TSTP Solution File: SWV348-2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV348-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%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 : 300s
% DateTime : Thu Sep 29 15:11:22 EDT 2022
% Result : Unsatisfiable 0.70s 0.70s
% Output : Proof 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV348-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 02:38:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.70/0.70 % SZS status Unsatisfiable
% 0.70/0.70 % SZS output start Proof
% 0.70/0.70 tff(c_in_type, type, (
% 0.70/0.70 c_in: ( $i * $i * $i ) > $o)).
% 0.70/0.70 tff(tc_Message_Omsg_type, type, (
% 0.70/0.70 tc_Message_Omsg: $i)).
% 0.70/0.70 tff(c_Message_Oanalz_type, type, (
% 0.70/0.70 c_Message_Oanalz: $i > $i)).
% 0.70/0.70 tff(c_Event_Oknows_type, type, (
% 0.70/0.70 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.70/0.70 tff(v_evs4_type, type, (
% 0.70/0.70 v_evs4: $i)).
% 0.70/0.70 tff(c_Message_Oagent_OSpy_type, type, (
% 0.70/0.70 c_Message_Oagent_OSpy: $i)).
% 0.70/0.70 tff(c_Message_Omsg_OMPair_type, type, (
% 0.70/0.70 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.70/0.70 tff(c_Message_Omsg_ONonce_type, type, (
% 0.70/0.70 c_Message_Omsg_ONonce: $i > $i)).
% 0.70/0.70 tff(v_NB_type, type, (
% 0.70/0.70 v_NB: $i)).
% 0.70/0.70 tff(v_NAa_type, type, (
% 0.70/0.70 v_NAa: $i)).
% 0.70/0.70 tff(c_Message_Omsg_OKey_type, type, (
% 0.70/0.70 c_Message_Omsg_OKey: $i > $i)).
% 0.70/0.70 tff(v_K_type, type, (
% 0.70/0.70 v_K: $i)).
% 0.70/0.70 tff(c_Message_Omsg_OAgent_type, type, (
% 0.70/0.70 c_Message_Omsg_OAgent: $i > $i)).
% 0.70/0.70 tff(v_Ba_type, type, (
% 0.70/0.70 v_Ba: $i)).
% 0.70/0.70 tff(c_Public_OshrK_type, type, (
% 0.70/0.70 c_Public_OshrK: $i > $i)).
% 0.70/0.70 tff(v_Aa_type, type, (
% 0.70/0.70 v_Aa: $i)).
% 0.70/0.70 tff(tc_Message_Oagent_type, type, (
% 0.70/0.70 tc_Message_Oagent: $i)).
% 0.70/0.70 tff(c_Event_Obad_type, type, (
% 0.70/0.70 c_Event_Obad: $i)).
% 0.70/0.70 tff(v_B_type, type, (
% 0.70/0.70 v_B: $i)).
% 0.70/0.70 tff(tc_Event_Oevent_type, type, (
% 0.70/0.70 tc_Event_Oevent: $i)).
% 0.70/0.70 tff(c_List_Oset_type, type, (
% 0.70/0.70 c_List_Oset: ( $i * $i ) > $i)).
% 0.70/0.70 tff(c_Event_Oevent_OGets_type, type, (
% 0.70/0.70 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.70/0.70 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.70/0.70 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.70/0.70 tff(c_Message_Oagent_OServer_type, type, (
% 0.70/0.70 c_Message_Oagent_OServer: $i)).
% 0.70/0.70 tff(c_Event_Oevent_OSays_type, type, (
% 0.70/0.70 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.70/0.70 tff(c_Message_Oparts_type, type, (
% 0.70/0.70 c_Message_Oparts: $i > $i)).
% 0.70/0.70 tff(v_X_type, type, (
% 0.70/0.70 v_X: $i)).
% 0.70/0.70 tff(tc_List_Olist_type, type, (
% 0.70/0.70 tc_List_Olist: $i > $i)).
% 0.70/0.70 tff(c_Yahalom_Oyahalom_type, type, (
% 0.70/0.70 c_Yahalom_Oyahalom: $i)).
% 0.70/0.70 tff(v_NA_type, type, (
% 0.70/0.70 v_NA: $i)).
% 0.70/0.70 tff(v_A_type, type, (
% 0.70/0.70 v_A: $i)).
