v_x)) ),
inference(spr,[status(thm),theory(equality)],[228,178]),
[iquote('0:SpR:228.0,178.1')] ).
cnf(7831,plain,
( ~ class_HOL_Ouminus(tc_bool)
| equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x),tc_bool),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)) ),
inference(spr,[status(thm),theory(equality)],[50,178]),
[iquote('0:SpR:50.0,178.1')] ).
cnf(7832,plain,
( ~ class_HOL_Ouminus(tc_bool)
| equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x),tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x)) ),
inference(spr,[status(thm),theory(equality)],[37,178]),
[iquote('0:SpR:37.0,178.1')] ).
cnf(7838,plain,
( ~ class_HOL_Ouminus(tc_bool)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_bool),hAPP(u,v_x)) ),
inference(rew,[status(thm),theory(equality)],[178,7830]),
[iquote('0:Rew:178.1,7830.1')] ).
cnf(7839,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_bool),hAPP(u,v_x)),
inference(ssi,[status(thm)],[7838,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:7838.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(7840,plain,
( ~ class_HOL_Ouminus(tc_bool)
| equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[1643,7831,51]),
[iquote('0:Rew:1643.0,7831.1,51.0,7831.1')] ).
cnf(7841,plain,
equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool)),
inference(ssi,[status(thm)],[7840,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:7840.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(7842,plain,
( ~ class_HOL_Ouminus(tc_bool)
| equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[1643,7832,51]),
[iquote('0:Rew:1643.0,7832.1,51.0,7832.1')] ).
cnf(7843,plain,
( ~ class_HOL_Ouminus(tc_bool)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[7841,7842]),
[iquote('0:Rew:7841.0,7842.1')] ).
cnf(7844,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(ssi,[status(thm)],[7843,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:7843.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(8245,plain,
hBOOL(c_in(u,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v,u),w,tc_Event_Oevent)),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[3042,579]),
[iquote('0:Res:3042.0,579.0')] ).
cnf(9292,plain,
( ~ class_Orderings_Oorder(tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Message_Osynth(u),u,tc_fun(tc_Message_Omsg,tc_bool))
| equal(c_Message_Osynth(u),u) ),
inference(res,[status(thm),theory(equality)],[290,157]),
[iquote('0:Res:290.0,157.1')] ).
cnf(9353,plain,
( ~ c_lessequals(c_Message_Osynth(u),u,tc_fun(tc_Message_Omsg,tc_bool))
| equal(c_Message_Osynth(u),u) ),
inference(ssi,[status(thm)],[9292,666,683,682,680,681,677,679,676,675,678,674,665,663,664,660,662,659,658,661,657]),
[iquote('0:SSi:9292.0,666.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,665.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,663.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,664.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,660.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,662.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,659.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,658.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,661.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,657.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1')] ).
cnf(9480,plain,
( ~ c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)
| c_Fun_Oinj__on(u,x,v,w) ),
inference(spl,[status(thm),theory(equality)],[124,225]),
[iquote('0:SpL:124.0,225.0')] ).
cnf(9572,plain,
( ~ class_Orderings_Otop(tc_bool)
| equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[7841,350]),
[iquote('0:SpR:7841.0,350.1')] ).
cnf(9575,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),
inference(ssi,[status(thm)],[9572,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:9572.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(9576,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(rew,[status(thm),theory(equality)],[9575,7844]),
[iquote('0:Rew:9575.0,7844.0')] ).
cnf(9577,plain,
equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool)),
inference(rew,[status(thm),theory(equality)],[9575,7841]),
[iquote('0:Rew:9575.0,7841.0')] ).
cnf(10712,plain,
( ~ c_List_Odistinct(c_List_Olist_ONil(u),u)
| c_List_Odistinct(c_List_Olist_OCons(v,c_List_Olist_ONil(u),u),u) ),
inference(res,[status(thm),theory(equality)],[453,1108]),
[iquote('0:Res:453.1,1108.0')] ).
cnf(10725,plain,
c_List_Odistinct(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),v),
inference(mrr,[status(thm)],[10712,168]),
[iquote('0:MRR:10712.0,168.0')] ).
cnf(10825,plain,
( ~ class_Orderings_Opreorder(tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Message_Osynth(u),v,tc_fun(tc_Message_Omsg,tc_bool))
| c_lessequals(u,v,tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(res,[status(thm),theory(equality)],[290,300]),
[iquote('0:Res:290.0,300.1')] ).
cnf(10887,plain,
( ~ c_lessequals(c_Message_Osynth(u),v,tc_fun(tc_Message_Omsg,tc_bool))
| c_lessequals(u,v,tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(ssi,[status(thm)],[10825,666,683,682,680,681,677,679,676,675,678,674,665,663,664,660,662,659,658,661,657]),
[iquote('0:SSi:10825.0,666.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,665.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,663.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,664.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,660.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,662.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,659.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,658.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,661.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1,657.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.1')] ).
cnf(12373,plain,
( ~ hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v))
| hBOOL(hAPP(w,v))
| hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),v)) ),
inference(spl,[status(thm),theory(equality)],[196,136]),
[iquote('0:SpL:196.0,136.0')] ).
cnf(12405,plain,
( hBOOL(hAPP(u,v))
| hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),v)) ),
inference(mrr,[status(thm)],[12373,545]),
[iquote('0:MRR:12373.0,545.0')] ).
cnf(12623,plain,
equal(c_List_Oremdups(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),w),c_List_Oremdups(c_List_Olist_OCons(u,v,w),w)),
inference(res,[status(thm),theory(equality)],[3042,444]),
[iquote('0:Res:3042.0,444.0')] ).
cnf(12652,plain,
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(u,v),hAPP(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v),tc_bool) ),
inference(res,[status(thm),theory(equality)],[175,235]),
[iquote('0:Res:175.0,235.1')] ).
cnf(12653,plain,
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(u,v),hAPP(c_Message_Osynth(u),v),tc_bool) ),
inference(res,[status(thm),theory(equality)],[290,235]),
[iquote('0:Res:290.0,235.1')] ).
cnf(12656,plain,
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(u,v),hAPP(c_Set_Oinsert(w,u,x),v),tc_bool) ),
inference(res,[status(thm),theory(equality)],[129,235]),
[iquote('0:Res:129.0,235.1')] ).
cnf(12689,plain,
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),hAPP(w,v),tc_bool) ),
inference(res,[status(thm),theory(equality)],[27,235]),
[iquote('0:Res:27.0,235.1')] ).
cnf(12690,plain,
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(c_List_Oset(c_List_Olist_ONil(u),u),v),hAPP(w,v),tc_bool) ),
inference(res,[status(thm),theory(equality)],[1100,235]),
[iquote('0:Res:1100.0,235.1')] ).
cnf(12716,plain,
c_lessequals(hAPP(u,v),hAPP(c_Message_Osynth(u),v),tc_bool),
inference(ssi,[status(thm)],[12653,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:12653.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(12722,plain,
c_lessequals(hAPP(u,v),hAPP(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v),tc_bool),
inference(ssi,[status(thm)],[12652,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:12652.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(12723,plain,
c_lessequals(hAPP(u,v),hAPP(c_Set_Oinsert(w,u,x),v),tc_bool),
inference(ssi,[status(thm)],[12656,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:12656.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(12731,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),hAPP(w,v),tc_bool),
inference(ssi,[status(thm)],[12689,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:12689.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(12732,plain,
c_lessequals(hAPP(c_List_Oset(c_List_Olist_ONil(u),u),v),hAPP(w,v),tc_bool),
inference(ssi,[status(thm)],[12690,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:12690.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(12794,plain,
c_lessequals(u,hAPP(c_Message_Osynth(c_Message_OinvKey),hAPP(c_Message_OinvKey,u)),tc_bool),
inference(spr,[status(thm),theory(equality)],[547,12716]),
[iquote('0:SpR:547.0,12716.0')] ).
