%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV348-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:32:14 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWV348-2 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:45:16 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(c_in_type, type, (
% 0.18/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.18/0.39 tff(tc_Event_Oevent_type, type, (
% 0.18/0.39 tc_Event_Oevent: $i)).
% 0.18/0.39 tff(c_List_Oset_type, type, (
% 0.18/0.39 c_List_Oset: ( $i * $i ) > $i)).
% 0.18/0.39 tff(v_evs4_type, type, (
% 0.18/0.39 v_evs4: $i)).
% 0.18/0.39 tff(c_Event_Oevent_ONotes_type, type, (
% 0.18/0.39 c_Event_Oevent_ONotes: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c_Message_Omsg_OMPair_type, type, (
% 0.18/0.39 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c_Message_Omsg_OKey_type, type, (
% 0.18/0.39 c_Message_Omsg_OKey: $i > $i)).
% 0.18/0.39 tff(v_K_type, type, (
% 0.18/0.39 v_K: $i)).
% 0.18/0.39 tff(c_Message_Omsg_ONonce_type, type, (
% 0.18/0.39 c_Message_Omsg_ONonce: $i > $i)).
% 0.18/0.39 tff(v_NB_type, type, (
% 0.18/0.39 v_NB: $i)).
% 0.18/0.39 tff(v_NA_type, type, (
% 0.18/0.39 v_NA: $i)).
% 0.18/0.39 tff(c_Message_Oagent_OSpy_type, type, (
% 0.18/0.39 c_Message_Oagent_OSpy: $i)).
% 0.18/0.39 tff(v_NAa_type, type, (
% 0.18/0.39 v_NAa: $i)).
% 0.18/0.39 tff(c_Event_Oevent_OGets_type, type, (
% 0.18/0.39 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.18/0.39 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c_Message_Omsg_OAgent_type, type, (
% 0.18/0.39 c_Message_Omsg_OAgent: $i > $i)).
% 0.18/0.39 tff(v_Aa_type, type, (
% 0.18/0.39 v_Aa: $i)).
% 0.18/0.39 tff(c_Public_OshrK_type, type, (
% 0.18/0.39 c_Public_OshrK: $i > $i)).
% 0.18/0.39 tff(v_Ba_type, type, (
% 0.18/0.39 v_Ba: $i)).
% 0.18/0.39 tff(c_Message_Oagent_OServer_type, type, (
% 0.18/0.39 c_Message_Oagent_OServer: $i)).
% 0.18/0.39 tff(c_Event_Oevent_OSays_type, type, (
% 0.18/0.39 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tc_Message_Omsg_type, type, (
% 0.18/0.39 tc_Message_Omsg: $i)).
% 0.18/0.39 tff(c_Message_Oparts_type, type, (
% 0.18/0.39 c_Message_Oparts: $i > $i)).
% 0.18/0.39 tff(c_Event_Oknows_type, type, (
% 0.18/0.39 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c_Message_Oanalz_type, type, (
% 0.18/0.39 c_Message_Oanalz: $i > $i)).
% 0.18/0.39 tff(v_X_type, type, (
% 0.18/0.39 v_X: $i)).
% 0.18/0.39 tff(tc_List_Olist_type, type, (
% 0.18/0.39 tc_List_Olist: $i > $i)).
% 0.18/0.39 tff(c_Yahalom_Oyahalom_type, type, (
% 0.18/0.39 c_Yahalom_Oyahalom: $i)).
% 0.18/0.39 tff(tc_Message_Oagent_type, type, (
% 0.18/0.39 tc_Message_Oagent: $i)).
% 0.18/0.39 tff(c_Event_Obad_type, type, (
% 0.18/0.39 c_Event_Obad: $i)).
% 0.18/0.39 tff(v_A_type, type, (
% 0.18/0.39 v_A: $i)).
% 0.18/0.39 tff(v_B_type, type, (
% 0.18/0.39 v_B: $i)).