% 0.70/0.70 tff(c_Event_Oevent_ONotes_type, type, (
% 0.70/0.70 c_Event_Oevent_ONotes: ( $i * $i ) > $i)).
% 0.70/0.70 tff(1,assumption,(~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)), introduced(assumption)).
% 0.70/0.70 tff(2,plain,
% 0.70/0.70 (^[V_H: $i] : refl((c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H)) <=> (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H)))),
% 0.70/0.70 inference(bind,[status(th)],[])).
% 0.70/0.70 tff(3,plain,
% 0.70/0.70 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H)) <=> ![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.70/0.70 inference(quant_intro,[status(thm)],[2])).
% 0.70/0.70 tff(4,plain,
% 0.70/0.70 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H)) <=> ![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(5,axiom,(![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oparts__analz_0')).
% 0.70/0.70 tff(6,plain,
% 0.70/0.70 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.70/0.70 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.70/0.70 tff(7,plain,(
% 0.70/0.70 ![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.70/0.70 inference(skolemize,[status(sab)],[6])).
% 0.70/0.70 tff(8,plain,
% 0.70/0.70 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.70/0.70 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.70/0.70 tff(9,plain,
% 0.70/0.70 ((~![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))) | (c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)))),
% 0.70/0.70 inference(quant_inst,[status(thm)],[])).
% 0.70/0.70 tff(10,plain,
% 0.70/0.70 (c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))),
% 0.70/0.70 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.70/0.70 tff(11,plain,
% 0.70/0.70 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.70/0.70 inference(monotonicity,[status(thm)],[10])).
% 0.70/0.70 tff(12,plain,
% 0.70/0.70 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.70/0.70 inference(symmetry,[status(thm)],[11])).
% 0.70/0.70 tff(13,plain,
% 0.70/0.70 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.70/0.70 inference(monotonicity,[status(thm)],[12])).
% 0.70/0.70 tff(14,assumption,(~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), introduced(assumption)).
% 0.70/0.70 tff(15,plain,
% 0.70/0.70 (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.70/0.70 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.70/0.70 tff(16,plain,
% 0.70/0.70 (c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) <=> c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(17,axiom,(c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.70/0.70 tff(18,plain,
% 0.70/0.70 (c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.70/0.71 tff(19,plain,
% 0.70/0.71 (c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) <=> c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(20,axiom,(c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.70/0.71 tff(21,plain,
% 0.70/0.71 (c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.70/0.71 tff(22,plain,
% 0.70/0.71 (^[V_X: $i, V_B: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.70/0.71 inference(bind,[status(th)],[])).
% 0.70/0.71 tff(23,plain,
% 0.70/0.71 (![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(quant_intro,[status(thm)],[22])).
% 0.70/0.71 tff(24,plain,
% 0.70/0.71 (![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(25,plain,
% 0.70/0.71 (^[V_X: $i, V_B: $i, V_evs: $i] : trans(monotonicity(rewrite(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))))),
% 0.70/0.71 inference(bind,[status(th)],[])).
% 0.70/0.71 tff(26,plain,
% 0.70/0.71 (![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(quant_intro,[status(thm)],[25])).
% 0.70/0.71 tff(27,axiom,(![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OGets__imp__analz__Spy__dest_0')).
% 0.70/0.71 tff(28,plain,
% 0.70/0.71 (![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.70/0.71 tff(29,plain,
% 0.70/0.71 (![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.70/0.71 tff(30,plain,(
% 0.70/0.71 ![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(skolemize,[status(sab)],[29])).
% 0.70/0.71 tff(31,plain,
% 0.70/0.71 (![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.70/0.71 tff(32,plain,
% 0.70/0.71 (((~![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(33,plain,
% 0.70/0.71 ((~![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.71 inference(quant_inst,[status(thm)],[])).
% 0.70/0.71 tff(34,plain,
% 0.70/0.71 ((~![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.70/0.71 tff(35,plain,
% 0.70/0.71 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[34, 31, 21, 18])).
% 0.70/0.71 tff(36,plain,
% 0.70/0.71 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.70/0.71 inference(bind,[status(th)],[])).
% 0.70/0.71 tff(37,plain,
% 0.70/0.71 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(quant_intro,[status(thm)],[36])).
% 0.70/0.71 tff(38,plain,
% 0.70/0.71 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(39,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__analz_1')).