cnf(12816,plain,
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_lessequals(u,hAPP(c_Message_Osynth(c_Message_OinvKey),hAPP(c_Message_OinvKey,c_Lattices_Oupper__semilattice__class_Osup(v,u,tc_bool))),tc_bool) ),
inference(res,[status(thm),theory(equality)],[12794,295]),
[iquote('0:Res:12794.0,295.1')] ).
cnf(12819,plain,
c_lessequals(u,hAPP(c_Message_Osynth(c_Message_OinvKey),hAPP(c_Message_OinvKey,c_Lattices_Oupper__semilattice__class_Osup(v,u,tc_bool))),tc_bool),
inference(ssi,[status(thm)],[12816,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:12816.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(17512,plain,
equal(c_List_Olist_OCons(u,c_List_Oremdups(c_List_Olist_ONil(v),v),v),c_List_Oremdups(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),v)),
inference(res,[status(thm),theory(equality)],[452,1108]),
[iquote('0:Res:452.0,1108.0')] ).
cnf(17532,plain,
equal(c_List_Oremdups(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),v),c_List_Olist_OCons(u,c_List_Olist_ONil(v),v)),
inference(rew,[status(thm),theory(equality)],[289,17512]),
[iquote('0:Rew:289.0,17512.0')] ).
cnf(17554,plain,
hBOOL(hAPP(c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(u,v),w,tc_Event_Oevent)),v)),
inference(res,[status(thm),theory(equality)],[8245,642]),
[iquote('0:Res:8245.0,642.0')] ).
cnf(17558,plain,
hBOOL(hAPP(c_Event_Oused(c_List_Oappend(c_List_Olist_OCons(c_Event_Oevent_ONotes(u,v),w,tc_Event_Oevent),x,tc_Event_Oevent)),v)),
inference(spr,[status(thm),theory(equality)],[203,17554]),
[iquote('0:SpR:203.0,17554.0')] ).
cnf(18007,plain,
c_lessequals(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spr,[status(thm),theory(equality)],[9577,12722]),
[iquote('0:SpR:9577.0,12722.0')] ).
cnf(18013,plain,
c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x),tc_bool),
inference(spr,[status(thm),theory(equality)],[9577,12722]),
[iquote('0:SpR:9577.0,12722.0')] ).
cnf(18260,plain,
( ~ class_Orderings_Oorder(tc_bool)
| ~ c_lessequals(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(res,[status(thm),theory(equality)],[18013,157]),
[iquote('0:Res:18013.0,157.1')] ).
cnf(18263,plain,
( ~ c_lessequals(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(ssi,[status(thm)],[18260,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:18260.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(18264,plain,
equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool)),
inference(mrr,[status(thm)],[18263,18007]),
[iquote('0:MRR:18263.0,18007.0')] ).
cnf(18277,plain,
c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x),tc_bool),
inference(spr,[status(thm),theory(equality)],[18264,12716]),
[iquote('0:SpR:18264.0,12716.0')] ).
cnf(18355,plain,
( ~ class_Orderings_Oorder(tc_bool)
| ~ c_lessequals(hAPP(c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| equal(hAPP(c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(res,[status(thm),theory(equality)],[18277,157]),
[iquote('0:Res:18277.0,157.1')] ).
cnf(18358,plain,
( ~ c_lessequals(hAPP(c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| equal(hAPP(c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(ssi,[status(thm)],[18355,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:18355.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(18359,plain,
equal(hAPP(c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool)),
inference(mrr,[status(thm)],[18358,18007]),
[iquote('0:MRR:18358.0,18007.0')] ).
cnf(19347,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_x),c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(spr,[status(thm),theory(equality)],[1643,12731]),
[iquote('0:SpR:1643.0,12731.0')] ).
cnf(19389,plain,
( ~ class_Orderings_Oorder(tc_bool)
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_x),tc_bool)
| equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_x),c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(res,[status(thm),theory(equality)],[19347,157]),
[iquote('0:Res:19347.0,157.1')] ).
cnf(19393,plain,
( ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_x),tc_bool)
| equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_x),c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(ssi,[status(thm)],[19389,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:19389.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(19647,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),hAPP(u,v_x),tc_bool),
inference(spr,[status(thm),theory(equality)],[1643,12732]),
[iquote('0:SpR:1643.0,12732.0')] ).
cnf(19651,plain,
equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_x),c_Orderings_Obot__class_Obot(tc_bool)),
inference(mrr,[status(thm)],[19393,19647]),
[iquote('0:MRR:19393.0,19647.0')] ).
cnf(19682,plain,
( ~ class_Orderings_Opreorder(tc_bool)
| ~ c_lessequals(hAPP(u,v_x),v,tc_bool)
| c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,tc_bool) ),
inference(res,[status(thm),theory(equality)],[19647,300]),
[iquote('0:Res:19647.0,300.1')] ).
cnf(19685,plain,
( ~ c_lessequals(hAPP(u,v_x),v,tc_bool)
| c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,tc_bool) ),
inference(ssi,[status(thm)],[19682,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:19682.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(21007,plain,
( ~ class_Orderings_Oorder(tc_bool)
| ~ c_lessequals(hAPP(c_Set_Oinsert(u,v,w),x),hAPP(v,x),tc_bool)
| equal(hAPP(c_Set_Oinsert(u,v,w),x),hAPP(v,x)) ),
inference(res,[status(thm),theory(equality)],[12723,157]),
[iquote('0:Res:12723.0,157.1')] ).
cnf(21010,plain,
( ~ c_lessequals(hAPP(c_Set_Oinsert(u,v,w),x),hAPP(v,x),tc_bool)
| equal(hAPP(c_Set_Oinsert(u,v,w),x),hAPP(v,x)) ),
inference(ssi,[status(thm)],[21007,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:21007.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(21587,plain,
equal(hAPP(u,c_ATP__Linkup_Osko__Set__XrangeE__1__1(hAPP(u,v),u,w,x)),hAPP(u,v)),
inference(res,[status(thm),theory(equality)],[529,443]),
[iquote('0:Res:529.0,443.0')] ).
cnf(31257,plain,
( ~ class_Orderings_Opreorder(tc_bool)
| ~ c_lessequals(hAPP(c_Message_Osynth(c_Message_OinvKey),hAPP(c_Message_OinvKey,c_Lattices_Oupper__semilattice__class_Osup(u,v,tc_bool))),w,tc_bool)
| c_lessequals(v,w,tc_bool) ),
inference(res,[status(thm),theory(equality)],[12819,300]),
[iquote('0:Res:12819.0,300.1')] ).
cnf(31266,plain,
( ~ c_lessequals(hAPP(c_Message_Osynth(c_Message_OinvKey),hAPP(c_Message_OinvKey,c_Lattices_Oupper__semilattice__class_Osup(u,v,tc_bool))),w,tc_bool)
| c_lessequals(v,w,tc_bool) ),
inference(ssi,[status(thm)],[31257,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:31257.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(31980,plain,
( ~ equal(c_Set_Oimage(c_Message_Omsg_OKey,u,tc_nat,tc_Message_Omsg),c_Event_OinitState(c_Message_Oagent_OSpy))
| ~ c_Fun_Oinj__on(c_Message_Omsg_OKey,c_Orderings_Otop__class_Otop(tc_fun(tc_nat,tc_bool)),tc_nat,tc_Message_Omsg)
| equal(u,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OshrK,c_Event_Obad,tc_Message_Oagent,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OEncryption),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OSignature),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat),c_Set_Oimage(c_Message_OinvKey,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OEncryption),c_Event_Obad,tc_Message_Oagent,tc_nat),c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OSignature),c_Event_Obad,tc_Message_Oagent,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,tc_nat),tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_bool))) ),
inference(spl,[status(thm),theory(equality)],[731,346]),
[iquote('0:SpL:731.0,346.0')] ).
cnf(32501,plain,
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(hAPP(u,v_x),v,tc_bool),tc_bool) ),
inference(res,[status(thm),theory(equality)],[84,19685]),
[iquote('0:Res:84.1,19685.0')] ).