% 0.18/0.39 tff(1,assumption,(~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)), introduced(assumption)).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (^[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)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 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')).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.39 tff(7,plain,(
% 0.18/0.39 ![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.18/0.39 inference(skolemize,[status(sab)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 ((~![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)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (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))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.18/0.39 tff(11,plain,
% 0.18/0.39 (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)),
% 0.18/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.39 tff(12,assumption,(~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_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)), introduced(assumption)).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (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)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(14,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')).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (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)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (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))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(17,axiom,(c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.39 tff(24,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')).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.18/0.40 tff(27,plain,(
% 0.18/0.40 ![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)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[26])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 (((~![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(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(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(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)))) <=> ((~![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(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(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 (((~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))) <=> (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(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 (((~![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(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(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(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))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[30])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (((~![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(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(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(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)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[31, 29])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 ((~![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)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 ((~![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(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(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(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))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (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)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[34, 28, 18, 15])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (^[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)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(39,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')).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.40 tff(41,plain,(
% 0.18/0.40 ![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))),
% 0.18/0.40 inference(skolemize,[status(sab)],[40])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (((~![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_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_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_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_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_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_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 ((~![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_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_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_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[45, 42, 35, 12])).
% 0.18/0.40 tff(47,plain,(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_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(51,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(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_OMPair__parts_1')).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.40 tff(53,plain,(
% 0.18/0.40 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.40 inference(skolemize,[status(sab)],[52])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(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_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_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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(56,plain,
% 0.18/0.41 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 ((~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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 (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)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[58, 47])).
% 0.18/0.41 tff(60,plain,
% 0.18/0.41 (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)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[59, 11])).
% 0.18/0.41 tff(61,plain,
% 0.18/0.41 (^[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)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(62,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.41 tff(63,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(64,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')).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.41 tff(66,plain,(
% 0.18/0.41 ![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))),
% 0.18/0.41 inference(skolemize,[status(sab)],[65])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.18/0.41 tff(68,plain,
% 0.18/0.41 (((~![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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 ((~![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))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 ((~![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)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 ((~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)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 (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)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[71, 35])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 ((~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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(74,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')).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (^[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)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(79,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')).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.41 tff(81,plain,(
% 0.18/0.41 ![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))),
% 0.18/0.41 inference(skolemize,[status(sab)],[80])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 (((~![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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 ((~![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))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 ((~![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)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (~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)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[85, 82, 75])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 (((~![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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 ((~![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))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 ((~![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)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 (~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)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[89, 82, 86])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (((~![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))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(92,plain,
% 0.18/0.42 ((~![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))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(93,plain,
% 0.18/0.42 ((~![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)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.18/0.42 tff(94,plain,
% 0.18/0.42 (~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)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[93, 82, 90])).
% 0.18/0.42 tff(95,plain,
% 0.18/0.42 (^[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))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(96,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[95])).
% 0.18/0.42 tff(97,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(98,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(99,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[98])).
% 0.18/0.42 tff(100,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')).
% 0.18/0.42 tff(101,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.42 tff(102,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.18/0.42 tff(103,plain,(
% 0.18/0.42 ![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)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[102])).
% 0.18/0.42 tff(104,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.18/0.42 tff(105,plain,
% 0.18/0.42 (((~![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(106,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(107,plain,
% 0.18/0.42 ((~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.42 tff(108,plain,
% 0.18/0.42 ((~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))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[107, 104, 94])).
% 0.18/0.42 tff(109,plain,
% 0.18/0.42 (~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)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[108, 72])).
% 0.18/0.42 tff(110,plain,
% 0.18/0.42 (^[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))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(111,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.18/0.42 tff(112,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(113,plain,
% 0.18/0.42 (^[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))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(114,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.18/0.42 tff(115,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')).
% 0.18/0.42 tff(116,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.42 tff(117,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.18/0.42 tff(118,plain,(
% 0.18/0.42 ![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)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[117])).
% 0.18/0.42 tff(119,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.18/0.42 tff(120,plain,
% 0.18/0.42 (((~![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(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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(121,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(122,plain,
% 0.18/0.43 ((~![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))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.18/0.43 tff(123,plain,
% 0.18/0.43 (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))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[122, 119, 18])).
% 0.18/0.43 tff(124,plain,
% 0.18/0.43 (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[123, 109])).