% 0.70/0.71 tff(40,plain,
% 0.70/0.71 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.70/0.71 tff(41,plain,(
% 0.70/0.71 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(skolemize,[status(sab)],[40])).
% 0.70/0.71 tff(42,plain,
% 0.70/0.71 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.70/0.71 tff(43,plain,
% 0.70/0.71 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(44,plain,
% 0.70/0.71 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.70/0.71 inference(quant_inst,[status(thm)],[])).
% 0.70/0.71 tff(45,plain,
% 0.70/0.71 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.70/0.71 tff(46,plain,
% 0.70/0.71 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[45, 42, 35])).
% 0.70/0.71 tff(47,plain,
% 0.70/0.71 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.70/0.71 inference(bind,[status(th)],[])).
% 0.70/0.71 tff(48,plain,
% 0.70/0.71 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(quant_intro,[status(thm)],[47])).
% 0.70/0.71 tff(49,plain,
% 0.70/0.71 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(50,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oparts_OInj_0')).
% 0.70/0.71 tff(51,plain,
% 0.70/0.71 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.70/0.71 tff(52,plain,(
% 0.70/0.71 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(skolemize,[status(sab)],[51])).
% 0.70/0.71 tff(53,plain,
% 0.70/0.71 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.70/0.71 tff(54,plain,
% 0.70/0.71 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(55,plain,
% 0.70/0.71 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.70/0.71 inference(quant_inst,[status(thm)],[])).
% 0.70/0.71 tff(56,plain,
% 0.70/0.71 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.70/0.71 tff(57,plain,
% 0.70/0.71 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[56, 53, 46])).
% 0.70/0.71 tff(58,plain,
% 0.70/0.71 ($false),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[57, 15])).
% 0.70/0.71 tff(59,plain,(c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.71 tff(60,plain,
% 0.70/0.71 (^[V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))))),
% 0.70/0.71 inference(bind,[status(th)],[])).
% 0.70/0.71 tff(61,plain,
% 0.70/0.71 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.70/0.71 inference(quant_intro,[status(thm)],[60])).
% 0.70/0.71 tff(62,plain,
% 0.70/0.71 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(63,plain,
% 0.70/0.71 (^[V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(64,plain,
% 0.70/0.72 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[63])).
% 0.70/0.72 tff(65,axiom,(![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OA__trusts__YM3_0')).
% 0.70/0.72 tff(66,plain,
% 0.70/0.72 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.70/0.72 tff(67,plain,
% 0.70/0.72 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.70/0.72 tff(68,plain,(
% 0.70/0.72 ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.70/0.72 inference(skolemize,[status(sab)],[67])).
% 0.70/0.72 tff(69,plain,
% 0.70/0.72 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.70/0.72 tff(70,plain,
% 0.70/0.72 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(71,plain,
% 0.70/0.72 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(72,plain,
% 0.70/0.72 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[71])).
% 0.70/0.72 tff(73,plain,
% 0.70/0.72 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.70/0.72 inference(transitivity,[status(thm)],[72, 70])).
% 0.70/0.72 tff(74,plain,
% 0.70/0.72 ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(75,plain,
% 0.70/0.72 ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.70/0.72 tff(76,plain,
% 0.70/0.72 (c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[75, 69, 21])).
% 0.70/0.72 tff(77,plain,
% 0.70/0.72 (c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[76, 59])).
% 0.70/0.72 tff(78,plain,
% 0.70/0.72 (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[77, 1])).
% 0.70/0.72 tff(79,plain,
% 0.70/0.72 (^[V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(80,plain,
% 0.70/0.72 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[79])).
% 0.70/0.72 tff(81,plain,
% 0.70/0.72 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(82,plain,
% 0.70/0.72 (^[V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(83,plain,
% 0.70/0.72 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[82])).
% 0.70/0.72 tff(84,axiom,(![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OSays__Server__imp__YM2_0')).
% 0.70/0.72 tff(85,plain,
% 0.70/0.72 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.70/0.73 tff(86,plain,
% 0.70/0.73 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.70/0.73 tff(87,plain,(
% 0.70/0.73 ![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.73 inference(skolemize,[status(sab)],[86])).
% 0.70/0.73 tff(88,plain,
% 0.70/0.73 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.70/0.73 tff(89,plain,
% 0.70/0.73 (((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(90,plain,
% 0.70/0.73 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(91,plain,
% 0.70/0.73 (((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[90])).