cnf(32558,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(hAPP(u,v_x),v,tc_bool),tc_bool),
inference(ssi,[status(thm)],[32501,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:32501.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(32567,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),u,tc_bool),tc_bool),
inference(spr,[status(thm),theory(equality)],[19651,32558]),
[iquote('0:SpR:19651.0,32558.0')] ).
cnf(32662,plain,
( ~ class_Lattices_Obounded__lattice(tc_bool)
| c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),u,tc_bool) ),
inference(spr,[status(thm),theory(equality)],[33,32567]),
[iquote('0:SpR:33.1,32567.0')] ).
cnf(32682,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),u,tc_bool),
inference(ssi,[status(thm)],[32662,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:32662.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(33369,plain,
equal(c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Omsg,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Omsg,tc_bool))),
inference(res,[status(thm),theory(equality)],[175,9353]),
[iquote('0:Res:175.0,9353.0')] ).
cnf(34393,plain,
( ~ class_HOL_Ouminus(tc_bool)
| hBOOL(hAPP(u,v_x))
| hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[178,12405]),
[iquote('0:SpR:178.1,12405.1')] ).
cnf(34413,plain,
( hBOOL(hAPP(u,v_x))
| hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) ),
inference(ssi,[status(thm)],[34393,683,682,680,681,677,679,676,675,678,674]),
[iquote('0:SSi:34393.0,683.0,682.0,680.0,681.0,677.0,679.0,676.0,675.0,678.0,674.0')] ).
cnf(44668,plain,
equal(hAPP(c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_ATP__Linkup_Osko__Set__XrangeE__1__1(c_Orderings_Otop__class_Otop(tc_bool),c_Message_Osynth(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w)),c_Orderings_Otop__class_Otop(tc_bool)),
inference(spr,[status(thm),theory(equality)],[18359,21587]),
[iquote('0:SpR:18359.0,21587.0')] ).
cnf(50557,plain,
c_lessequals(u,c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(u),v,tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(res,[status(thm),theory(equality)],[81,10887]),
[iquote('0:Res:81.0,10887.0')] ).
cnf(66031,plain,
hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,u,v),v),w)),
inference(res,[status(thm),theory(equality)],[6755,3703]),
[iquote('0:Res:6755.0,3703.0')] ).
cnf(66032,plain,
hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),v),w)),
inference(rew,[status(thm),theory(equality)],[87,66031]),
[iquote('0:Rew:87.0,66031.0')] ).
cnf(66072,plain,
( hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),w))
| equal(c_Public_Okeymode_OEncryption,w) ),
inference(res,[status(thm),theory(equality)],[66032,126]),
[iquote('0:Res:66032.0,126.0')] ).
cnf(66233,plain,
( equal(c_Public_Okeymode_OEncryption,u)
| equal(u,c_Public_Okeymode_OSignature) ),
inference(res,[status(thm),theory(equality)],[66072,5449]),
[iquote('0:Res:66072.0,5449.0')] ).
cnf(66280,plain,
( equal(v_evs,c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Event_Oused(c_Public_Okeymode_OSignature),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))) ),
inference(spr,[status(thm),theory(equality)],[66233,1228]),
[iquote('0:SpR:66233.1,1228.0')] ).
cnf(66769,plain,
( equal(c_Event_Oknows(u,c_List_Olist_ONil(tc_Event_Oevent)),c_Public_Okeymode_OEncryption)
| equal(c_Event_OinitState(u),c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[66233,384]),
[iquote('0:SpR:66233.1,384.0')] ).
cnf(68080,plain,
( equal(hAPP(c_Message_Osynth(c_List_Oset(c_List_Olist_OCons(u,v,tc_Message_Omsg),tc_Message_Omsg)),u),c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[66233,5793]),
[iquote('0:SpR:66233.1,5793.0')] ).
cnf(68092,plain,
( equal(hAPP(c_List_Oset(c_List_Olist_OCons(u,v,w),w),u),c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[66233,3040]),
[iquote('0:SpR:66233.1,3040.0')] ).
cnf(68761,plain,
( equal(hAPP(u,v_x),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(u,v_x))
| hBOOL(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OSignature,tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[66233,34413]),
[iquote('0:SpR:66233.1,34413.1')] ).
cnf(69224,plain,
( equal(c_List_Olist_ONil(u),c_Public_Okeymode_OEncryption)
| c_List_Odistinct(c_Public_Okeymode_OSignature,u) ),
inference(spr,[status(thm),theory(equality)],[66233,168]),
[iquote('0:SpR:66233.1,168.0')] ).
cnf(70184,plain,
( equal(c_Message_Osynth(u),c_Public_Okeymode_OEncryption)
| equal(c_Message_Osynth(c_Public_Okeymode_OSignature),c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[66233,527]),
[iquote('0:SpR:66233.1,527.0')] ).
cnf(71332,plain,
( equal(c_Message_Omsg_ONonce(v_NB),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Event_Oused(v_evs),c_Public_Okeymode_OSignature)) ),
inference(spr,[status(thm),theory(equality)],[66233,4649]),
[iquote('0:SpR:66233.1,4649.0')] ).
cnf(73209,plain,
( equal(c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Omsg,tc_bool)),c_Public_Okeymode_OEncryption)
| equal(c_Message_Osynth(c_Public_Okeymode_OSignature),c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[66233,33369]),
[iquote('0:SpR:66233.1,33369.0')] ).
cnf(73746,plain,
( equal(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),c_Public_Okeymode_OEncryption)
| c_List_Odistinct(c_Public_Okeymode_OSignature,v) ),
inference(spr,[status(thm),theory(equality)],[66233,10725]),
[iquote('0:SpR:66233.1,10725.0')] ).
cnf(73879,plain,
( equal(c_Orderings_Obot__class_Obot(tc_bool),c_Public_Okeymode_OEncryption)
| equal(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OSignature,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[66233,9575]),
[iquote('0:SpR:66233.1,9575.0')] ).
cnf(74652,plain,
( equal(c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(u,v),w,tc_Event_Oevent)),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OSignature,v)) ),
inference(spr,[status(thm),theory(equality)],[66233,17554]),
[iquote('0:SpR:66233.1,17554.0')] ).
cnf(74757,plain,
( equal(v_NB,c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Event_Oused(v_evs),c_Message_Omsg_ONonce(c_Public_Okeymode_OSignature))) ),
inference(spr,[status(thm),theory(equality)],[66233,4649]),
[iquote('0:SpR:66233.1,4649.0')] ).
cnf(74982,plain,
( equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Public_Okeymode_OEncryption)
| equal(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OSignature,tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[66233,7839]),
[iquote('0:SpR:66233.1,7839.0')] ).
cnf(74985,plain,
( equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(u,v_x))
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[66233,34413]),
[iquote('0:SpR:66233.1,34413.1')] ).
cnf(74986,plain,
( equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_bool),c_Public_Okeymode_OEncryption)
| equal(hAPP(u,v_x),c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[66233,7839]),
[iquote('0:SpR:66233.1,7839.0')] ).
cnf(75033,plain,
( equal(c_List_Oset(c_List_Olist_OCons(u,v,w),w),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OSignature,u)) ),
inference(spr,[status(thm),theory(equality)],[66233,3040]),
[iquote('0:SpR:66233.1,3040.0')] ).
cnf(75559,plain,
( equal(c_Public_Okeymode_OEncryption,u)
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,c_Set_Oinsert(u,v,w),w),x)) ),
inference(spr,[status(thm),theory(equality)],[66233,66032]),
[iquote('0:SpR:66233.1,66032.0')] ).
cnf(75786,plain,
( ~ hBOOL(c_Public_Okeymode_OSignature)
| equal(hAPP(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),c_Message_Omsg_ONonce(u)),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1214]),
[iquote('0:SpL:66233.1,1214.0')] ).
cnf(75808,plain,
( ~ hBOOL(c_Public_Okeymode_OSignature)
| equal(hAPP(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),v_X),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1501]),
[iquote('0:SpL:66233.1,1501.0')] ).