% 0.18/0.43 tff(125,plain,
% 0.18/0.43 (^[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))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(126,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[125])).
% 0.18/0.43 tff(127,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(128,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(129,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.43 tff(130,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')).
% 0.18/0.43 tff(131,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.43 tff(132,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.18/0.43 tff(133,plain,(
% 0.18/0.43 ![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)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[132])).
% 0.18/0.43 tff(134,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.18/0.43 tff(135,plain,
% 0.18/0.43 (((~![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(136,plain,
% 0.18/0.43 (((~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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(137,plain,
% 0.18/0.43 (((~![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))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.18/0.43 tff(138,plain,
% 0.18/0.43 (((~![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)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[137, 135])).
% 0.18/0.43 tff(139,plain,
% 0.18/0.43 ((~![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)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(140,plain,
% 0.18/0.43 ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.18/0.43 tff(141,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[140, 134, 18, 124, 60, 1])).
% 0.18/0.43 tff(142,plain,(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)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(143,assumption,(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)), introduced(assumption)).
% 0.18/0.44 tff(144,assumption,(~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)), introduced(assumption)).
% 0.18/0.44 tff(145,plain,
% 0.18/0.44 (^[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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(146,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[145])).
% 0.18/0.44 tff(147,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(148,plain,
% 0.18/0.44 (^[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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(149,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[148])).
% 0.18/0.44 tff(150,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')).
% 0.18/0.44 tff(151,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.18/0.44 tff(152,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.18/0.44 tff(153,plain,(
% 0.18/0.44 ![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)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[152])).
% 0.18/0.44 tff(154,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.18/0.44 tff(155,plain,
% 0.18/0.44 (((~![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_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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(156,plain,
% 0.18/0.44 ((~![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)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(157,plain,
% 0.18/0.44 ((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_k, c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.18/0.44 tff(158,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[157, 154, 18, 144, 143])).
% 0.18/0.44 tff(159,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(160,plain,
% 0.18/0.44 (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)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[159, 142])).
% 0.18/0.44 tff(161,plain,
% 0.18/0.44 (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)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(162,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')).
% 0.18/0.44 tff(163,plain,
% 0.18/0.44 (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)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.18/0.44 tff(164,plain,
% 0.18/0.44 (^[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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(165,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[164])).
% 0.18/0.44 tff(166,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(167,plain,
% 0.18/0.44 (^[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)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(168,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[167])).
% 0.18/0.44 tff(169,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')).
% 0.18/0.44 tff(170,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.18/0.44 tff(171,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.18/0.44 tff(172,plain,(
% 0.18/0.44 ![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)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[171])).
% 0.18/0.44 tff(173,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.18/0.44 tff(174,plain,
% 0.18/0.44 (((~![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))) | (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)) | (~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))) | (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)) | (~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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(175,plain,
% 0.18/0.44 (((~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))) | (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)) | (~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)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(176,plain,
% 0.18/0.45 (((~![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))) | (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)) | (~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))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[175])).
% 0.18/0.45 tff(177,plain,
% 0.18/0.45 (((~![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))) | (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)) | (~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)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[176, 174])).
% 0.18/0.45 tff(178,plain,
% 0.18/0.45 ((~![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)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(179,plain,
% 0.18/0.45 ((~![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))) | (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)) | (~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))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.18/0.45 tff(180,plain,
% 0.18/0.45 (v_NAa = v_NA),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[179, 173, 18, 163, 75, 160])).
% 0.18/0.45 tff(181,plain,
% 0.18/0.45 (c_Message_Omsg_ONonce(v_NAa) = c_Message_Omsg_ONonce(v_NA)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[180])).
% 0.18/0.45 tff(182,plain,
% 0.18/0.45 (c_Message_Omsg_ONonce(v_NA) = c_Message_Omsg_ONonce(v_NAa)),
% 0.18/0.45 inference(symmetry,[status(thm)],[181])).
% 0.18/0.45 tff(183,plain,
% 0.18/0.45 (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_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)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[182])).