% 0.70/0.73 tff(92,plain,
% 0.70/0.73 (((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.70/0.73 inference(transitivity,[status(thm)],[91, 89])).
% 0.70/0.73 tff(93,plain,
% 0.70/0.73 ((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(94,plain,
% 0.70/0.73 ((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.70/0.73 tff(95,plain,
% 0.70/0.73 (c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[94, 88, 21, 78])).
% 0.70/0.73 tff(96,plain,
% 0.70/0.73 ((~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(97,axiom,(~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_10')).
% 0.70/0.73 tff(98,plain,
% 0.70/0.73 (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.70/0.73 tff(99,plain,
% 0.70/0.73 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) <=> c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(100,axiom,(c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_9')).
% 0.70/0.73 tff(101,plain,
% 0.70/0.73 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.70/0.73 tff(102,plain,
% 0.70/0.73 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B)))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(103,plain,
% 0.70/0.73 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[102])).
% 0.70/0.73 tff(104,plain,
% 0.70/0.73 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(105,plain,
% 0.70/0.73 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))), ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_B_H = V_B)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_B_H = V_B)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_B_H = V_B)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))), ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_B_H = V_B)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(106,plain,
% 0.70/0.73 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_B_H = V_B)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))),
% 0.70/0.74 inference(quant_intro,[status(thm)],[105])).
% 0.70/0.74 tff(107,axiom,(![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_B_H = V_B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OSays__unique__NB_2')).
% 0.70/0.74 tff(108,plain,
% 0.70/0.74 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.70/0.74 tff(109,plain,
% 0.70/0.74 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.70/0.74 tff(110,plain,(
% 0.70/0.74 ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))),
% 0.70/0.74 inference(skolemize,[status(sab)],[109])).
% 0.70/0.74 tff(111,plain,
% 0.70/0.74 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.70/0.74 tff(112,plain,
% 0.70/0.74 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))) | (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(113,plain,
% 0.70/0.74 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B)) <=> (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(114,plain,
% 0.70/0.74 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))) | (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B)))),
% 0.79/0.74 inference(monotonicity,[status(thm)],[113])).
% 0.79/0.74 tff(115,plain,
% 0.79/0.74 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B))),
% 0.79/0.74 inference(transitivity,[status(thm)],[114, 112])).
% 0.79/0.74 tff(116,plain,
% 0.79/0.74 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B))),
% 0.79/0.74 inference(quant_inst,[status(thm)],[])).
% 0.79/0.74 tff(117,plain,
% 0.79/0.74 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B_H = V_B))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_Ba = v_B)),
% 0.79/0.74 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.79/0.74 tff(118,plain,
% 0.79/0.74 (v_Ba = v_B),
% 0.79/0.74 inference(unit_resolution,[status(thm)],[117, 111, 21, 101, 98, 95])).
% 0.79/0.74 tff(119,plain,
% 0.79/0.74 (c_in(v_Ba, c_Event_Obad, tc_Message_Oagent) <=> c_in(v_B, c_Event_Obad, tc_Message_Oagent)),
% 0.79/0.74 inference(monotonicity,[status(thm)],[118])).
% 0.79/0.74 tff(120,plain,
% 0.79/0.74 (c_in(v_B, c_Event_Obad, tc_Message_Oagent) <=> c_in(v_Ba, c_Event_Obad, tc_Message_Oagent)),
% 0.79/0.74 inference(symmetry,[status(thm)],[119])).
% 0.79/0.74 tff(121,plain,
% 0.79/0.74 ((~c_in(v_B, c_Event_Obad, tc_Message_Oagent)) <=> (~c_in(v_Ba, c_Event_Obad, tc_Message_Oagent))),
% 0.79/0.74 inference(monotonicity,[status(thm)],[120])).
% 0.79/0.74 tff(122,plain,
% 0.79/0.74 ((~c_in(v_B, c_Event_Obad, tc_Message_Oagent)) <=> (~c_in(v_B, c_Event_Obad, tc_Message_Oagent))),
% 0.79/0.74 inference(rewrite,[status(thm)],[])).