cnf(75842,plain,
( ~ hBOOL(c_Public_Okeymode_OSignature)
| equal(hAPP(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),w),c_Public_Okeymode_OEncryption)
| equal(w,u) ),
inference(spl,[status(thm),theory(equality)],[66233,5449]),
[iquote('0:SpL:66233.1,5449.0')] ).
cnf(76054,plain,
( ~ hBOOL(hAPP(c_Set_Oimage(c_Public_OshrK,c_Event_Obad,tc_Message_Oagent,c_Public_Okeymode_OSignature),hAPP(c_Public_OshrK,v_A)))
| equal(tc_nat,c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1637]),
[iquote('0:SpL:66233.1,1637.0')] ).
cnf(76146,plain,
( ~ hBOOL(hAPP(c_Set_Oimage(c_Public_OshrK,c_Event_Obad,c_Public_Okeymode_OSignature,tc_nat),hAPP(c_Public_OshrK,v_A)))
| equal(tc_Message_Oagent,c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1637]),
[iquote('0:SpL:66233.1,1637.0')] ).
cnf(76186,plain,
( ~ hBOOL(hAPP(c_Set_Oimage(c_Public_OshrK,c_Public_Okeymode_OSignature,tc_Message_Oagent,tc_nat),hAPP(c_Public_OshrK,v_A)))
| equal(c_Event_Obad,c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1637]),
[iquote('0:SpL:66233.1,1637.0')] ).
cnf(76215,plain,
( ~ hBOOL(hAPP(c_List_Oset(v_evs,tc_Event_Oevent),c_Event_Oevent_OSays(v_B,c_Public_Okeymode_OSignature,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))))
| equal(v_A,c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,864]),
[iquote('0:SpL:66233.1,864.0')] ).
cnf(76338,plain,
( ~ hBOOL(hAPP(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),c_Public_Okeymode_OSignature))
| equal(c_Message_Omsg_ONonce(u),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1214]),
[iquote('0:SpL:66233.1,1214.0')] ).
cnf(76449,plain,
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(c_Public_Okeymode_OSignature),u))
| equal(tc_fun(v,tc_bool),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,38]),
[iquote('0:SpL:66233.1,38.0')] ).
cnf(76535,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,u))
| equal(c_Set_Oinsert(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),w),c_Public_Okeymode_OEncryption)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[66233,5449]),
[iquote('0:SpL:66233.1,5449.0')] ).
cnf(76591,plain,
( ~ hBOOL(hAPP(c_Set_Oimage(c_Public_Okeymode_OSignature,c_Event_Obad,tc_Message_Oagent,tc_nat),hAPP(c_Public_Okeymode_OSignature,v_A)))
| equal(c_Public_OshrK,c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1637]),
[iquote('0:SpL:66233.1,1637.0')] ).
cnf(76794,plain,
( ~ hBOOL(hAPP(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),c_Public_Okeymode_OSignature))
| equal(c_Message_Omsg_OCrypt(u,v),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1211]),
[iquote('0:SpL:66233.1,1211.0')] ).
cnf(76905,plain,
( ~ c_List_Odistinct(c_Public_Okeymode_OSignature,u)
| equal(c_List_Olist_OCons(v,c_List_Olist_OCons(v,w,u),u),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,5607]),
[iquote('0:SpL:66233.1,5607.0')] ).
cnf(76918,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,u))
| equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,38]),
[iquote('0:SpL:66233.1,38.0')] ).
cnf(76933,plain,
( ~ hBOOL(c_Public_Okeymode_OSignature)
| equal(c_Orderings_Obot__class_Obot(tc_bool),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1642]),
[iquote('0:SpL:66233.1,1642.0')] ).
cnf(76976,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,c_Message_Omsg_ONonce(c_Public_Osko__Public__XNonce__supply1__1__1(u))))
| equal(c_Event_Oused(u),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1215]),
[iquote('0:SpL:66233.1,1215.0')] ).
cnf(77018,plain,
( ~ equal(c_Message_Osynth(u),c_Public_Okeymode_OSignature)
| equal(c_List_Oset(c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,2110]),
[iquote('0:SpL:66233.1,2110.0')] ).
cnf(77021,plain,
( ~ equal(c_Event_OinitState(u),c_Public_Okeymode_OSignature)
| equal(c_List_Oset(c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,3662]),
[iquote('0:SpL:66233.1,3662.0')] ).
cnf(77092,plain,
( ~ hBOOL(hAPP(c_Message_OsymKeys,hAPP(c_Message_OinvKey,hAPP(c_Public_Okeymode_OSignature,u))))
| equal(c_Public_OpublicKey(v),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1285]),
[iquote('0:SpL:66233.1,1285.0')] ).
cnf(77177,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,v_X))
| equal(c_Set_Oimage(c_Message_Omsg_OKey,u,tc_nat,tc_Message_Omsg),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1660]),
[iquote('0:SpL:66233.1,1660.0')] ).
cnf(77187,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,hAPP(c_Public_OpublicKey(u),v)))
| equal(c_Set_Oimage(c_Public_OshrK,w,tc_Message_Oagent,tc_nat),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,2276]),
[iquote('0:SpL:66233.1,2276.0')] ).
cnf(77213,plain,
( ~ hBOOL(c_in(hAPP(c_Public_OshrK,u),c_Public_Okeymode_OSignature,tc_nat))
| equal(c_Set_Oimage(c_Message_OinvKey,c_Set_Oimage(c_Public_OpublicKey(v),w,tc_Message_Oagent,tc_nat),tc_nat,tc_nat),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,399]),
[iquote('0:SpL:66233.1,399.0')] ).
cnf(77222,plain,
( ~ hBOOL(hAPP(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),c_Public_Okeymode_OSignature))
| equal(v_X,c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[66233,1501]),
[iquote('0:SpL:66233.1,1501.0')] ).
cnf(77270,plain,
( equal(c_Event_OinitState(u),c_Public_Okeymode_OEncryption)
| equal(c_Event_OinitState(u),c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[384,66769]),
[iquote('0:Rew:384.0,66769.0')] ).
cnf(77302,plain,
( equal(c_List_Olist_OCons(u,c_Public_Okeymode_OEncryption,v),c_Public_Okeymode_OEncryption)
| c_List_Odistinct(c_Public_Okeymode_OSignature,v) ),
inference(rew,[status(thm),theory(equality)],[69224,73746]),
[iquote('0:Rew:69224.0,73746.0')] ).
cnf(77303,plain,
c_List_Odistinct(c_Public_Okeymode_OSignature,u),
inference(mrr,[status(thm)],[77302,525]),
[iquote('0:MRR:77302.0,525.0')] ).
cnf(78096,plain,
equal(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[76905,77303]),
[iquote('0:MRR:76905.0,77303.0')] ).
cnf(78102,plain,
equal(c_List_Oset(c_List_Olist_OCons(u,v,w),w),c_List_Oset(c_Public_Okeymode_OEncryption,w)),
inference(rew,[status(thm),theory(equality)],[78096,3121]),
[iquote('0:Rew:78096.0,3121.0')] ).
cnf(78105,plain,
equal(c_List_Oremdups(c_List_Olist_OCons(u,v,w),w),c_List_Oremdups(c_Public_Okeymode_OEncryption,w)),
inference(rew,[status(thm),theory(equality)],[78096,12623]),
[iquote('0:Rew:78096.0,12623.0')] ).
cnf(78196,plain,
hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v)),
inference(rew,[status(thm),theory(equality)],[78102,3040]),
[iquote('0:Rew:78102.0,3040.0')] ).
cnf(78455,plain,
( equal(hAPP(c_Message_Osynth(c_List_Oset(c_Public_Okeymode_OEncryption,tc_Message_Omsg)),u),c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[78102,68080]),
[iquote('0:Rew:78102.0,68080.0')] ).
cnf(78755,plain,
equal(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),c_List_Oset(c_Public_Okeymode_OEncryption,v)),
inference(rew,[status(thm),theory(equality)],[78102,3114]),
[iquote('0:Rew:78102.0,3114.0')] ).
cnf(78770,plain,
( equal(c_List_Oset(c_Public_Okeymode_OEncryption,u),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OSignature,v)) ),
inference(rew,[status(thm),theory(equality)],[78102,75033]),
[iquote('0:Rew:78102.0,75033.0')] ).