% 0.79/0.74 tff(123,axiom,(~c_in(v_B, c_Event_Obad, tc_Message_Oagent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.79/0.74 tff(124,plain,
% 0.79/0.74 (~c_in(v_B, c_Event_Obad, tc_Message_Oagent)),
% 0.79/0.74 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.79/0.74 tff(125,plain,
% 0.79/0.74 (~c_in(v_Ba, c_Event_Obad, tc_Message_Oagent)),
% 0.79/0.74 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.79/0.74 tff(126,plain,
% 0.79/0.74 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.79/0.74 inference(bind,[status(th)],[])).
% 0.79/0.74 tff(127,plain,
% 0.79/0.74 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.74 inference(quant_intro,[status(thm)],[126])).
% 0.79/0.74 tff(128,plain,
% 0.79/0.74 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.74 inference(rewrite,[status(thm)],[])).
% 0.79/0.74 tff(129,plain,
% 0.79/0.74 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))), ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_NA_H = V_NA)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_NA_H = V_NA)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_NA_H = V_NA)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_NA_H = V_NA)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))))),
% 0.79/0.75 inference(bind,[status(th)],[])).
% 0.79/0.75 tff(130,plain,
% 0.79/0.75 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_NA_H = V_NA)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(quant_intro,[status(thm)],[129])).
% 0.79/0.75 tff(131,axiom,(![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_NA_H = V_NA))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OSays__unique__NB_0')).
% 0.79/0.75 tff(132,plain,
% 0.79/0.75 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.79/0.75 tff(133,plain,
% 0.79/0.75 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.79/0.75 tff(134,plain,(
% 0.79/0.75 ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(skolemize,[status(sab)],[133])).
% 0.79/0.75 tff(135,plain,
% 0.79/0.75 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.79/0.75 tff(136,plain,
% 0.79/0.75 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_NAa = v_NA) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_NAa = v_NA) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(rewrite,[status(thm)],[])).
% 0.79/0.75 tff(137,plain,
% 0.79/0.75 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_NAa = v_NA) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))) <=> (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_NAa = v_NA) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(rewrite,[status(thm)],[])).
% 0.79/0.75 tff(138,plain,
% 0.79/0.75 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_NAa = v_NA) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_NAa = v_NA) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.79/0.75 inference(monotonicity,[status(thm)],[137])).
% 0.79/0.75 tff(139,plain,
% 0.79/0.75 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_NAa = v_NA) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_NAa = v_NA) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(transitivity,[status(thm)],[138, 136])).
% 0.79/0.75 tff(140,plain,
% 0.79/0.75 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_NAa = v_NA) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.75 inference(quant_inst,[status(thm)],[])).
% 0.79/0.75 tff(141,plain,
% 0.79/0.75 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_NAa = v_NA) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.79/0.75 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.79/0.75 tff(142,plain,
% 0.79/0.75 (v_NAa = v_NA),
% 0.79/0.75 inference(unit_resolution,[status(thm)],[141, 135, 21, 101, 98, 95])).
% 0.79/0.75 tff(143,plain,
% 0.79/0.75 (c_Message_Omsg_ONonce(v_NAa) = c_Message_Omsg_ONonce(v_NA)),
% 0.79/0.75 inference(monotonicity,[status(thm)],[142])).
% 0.79/0.75 tff(144,plain,
% 0.79/0.75 (c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))) = c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))),
% 0.79/0.75 inference(monotonicity,[status(thm)],[143])).
% 0.79/0.75 tff(145,plain,
% 0.79/0.75 (c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))) = c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))),
% 0.79/0.75 inference(monotonicity,[status(thm)],[144])).
% 0.79/0.75 tff(146,plain,
% 0.79/0.75 (c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) <=> c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.79/0.75 inference(monotonicity,[status(thm)],[145])).
% 0.79/0.75 tff(147,plain,
% 0.79/0.75 (c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) <=> c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.79/0.75 inference(symmetry,[status(thm)],[146])).
% 0.79/0.75 tff(148,plain,
% 0.79/0.75 ((~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) <=> (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.79/0.75 inference(monotonicity,[status(thm)],[147])).
% 0.79/0.75 tff(149,assumption,(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)), introduced(assumption)).
% 0.79/0.76 tff(150,plain,
% 0.79/0.76 (^[V_U: $i] : refl((~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) <=> (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.76 inference(bind,[status(th)],[])).
% 0.79/0.76 tff(151,plain,
% 0.79/0.76 (![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.79/0.76 inference(quant_intro,[status(thm)],[150])).
% 0.79/0.76 tff(152,plain,
% 0.79/0.76 (![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(153,axiom,(![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_8')).
% 0.79/0.76 tff(154,plain,
% 0.79/0.76 (![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.79/0.76 tff(155,plain,(
% 0.79/0.76 ![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.79/0.76 inference(skolemize,[status(sab)],[154])).
% 0.79/0.76 tff(156,plain,
% 0.79/0.76 (![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.79/0.76 tff(157,plain,
% 0.79/0.76 ((~![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.79/0.76 inference(quant_inst,[status(thm)],[])).
% 0.79/0.76 tff(158,plain,
% 0.79/0.76 ($false),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[157, 156, 149])).
% 0.79/0.76 tff(159,plain,(~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.76 tff(160,plain,
% 0.79/0.76 (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[159, 148])).
% 0.79/0.76 tff(161,plain,
% 0.79/0.76 (c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(162,axiom,(c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_11')).
% 0.79/0.76 tff(163,plain,
% 0.79/0.76 (c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.79/0.76 tff(164,plain,
% 0.79/0.76 (^[V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.79/0.76 inference(bind,[status(th)],[])).
% 0.79/0.76 tff(165,plain,
% 0.79/0.76 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.76 inference(quant_intro,[status(thm)],[164])).
% 0.79/0.76 tff(166,plain,
% 0.79/0.76 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(167,plain,
% 0.79/0.76 (^[V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))), ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))), (((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))))),
% 0.81/0.76 inference(bind,[status(th)],[])).
% 0.81/0.76 tff(168,plain,
% 0.81/0.76 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.81/0.76 inference(quant_intro,[status(thm)],[167])).
% 0.81/0.76 tff(169,axiom,(![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OSpy__not__see__encrypted__key_0')).
% 0.81/0.76 tff(170,plain,
% 0.81/0.76 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.81/0.76 tff(171,plain,
% 0.81/0.76 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.81/0.76 tff(172,plain,(
% 0.81/0.76 ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.81/0.76 inference(skolemize,[status(sab)],[171])).
% 0.81/0.76 tff(173,plain,
% 0.81/0.76 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.81/0.76 tff(174,plain,
% 0.81/0.76 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(175,plain,
% 0.81/0.76 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(176,plain,
% 0.81/0.76 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(monotonicity,[status(thm)],[175])).
% 0.81/0.77 tff(177,plain,
% 0.81/0.77 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent))),
% 0.81/0.77 inference(transitivity,[status(thm)],[176, 174])).
% 0.81/0.77 tff(178,plain,
% 0.81/0.77 ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(179,plain,
% 0.81/0.77 ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(V_na, c_Message_Omsg_OMPair(V_nb, c_Message_Omsg_OKey(V_K)))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(V_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent)),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.81/0.77 tff(180,plain,
% 0.81/0.77 (c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Ba, c_Event_Obad, tc_Message_Oagent)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[179, 173, 21, 163, 1, 78])).
% 0.81/0.77 tff(181,plain,
% 0.81/0.77 ($false),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[180, 160, 125])).
% 0.81/0.77 tff(182,plain,(c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.77 tff(183,assumption,(~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), introduced(assumption)).
% 0.81/0.77 tff(184,plain,
% 0.81/0.77 (^[V_A: $i, V_evs: $i] : refl((c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))) <=> (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))))),
% 0.81/0.77 inference(bind,[status(th)],[])).
% 0.81/0.77 tff(185,plain,
% 0.81/0.77 (![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))) <=> ![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(quant_intro,[status(thm)],[184])).
% 0.81/0.77 tff(186,plain,
% 0.81/0.77 (![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))) <=> ![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(187,plain,
% 0.81/0.77 (^[V_A: $i, V_evs: $i] : rewrite((((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))))),
% 0.81/0.77 inference(bind,[status(th)],[])).
% 0.81/0.77 tff(188,plain,
% 0.81/0.77 (![V_A: $i, V_evs: $i] : (((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(quant_intro,[status(thm)],[187])).
% 0.81/0.77 tff(189,axiom,(![V_A: $i, V_evs: $i] : (((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OSpy__analz__shrK_1')).
% 0.81/0.77 tff(190,plain,
% 0.81/0.77 (![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.81/0.77 tff(191,plain,
% 0.81/0.77 (![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.81/0.77 tff(192,plain,(
% 0.81/0.77 ![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(skolemize,[status(sab)],[191])).