cnf(78772,plain,
( equal(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v),c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[78102,68092]),
[iquote('0:Rew:78102.0,68092.0')] ).
cnf(79169,plain,
equal(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),c_List_Oremdups(c_Public_Okeymode_OEncryption,v)),
inference(rew,[status(thm),theory(equality)],[78105,17532]),
[iquote('0:Rew:78105.0,17532.0')] ).
cnf(79181,plain,
equal(c_List_Oappend(c_List_Oremdups(c_Public_Okeymode_OEncryption,u),v,u),c_List_Olist_OCons(w,v,u)),
inference(rew,[status(thm),theory(equality)],[79169,6697]),
[iquote('0:Rew:79169.0,6697.0')] ).
cnf(79362,plain,
equal(c_Event_Oused(c_List_Oappend(c_List_Oremdups(c_Public_Okeymode_OEncryption,tc_Event_Oevent),u,tc_Event_Oevent)),c_Event_Oused(u)),
inference(rew,[status(thm),theory(equality)],[79181,553]),
[iquote('0:Rew:79181.0,553.0')] ).
cnf(79879,plain,
( equal(c_Event_Oused(c_List_Oappend(c_List_Oremdups(c_Public_Okeymode_OEncryption,tc_Event_Oevent),u,tc_Event_Oevent)),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OSignature,v)) ),
inference(rew,[status(thm),theory(equality)],[79181,74652]),
[iquote('0:Rew:79181.0,74652.0')] ).
cnf(79885,plain,
hBOOL(hAPP(c_Event_Oused(c_List_Oappend(c_List_Oappend(c_List_Oremdups(c_Public_Okeymode_OEncryption,tc_Event_Oevent),u,tc_Event_Oevent),v,tc_Event_Oevent)),w)),
inference(rew,[status(thm),theory(equality)],[79181,17558]),
[iquote('0:Rew:79181.0,17558.0')] ).
cnf(80823,plain,
( equal(c_Event_Oused(u),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OSignature,v)) ),
inference(rew,[status(thm),theory(equality)],[79362,79879]),
[iquote('0:Rew:79362.0,79879.0')] ).
cnf(80825,plain,
equal(c_Event_Oused(u),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[76976,80823]),
[iquote('0:MRR:76976.0,80823.1')] ).
cnf(80875,plain,
~ hBOOL(hAPP(c_Public_Okeymode_OEncryption,c_Message_Omsg_OCrypt(u,v))),
inference(rew,[status(thm),theory(equality)],[80825,1211]),
[iquote('0:Rew:80825.0,1211.0')] ).
cnf(80876,plain,
~ hBOOL(hAPP(c_Public_Okeymode_OEncryption,v_X)),
inference(rew,[status(thm),theory(equality)],[80825,1501]),
[iquote('0:Rew:80825.0,1501.0')] ).
cnf(80926,plain,
~ equal(c_List_Oset(c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[80825,3683]),
[iquote('0:Rew:80825.0,3683.0')] ).
cnf(81449,plain,
( equal(v_evs,c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OEncryption,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))) ),
inference(rew,[status(thm),theory(equality)],[80825,66280]),
[iquote('0:Rew:80825.0,66280.1')] ).
cnf(81510,plain,
( ~ hBOOL(c_Public_Okeymode_OSignature)
| equal(hAPP(c_Public_Okeymode_OEncryption,v_X),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[80825,75808]),
[iquote('0:Rew:80825.0,75808.1')] ).
cnf(81511,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OEncryption,c_Public_Okeymode_OSignature))
| equal(c_Message_Omsg_OCrypt(u,v),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[80825,76794]),
[iquote('0:Rew:80825.0,76794.0')] ).
cnf(81512,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OEncryption,c_Public_Okeymode_OSignature))
| equal(c_Message_Omsg_ONonce(u),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[80825,76338]),
[iquote('0:Rew:80825.0,76338.0')] ).
cnf(81513,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OEncryption,c_Public_Okeymode_OSignature))
| equal(v_X,c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[80825,77222]),
[iquote('0:Rew:80825.0,77222.0')] ).
cnf(81514,plain,
( ~ hBOOL(c_Public_Okeymode_OSignature)
| equal(hAPP(c_Public_Okeymode_OEncryption,c_Message_Omsg_ONonce(u)),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[80825,75786]),
[iquote('0:Rew:80825.0,75786.1')] ).
cnf(82345,plain,
( equal(c_Message_Omsg_ONonce(v_NB),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OEncryption,c_Public_Okeymode_OSignature)) ),
inference(rew,[status(thm),theory(equality)],[80825,71332]),
[iquote('0:Rew:80825.0,71332.1')] ).
cnf(82346,plain,
( equal(v_NB,c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OEncryption,c_Message_Omsg_ONonce(c_Public_Okeymode_OSignature))) ),
inference(rew,[status(thm),theory(equality)],[80825,74757]),
[iquote('0:Rew:80825.0,74757.1')] ).
cnf(82660,plain,
~ equal(c_Message_Osynth(u),c_Public_Okeymode_OSignature),
inference(mrr,[status(thm)],[77018,80926]),
[iquote('0:MRR:77018.1,80926.0')] ).
cnf(82661,plain,
~ equal(c_Event_OinitState(u),c_Public_Okeymode_OSignature),
inference(mrr,[status(thm)],[77021,80926]),
[iquote('0:MRR:77021.1,80926.0')] ).
cnf(82840,plain,
equal(c_Message_Osynth(u),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[70184,82660]),
[iquote('0:MRR:70184.1,82660.0')] ).
cnf(82841,plain,
equal(c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Omsg,tc_bool)),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[73209,82660]),
[iquote('0:MRR:73209.1,82660.0')] ).
cnf(83360,plain,
c_lessequals(u,c_Lattices_Oupper__semilattice__class_Osup(c_Public_Okeymode_OEncryption,v,tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(rew,[status(thm),theory(equality)],[82840,50557]),
[iquote('0:Rew:82840.0,50557.0')] ).
cnf(83663,plain,
equal(hAPP(c_Public_Okeymode_OEncryption,c_ATP__Linkup_Osko__Set__XrangeE__1__1(c_Orderings_Otop__class_Otop(tc_bool),c_Public_Okeymode_OEncryption,u,v)),c_Orderings_Otop__class_Otop(tc_bool)),
inference(rew,[status(thm),theory(equality)],[82840,44668]),
[iquote('0:Rew:82840.0,44668.0')] ).
cnf(83766,plain,
( ~ c_lessequals(hAPP(c_Public_Okeymode_OEncryption,hAPP(c_Message_OinvKey,c_Lattices_Oupper__semilattice__class_Osup(u,v,tc_bool))),w,tc_bool)
| c_lessequals(v,w,tc_bool) ),
inference(rew,[status(thm),theory(equality)],[82840,31266]),
[iquote('0:Rew:82840.0,31266.0')] ).
cnf(84106,plain,
( equal(hAPP(c_Public_Okeymode_OEncryption,u),c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[82840,78455]),
[iquote('0:Rew:82840.0,78455.0')] ).
cnf(88322,plain,
equal(c_Event_OinitState(u),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[77270,82661]),
[iquote('0:MRR:77270.1,82661.0')] ).
cnf(88581,plain,
( ~ equal(c_Set_Oimage(c_Message_Omsg_OKey,u,tc_nat,tc_Message_Omsg),c_Public_Okeymode_OEncryption)
| ~ c_Fun_Oinj__on(c_Message_Omsg_OKey,c_Orderings_Otop__class_Otop(tc_fun(tc_nat,tc_bool)),tc_nat,tc_Message_Omsg)
| equal(u,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OshrK,c_Event_Obad,tc_Message_Oagent,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OEncryption),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OSignature),c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat),c_Set_Oimage(c_Message_OinvKey,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OEncryption),c_Event_Obad,tc_Message_Oagent,tc_nat),c_Set_Oimage(c_Public_OpublicKey(c_Public_Okeymode_OSignature),c_Event_Obad,tc_Message_Oagent,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,tc_nat),tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_bool))) ),
inference(rew,[status(thm),theory(equality)],[88322,31980]),
[iquote('0:Rew:88322.0,31980.0')] ).