% 0.81/0.77 tff(193,plain,
% 0.81/0.77 (![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.81/0.77 tff(194,plain,
% 0.81/0.77 (((~![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))) <=> ((~![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(195,plain,
% 0.81/0.77 ((c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent))) <=> ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(196,plain,
% 0.81/0.77 (((~![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))) <=> ((~![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent))))),
% 0.81/0.77 inference(monotonicity,[status(thm)],[195])).
% 0.81/0.77 tff(197,plain,
% 0.81/0.77 (((~![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))) <=> ((~![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(transitivity,[status(thm)],[196, 194])).
% 0.81/0.77 tff(198,plain,
% 0.81/0.77 ((~![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(199,plain,
% 0.81/0.77 ((~![V_A: $i, V_evs: $i] : (c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.81/0.77 tff(200,plain,
% 0.81/0.77 ($false),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[199, 193, 21, 183, 182])).
% 0.81/0.77 tff(201,plain,(c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.77 tff(202,plain,
% 0.81/0.77 (^[V_H: $i, V_X: $i, V_A: $i] : refl((c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))) <=> (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))))),
% 0.81/0.77 inference(bind,[status(th)],[])).
% 0.81/0.77 tff(203,plain,
% 0.81/0.77 (![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.81/0.77 inference(quant_intro,[status(thm)],[202])).
% 0.81/0.77 tff(204,plain,
% 0.81/0.77 (![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(205,plain,
% 0.81/0.77 (^[V_H: $i, V_X: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg))) <=> ((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))), ((((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> (((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))), rewrite((((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))), ((((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))))),
% 0.81/0.77 inference(bind,[status(th)],[])).
% 0.81/0.77 tff(206,plain,
% 0.81/0.77 (![V_H: $i, V_X: $i, V_A: $i] : (((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.81/0.77 inference(quant_intro,[status(thm)],[205])).
% 0.81/0.77 tff(207,axiom,(![V_H: $i, V_X: $i, V_A: $i] : (((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Public_Oanalz__shrK__Decrypt_0')).
% 0.81/0.77 tff(208,plain,
% 0.81/0.77 (![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.81/0.77 tff(209,plain,
% 0.81/0.77 (![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.81/0.77 tff(210,plain,(
% 0.81/0.77 ![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.81/0.77 inference(skolemize,[status(sab)],[209])).
% 0.81/0.77 tff(211,plain,
% 0.81/0.77 (![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.81/0.77 tff(212,plain,
% 0.81/0.77 (((~![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(213,plain,
% 0.81/0.78 ((~![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(214,plain,
% 0.81/0.78 ((~![V_H: $i, V_X: $i, V_A: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.81/0.78 tff(215,plain,
% 0.81/0.78 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[214, 211, 46])).
% 0.81/0.78 tff(216,plain,
% 0.81/0.78 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[215, 201])).
% 0.81/0.78 tff(217,plain,
% 0.81/0.78 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.81/0.78 inference(bind,[status(th)],[])).
% 0.81/0.78 tff(218,plain,
% 0.81/0.78 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.81/0.78 inference(quant_intro,[status(thm)],[217])).
% 0.81/0.78 tff(219,plain,
% 0.81/0.78 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(220,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__analz_0')).
% 0.81/0.78 tff(221,plain,
% 0.81/0.78 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.81/0.78 tff(222,plain,(
% 0.81/0.78 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.81/0.78 inference(skolemize,[status(sab)],[221])).
% 0.81/0.78 tff(223,plain,
% 0.81/0.78 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.81/0.78 tff(224,plain,
% 0.81/0.78 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(225,plain,
% 0.81/0.78 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(226,plain,
% 0.81/0.78 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.81/0.78 tff(227,plain,
% 0.81/0.78 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[226, 223, 216])).
% 0.81/0.78 tff(228,plain,
% 0.81/0.78 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(229,plain,
% 0.81/0.78 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(230,plain,
% 0.81/0.78 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.81/0.78 tff(231,plain,
% 0.81/0.78 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[230, 223, 227])).
% 0.81/0.78 tff(232,plain,
% 0.81/0.78 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(233,plain,
% 0.81/0.78 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(234,plain,
% 0.81/0.78 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.81/0.78 tff(235,plain,
% 0.81/0.78 ($false),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[234, 223, 98, 231])).
% 0.81/0.78 % SZS output end Proof
%------------------------------------------------------------------------------