cnf(89294,plain,
equal(hAPP(c_Public_Okeymode_OEncryption,v_X),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[81510,84106]),
[iquote('0:MRR:81510.0,84106.1')] ).
cnf(89295,plain,
~ hBOOL(c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[89294,80876]),
[iquote('0:Rew:89294.0,80876.0')] ).
cnf(89509,plain,
equal(c_Message_Omsg_ONonce(v_NB),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[82345,81512]),
[iquote('0:MRR:82345.1,81512.0')] ).
cnf(89616,plain,
equal(hAPP(c_Public_Okeymode_OEncryption,c_Message_Omsg_ONonce(u)),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[81514,84106]),
[iquote('0:MRR:81514.0,84106.1')] ).
cnf(89617,plain,
( equal(v_NB,c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[89616,82346]),
[iquote('0:Rew:89616.0,82346.1')] ).
cnf(89619,plain,
equal(v_NB,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[89617,89295]),
[iquote('0:MRR:89617.1,89295.0')] ).
cnf(89620,plain,
equal(c_Message_Omsg_ONonce(c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[89619,89509]),
[iquote('0:Rew:89619.0,89509.0')] ).
cnf(89992,plain,
( equal(v_evs,c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OEncryption,c_Message_Omsg_OCrypt(v_K,c_Public_Okeymode_OEncryption))) ),
inference(rew,[status(thm),theory(equality)],[89620,81449,89619]),
[iquote('0:Rew:89620.0,81449.1,89619.0,81449.1')] ).
cnf(89993,plain,
equal(v_evs,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[89992,80875]),
[iquote('0:MRR:89992.1,80875.0')] ).
cnf(91660,plain,
hBOOL(hAPP(c_Event_Oused(c_List_Oappend(c_List_Oremdups(c_Public_Okeymode_OEncryption,tc_Event_Oevent),c_List_Oappend(u,v,tc_Event_Oevent),tc_Event_Oevent)),w)),
inference(rew,[status(thm),theory(equality)],[328,79885]),
[iquote('0:Rew:328.0,79885.0')] ).
cnf(91661,plain,
hBOOL(hAPP(c_Public_Okeymode_OEncryption,u)),
inference(rew,[status(thm),theory(equality)],[80825,91660]),
[iquote('0:Rew:80825.0,91660.0')] ).
cnf(91662,plain,
equal(v_X,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[81513,91661]),
[iquote('0:MRR:81513.0,91661.0')] ).
cnf(91665,plain,
equal(c_Message_Omsg_OCrypt(u,v),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[81511,91661]),
[iquote('0:MRR:81511.0,91661.0')] ).
cnf(91958,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,c_Public_Okeymode_OEncryption))
| equal(c_Set_Oimage(c_Message_Omsg_OKey,u,tc_nat,tc_Message_Omsg),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[91662,77177]),
[iquote('0:Rew:91662.0,77177.0')] ).
cnf(95282,plain,
( equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Public_Okeymode_OEncryption)
| hBOOL(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OSignature,tc_bool))
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[74982,74985]),
[iquote('0:Rew:74982.1,74985.1')] ).
cnf(95283,plain,
( equal(hAPP(u,v_x),c_Public_Okeymode_OEncryption)
| equal(hAPP(u,v_x),c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[7839,74986]),
[iquote('0:Rew:7839.0,74986.0')] ).
cnf(95284,plain,
( equal(hAPP(u,v_x),c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OSignature)
| hBOOL(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OSignature,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[95283,68761]),
[iquote('0:Rew:95283.1,68761.1')] ).
cnf(95285,plain,
( equal(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OEncryption,tc_bool),c_Public_Okeymode_OEncryption)
| hBOOL(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OSignature,tc_bool))
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[95284,95282]),
[iquote('0:Rew:95284.0,95282.0')] ).
cnf(98448,plain,
( ~ hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,tc_Event_Oevent),c_Event_Oevent_OSays(v_B,c_Public_Okeymode_OSignature,c_Public_Okeymode_OEncryption)))
| equal(v_A,c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[89993,76215,91665]),
[iquote('0:Rew:89993.0,76215.0,91665.0,76215.0')] ).
cnf(98449,plain,
equal(v_A,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[98448,78196]),
[iquote('0:MRR:98448.0,78196.0')] ).
cnf(98468,plain,
( ~ hBOOL(hAPP(c_Set_Oimage(c_Public_OshrK,c_Event_Obad,tc_Message_Oagent,c_Public_Okeymode_OSignature),hAPP(c_Public_OshrK,c_Public_Okeymode_OEncryption)))
| equal(tc_nat,c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[98449,76054]),
[iquote('0:Rew:98449.0,76054.0')] ).
cnf(98469,plain,
( ~ hBOOL(hAPP(c_Set_Oimage(c_Public_OshrK,c_Event_Obad,c_Public_Okeymode_OSignature,tc_nat),hAPP(c_Public_OshrK,c_Public_Okeymode_OEncryption)))
| equal(tc_Message_Oagent,c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[98449,76146]),
[iquote('0:Rew:98449.0,76146.0')] ).
cnf(98470,plain,
( ~ hBOOL(hAPP(c_Set_Oimage(c_Public_OshrK,c_Public_Okeymode_OSignature,tc_Message_Oagent,tc_nat),hAPP(c_Public_OshrK,c_Public_Okeymode_OEncryption)))
| equal(c_Event_Obad,c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[98449,76186]),
[iquote('0:Rew:98449.0,76186.0')] ).
cnf(98594,plain,
( ~ hBOOL(hAPP(c_Set_Oimage(c_Public_Okeymode_OSignature,c_Event_Obad,tc_Message_Oagent,tc_nat),hAPP(c_Public_Okeymode_OSignature,c_Public_Okeymode_OEncryption)))
| equal(c_Public_OshrK,c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[98449,76591]),
[iquote('0:Rew:98449.0,76591.0')] ).
cnf(99308,plain,
( ~ hBOOL(c_Public_Okeymode_OSignature)
| equal(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v),c_Public_Okeymode_OEncryption)
| equal(v,w) ),
inference(rew,[status(thm),theory(equality)],[78755,75842]),
[iquote('0:Rew:78755.0,75842.1')] ).
cnf(99309,plain,
( equal(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v),c_Public_Okeymode_OEncryption)
| equal(v,w) ),
inference(mrr,[status(thm)],[99308,78772]),
[iquote('0:MRR:99308.0,78772.1')] ).
cnf(99340,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,u))
| equal(c_List_Oset(c_Public_Okeymode_OEncryption,v),c_Public_Okeymode_OEncryption)
| equal(u,w) ),
inference(rew,[status(thm),theory(equality)],[78755,76535]),
[iquote('0:Rew:78755.0,76535.1')] ).
cnf(99341,plain,
( equal(c_List_Oset(c_Public_Okeymode_OEncryption,u),c_Public_Okeymode_OEncryption)
| equal(v,w) ),
inference(mrr,[status(thm)],[99340,78770]),
[iquote('0:MRR:99340.0,78770.1')] ).
cnf(99343,plain,
( equal(hAPP(c_Public_Okeymode_OEncryption,u),c_Public_Okeymode_OEncryption)
| equal(u,v) ),
inference(rew,[status(thm),theory(equality)],[99341,99309]),
[iquote('0:Rew:99341.0,99309.0')] ).
cnf(99350,plain,
equal(hAPP(c_Public_Okeymode_OEncryption,u),c_Public_Okeymode_OEncryption),
inference(aed,[status(thm),theory(equality)],[29,99343]),
[iquote('0:AED:29.0,99343.1')] ).
cnf(99353,plain,
equal(c_Orderings_Otop__class_Otop(tc_bool),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[99350,83663]),
[iquote('0:Rew:99350.0,83663.0')] ).
cnf(99379,plain,
( ~ c_lessequals(c_Public_Okeymode_OEncryption,u,tc_bool)
| c_lessequals(v,u,tc_bool) ),
inference(rew,[status(thm),theory(equality)],[99350,83766]),
[iquote('0:Rew:99350.0,83766.0')] ).
cnf(99395,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OEncryption,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(rew,[status(thm),theory(equality)],[99353,9576]),
[iquote('0:Rew:99353.0,9576.0')] ).
cnf(99537,plain,
( equal(c_Orderings_Obot__class_Obot(tc_bool),c_Public_Okeymode_OEncryption)
| equal(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OSignature,tc_bool),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[99353,73879]),
[iquote('0:Rew:99353.0,73879.1')] ).
cnf(99558,plain,
( equal(c_Orderings_Obot__class_Obot(tc_bool),c_Public_Okeymode_OEncryption)
| hBOOL(c_HOL_Ouminus__class_Ouminus(c_Public_Okeymode_OSignature,tc_bool))
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[99395,95285]),
[iquote('0:Rew:99395.0,95285.0')] ).
cnf(99564,plain,
( equal(c_Orderings_Obot__class_Obot(tc_bool),c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OEncryption)
| hBOOL(c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[99537,99558]),
[iquote('0:Rew:99537.1,99558.1')] ).
cnf(99565,plain,
equal(c_Orderings_Obot__class_Obot(tc_bool),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[99564,89295,76933]),
[iquote('0:MRR:99564.1,99564.2,89295.0,76933.0')] ).
cnf(99570,plain,
c_lessequals(c_Public_Okeymode_OEncryption,u,tc_bool),
inference(rew,[status(thm),theory(equality)],[99565,32682]),
[iquote('0:Rew:99565.0,32682.0')] ).
cnf(99635,plain,
c_lessequals(u,v,tc_bool),
inference(mrr,[status(thm)],[99379,99570]),
[iquote('0:MRR:99379.0,99570.0')] ).
cnf(99652,plain,
equal(hAPP(c_Set_Oinsert(u,v,w),x),hAPP(v,x)),
inference(mrr,[status(thm)],[21010,99635]),
[iquote('0:MRR:21010.0,99635.0')] ).
cnf(100049,plain,
( equal(c_Public_Okeymode_OEncryption,u)
| hBOOL(hAPP(c_Set_Oinsert(u,v,w),x)) ),
inference(rew,[status(thm),theory(equality)],[99652,75559]),
[iquote('0:Rew:99652.0,75559.1')] ).
cnf(100222,plain,
( equal(c_Public_Okeymode_OEncryption,u)
| hBOOL(hAPP(v,w)) ),
inference(rew,[status(thm),theory(equality)],[99652,100049]),
[iquote('0:Rew:99652.0,100049.1')] ).
cnf(100238,plain,
equal(c_Public_OpublicKey(u),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[77092,100222]),
[iquote('0:MRR:77092.0,100222.1')] ).
cnf(100240,plain,
equal(tc_fun(u,tc_bool),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[76449,100222]),
[iquote('0:MRR:76449.0,100222.1')] ).
cnf(100242,plain,
equal(c_Public_OshrK,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[98594,100222]),
[iquote('0:MRR:98594.0,100222.1')] ).
cnf(100245,plain,
equal(c_Event_Obad,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[98470,100222]),
[iquote('0:MRR:98470.0,100222.1')] ).
cnf(100249,plain,
equal(tc_nat,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[98468,100222]),
[iquote('0:MRR:98468.0,100222.1')] ).
cnf(100253,plain,
equal(tc_Message_Oagent,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[98469,100222]),
[iquote('0:MRR:98469.0,100222.1')] ).
cnf(100272,plain,
equal(c_Set_Oimage(c_Public_OshrK,u,tc_Message_Oagent,tc_nat),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[77187,100222]),
[iquote('0:MRR:77187.0,100222.1')] ).
cnf(100275,plain,
equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[76918,100222]),
[iquote('0:MRR:76918.0,100222.1')] ).
cnf(100279,plain,
equal(c_Set_Oimage(c_Message_Omsg_OKey,u,tc_nat,tc_Message_Omsg),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[91958,100222]),
[iquote('0:MRR:91958.0,100222.1')] ).
cnf(101195,plain,
( ~ c_lessequals(u,v,tc_fun(w,tc_bool))
| equal(c_Lattices_Oupper__semilattice__class_Osup(u,v,c_Public_Okeymode_OEncryption),v) ),
inference(rew,[status(thm),theory(equality)],[100240,161]),
[iquote('0:Rew:100240.0,161.1')] ).
cnf(101248,plain,
equal(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(c_Public_Okeymode_OEncryption),u,c_Public_Okeymode_OEncryption),u),
inference(rew,[status(thm),theory(equality)],[100240,34]),
[iquote('0:Rew:100240.0,34.0')] ).
cnf(101318,plain,
( ~ c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(c_Public_Okeymode_OEncryption),v,w)
| c_Fun_Oinj__on(u,x,v,w) ),
inference(rew,[status(thm),theory(equality)],[100240,9480]),
[iquote('0:Rew:100240.0,9480.0')] ).
cnf(101322,plain,
c_Fun_Oinj__on(u,c_Orderings_Obot__class_Obot(c_Public_Okeymode_OEncryption),v,w),
inference(rew,[status(thm),theory(equality)],[100240,19]),
[iquote('0:Rew:100240.0,19.0')] ).
cnf(102710,plain,
equal(c_Orderings_Otop__class_Otop(c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[100240,82841]),
[iquote('0:Rew:100240.0,82841.0')] ).
cnf(102728,plain,
c_lessequals(u,c_Lattices_Oupper__semilattice__class_Osup(c_Public_Okeymode_OEncryption,v,c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[100240,83360]),
[iquote('0:Rew:100240.0,83360.0')] ).
cnf(102853,plain,
( ~ c_lessequals(c_Orderings_Otop__class_Otop(c_Public_Okeymode_OEncryption),u,c_Public_Okeymode_OEncryption)
| hBOOL(c_in(v,u,w)) ),
inference(rew,[status(thm),theory(equality)],[100240,5674]),
[iquote('0:Rew:100240.0,5674.0')] ).
cnf(103004,plain,
equal(c_Orderings_Obot__class_Obot(c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[100240,100275]),
[iquote('0:Rew:100240.0,100275.0')] ).
cnf(103108,plain,
c_Fun_Oinj__on(u,c_Public_Okeymode_OEncryption,v,w),
inference(rew,[status(thm),theory(equality)],[103004,101322]),
[iquote('0:Rew:103004.0,101322.0')] ).
cnf(103119,plain,
equal(c_Set_Oimage(c_Public_Okeymode_OEncryption,u,c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[100242,100272,100253,100249]),
[iquote('0:Rew:100242.0,100272.0,100253.0,100272.0,100249.0,100272.0')] ).
cnf(103120,plain,
equal(c_Set_Oimage(c_Message_Omsg_OKey,u,c_Public_Okeymode_OEncryption,tc_Message_Omsg),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[100249,100279]),
[iquote('0:Rew:100249.0,100279.0')] ).
cnf(103324,plain,
equal(c_Lattices_Oupper__semilattice__class_Osup(c_Public_Okeymode_OEncryption,u,c_Public_Okeymode_OEncryption),u),
inference(rew,[status(thm),theory(equality)],[103004,101248]),
[iquote('0:Rew:103004.0,101248.0')] ).
cnf(103508,plain,
c_lessequals(u,v,c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[103324,102728]),
[iquote('0:Rew:103324.0,102728.0')] ).
cnf(103927,plain,
( ~ c_lessequals(c_Public_Okeymode_OEncryption,u,c_Public_Okeymode_OEncryption)
| hBOOL(c_in(v,u,w)) ),
inference(rew,[status(thm),theory(equality)],[102710,102853]),
[iquote('0:Rew:102710.0,102853.0')] ).
cnf(103928,plain,
hBOOL(c_in(u,v,w)),
inference(mrr,[status(thm)],[103927,103508]),
[iquote('0:MRR:103927.0,103508.0')] ).
cnf(104010,plain,
( ~ c_Fun_Oinj__on(u,c_Public_Okeymode_OEncryption,v,w)
| c_Fun_Oinj__on(u,x,v,w) ),
inference(rew,[status(thm),theory(equality)],[102710,101318]),
[iquote('0:Rew:102710.0,101318.0')] ).
cnf(104011,plain,
c_Fun_Oinj__on(u,v,w,x),
inference(mrr,[status(thm)],[104010,103108]),
[iquote('0:MRR:104010.0,103108.0')] ).
cnf(104089,plain,
( ~ c_lessequals(u,v,c_Public_Okeymode_OEncryption)
| equal(c_Lattices_Oupper__semilattice__class_Osup(u,v,c_Public_Okeymode_OEncryption),v) ),
inference(rew,[status(thm),theory(equality)],[100240,101195]),
[iquote('0:Rew:100240.0,101195.0')] ).
cnf(104090,plain,
equal(c_Lattices_Oupper__semilattice__class_Osup(u,v,c_Public_Okeymode_OEncryption),v),
inference(mrr,[status(thm)],[104089,103508]),
[iquote('0:MRR:104089.0,103508.0')] ).
cnf(105412,plain,
( ~ hBOOL(c_in(c_Public_Okeymode_OEncryption,c_Public_Okeymode_OSignature,c_Public_Okeymode_OEncryption))
| equal(c_Set_Oimage(c_Message_OinvKey,c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[103119,77213,100238,100253,100249,99350,100242]),
[iquote('0:Rew:103119.0,77213.1,100238.0,77213.1,100253.0,77213.1,100249.0,77213.1,99350.0,77213.0,100242.0,77213.0,100249.0,77213.0')] ).
cnf(105413,plain,
equal(c_Set_Oimage(c_Message_OinvKey,c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[105412,103928]),
[iquote('0:MRR:105412.0,103928.0')] ).
cnf(107647,plain,
( ~ equal(c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption)
| ~ c_Fun_Oinj__on(c_Message_Omsg_OKey,c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption,tc_Message_Omsg)
| equal(u,c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[105413,88581,103119,100238,100245,100253,104090,100249,100240,102710,103120]),
[iquote('0:Rew:105413.0,88581.2,103119.0,88581.2,100238.0,88581.2,100245.0,88581.2,100253.0,88581.2,104090.0,88581.2,100249.0,88581.2,104090.0,88581.2,104090.0,88581.2,104090.0,88581.2,100240.0,88581.2,102710.0,88581.1,100240.0,88581.1,100249.0,88581.1,103120.0,88581.0,100249.0,88581.0')] ).
cnf(107648,plain,
( ~ c_Fun_Oinj__on(c_Message_Omsg_OKey,c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption,tc_Message_Omsg)
| equal(u,c_Public_Okeymode_OEncryption) ),
inference(obv,[status(thm),theory(equality)],[107647]),
[iquote('0:Obv:107647.0')] ).
cnf(107649,plain,
equal(u,c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[107648,104011]),
[iquote('0:MRR:107648.0,104011.0')] ).
cnf(107650,plain,
$false,
inference(unc,[status(thm)],[107649,525]),
[iquote('0:UnC:107649.0,525.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV758-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 15 07:24:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 117.15/117.37
% 117.15/117.37 SPASS V 3.9
% 117.15/117.37 SPASS beiseite: Proof found.
% 117.15/117.37 % SZS status Theorem
% 117.15/117.37 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 117.15/117.37 SPASS derived 81442 clauses, backtracked 0 clauses, performed 1 splits and kept 23934 clauses.
% 117.15/117.37 SPASS allocated 163657 KBytes.
% 117.15/117.37 SPASS spent 0:1:56.88 on the problem.
% 117.15/117.37 0:00:00.06 for the input.
% 117.15/117.37 0:00:00.00 for the FLOTTER CNF translation.
% 117.15/117.37 0:00:01.58 for inferences.
% 117.15/117.37 0:00:00.01 for the backtracking.
% 117.15/117.37 0:1:53.92 for the reduction.
% 117.15/117.37
% 117.15/117.37
% 117.15/117.37 Here is a proof with depth 7, length 389 :
% 117.15/117.37 % SZS output start Refutation
% See solution above
% 117.15/117.38 Formulae used in the proof : cls_ex__in__conv_0 cls_inj__on__empty_0 cls_singletonE_0 cls_bot__fun__eq_0 cls_empty__subsetI_0 cls_bot__least_0 cls_insert__not__empty_0 cls_sup__bot__left_0 cls_Un__empty__left_0 cls_Compl__UNIV__eq_0 cls_bot1E_0 cls_empty__not__insert_0 cls_Compl__empty__eq_0 cls_set__empty2_1 cls_Un__assoc_0 cls_Un__upper1_0 cls_sup__ge1_0 cls_insert__commute_0 cls_keymode_Oinduct_0 cls_self__append__conv2_1 cls_Un__UNIV__right_0 cls_insert__absorb2_0 cls_insert__code_0 cls_subset__insertI_0 cls_sup1E_0 cls_order__antisym__conv_0 cls_Un__absorb1_0 cls_distinct_Osimps_I1_J_0 cls_analz__image__freshK__simps_I57_J_0 cls_subset__UNIV_0 cls_fun__Compl__def_0 cls_insert__code_1 cls_Compl__partition_0 cls_insert__subset_0 cls_Cons__eq__appendI_0 cls_Un__commute_0 cls_inj__on__Un_0 cls_double__complement_0 cls_le__funD_0 cls_insertCI_1 cls_insert__absorb_0 cls_remdups__eq__nil__right__iff_1 cls_synth__increasing_0 cls_le__supE_1 cls_order__trans_0 cls_append__eq__append__conv2_5 cls_List_Oset_Osimps_I2_J_0 cls_inj__image__eq__iff_0 cls_top__fun__eq_0 cls_knows__Nil_0 cls_shrK__notin__image__privateKey_0 cls_Nonce__supply1_0 cls_Nonce__notin__used__empty_0 cls_Crypt__notin__used__empty_0 cls_rangeE_0 cls_remdups_Osimps_I2_J_0 cls_distinct_Osimps_I2_J_0 cls_remdups_Osimps_I2_J_1 cls_distinct_Osimps_I2_J_2 cls_initState__Spy_0 cls_synth_OAgent_0 cls_shrK__image__eq_0 cls_UNIV__I_0 cls_not__Cons__self2_0 cls_synth__idem_0 cls_rangeI_0 cls_publicKey__notin__image__shrK_0 cls_top1I_0 cls_invKey_0 cls_not__symKeys__priK_0 cls_used__Gets_0 cls_Crypt__notin__image__Key_0 cls_shrK__in__initState_0 cls_neq__shrK_0 cls_usedI_0 cls_Notes__imp__used_0 cls_parts_OBody_0 cls_cert__A__form_1 cls_mem__def_1 cls_mem__def_0 clsarity_fun__Lattices_Oupper__semilattice clsarity_fun__Lattices_Obounded__lattice clsarity_fun__Lattices_Oboolean__algebra clsarity_fun__Orderings_Opreorder clsarity_fun__Lattices_Olattice clsarity_fun__Orderings_Oorder clsarity_fun__Orderings_Otop clsarity_fun__Orderings_Obot clsarity_fun__HOL_Ouminus clsarity_fun__HOL_Oord clsarity_bool__Lattices_Oupper__semilattice clsarity_bool__Lattices_Obounded__lattice clsarity_bool__Lattices_Oboolean__algebra clsarity_bool__Orderings_Opreorder clsarity_bool__Lattices_Olattice clsarity_bool__Orderings_Oorder clsarity_bool__Orderings_Otop clsarity_bool__Orderings_Obot clsarity_bool__HOL_Ouminus clsarity_bool__HOL_Oord cls_conjecture_0 cls_conjecture_1 cls_conjecture_3 cls_conjecture_5 cls_conjecture_6
% 118.35/118.54
%------------------------------------------------------------------------------