% 0.18/0.45 tff(184,plain,
% 0.18/0.45 (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_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))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[183])).
% 0.18/0.45 tff(185,plain,
% 0.18/0.45 (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)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[184])).
% 0.18/0.45 tff(186,plain,
% 0.18/0.45 (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)),
% 0.18/0.45 inference(symmetry,[status(thm)],[185])).
% 0.18/0.45 tff(187,plain,
% 0.18/0.45 (((~![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_Aa), 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_OAgent(v_Aa), 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))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(188,plain,
% 0.18/0.45 ((~![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_Aa), 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))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(189,plain,
% 0.18/0.45 ((~![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_Aa), 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)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.18/0.45 tff(190,plain,
% 0.18/0.45 (~c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[189, 82, 86])).
% 0.18/0.45 tff(191,assumption,(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)), introduced(assumption)).
% 0.18/0.45 tff(192,assumption,(~c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), introduced(assumption)).
% 0.18/0.45 tff(193,plain,
% 0.18/0.45 (((~![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_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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), 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)))) | (~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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(194,plain,
% 0.18/0.45 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~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(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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(195,plain,
% 0.18/0.45 (((~![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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~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_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_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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[194])).
% 0.18/0.45 tff(196,plain,
% 0.18/0.45 (((~![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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~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_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_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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.18/0.45 inference(transitivity,[status(thm)],[195, 193])).
% 0.18/0.45 tff(197,plain,
% 0.18/0.45 ((~![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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~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)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(198,plain,
% 0.18/0.45 ((~![V_X: $i, V_B: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.18/0.45 tff(199,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[198, 28, 18, 192, 191])).
% 0.18/0.45 tff(200,plain,((~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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(201,plain,
% 0.18/0.45 (c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[200, 160])).
% 0.18/0.45 tff(202,plain,
% 0.18/0.45 (((~![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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(203,plain,
% 0.18/0.45 ((~![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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(204,plain,
% 0.18/0.45 ((~![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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.18/0.45 tff(205,plain,
% 0.18/0.45 (c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[204, 82, 201])).
% 0.18/0.45 tff(206,plain,
% 0.18/0.45 (((~![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_OKey(c_Public_OshrK(v_Ba)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(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_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_OKey(c_Public_OshrK(v_Ba)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(207,plain,
% 0.18/0.45 ((c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Ba)), 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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Ba)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(208,plain,
% 0.18/0.45 (((~![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_Aa), 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_Ba)), 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_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_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_OKey(c_Public_OshrK(v_Ba)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[207])).
% 0.18/0.45 tff(209,plain,
% 0.18/0.45 (((~![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_Aa), 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_Ba)), 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_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_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_OKey(c_Public_OshrK(v_Ba)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[208, 206])).
% 0.18/0.45 tff(210,plain,
% 0.18/0.45 ((~![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_Aa), 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_Ba)), 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_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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(211,plain,
% 0.18/0.45 ((~![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_OKey(c_Public_OshrK(v_Ba)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.18/0.46 tff(212,plain,
% 0.18/0.46 (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Ba)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[211, 104, 205, 190])).
% 0.18/0.46 tff(213,plain,
% 0.18/0.46 (((~![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_Ba)), 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_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_Ba)), 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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(214,plain,
% 0.18/0.46 ((c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Ba)), 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_Ba, 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_Ba)), 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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(215,plain,
% 0.18/0.46 (((~![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_Ba)), 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_Ba, 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_Ba)), 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))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[214])).
% 0.18/0.46 tff(216,plain,
% 0.18/0.46 (((~![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_Ba)), 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_Ba, 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_Ba)), 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)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[215, 213])).
% 0.18/0.46 tff(217,plain,
% 0.18/0.46 ((~![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_Ba)), 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_Ba, c_Event_Obad, tc_Message_Oagent)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(218,plain,
% 0.18/0.46 ((~![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_Ba)), 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))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.18/0.46 tff(219,plain,
% 0.18/0.46 (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Ba)), 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))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[218, 119, 18])).
% 0.18/0.46 tff(220,plain,
% 0.18/0.46 (~c_in(v_Ba, c_Event_Obad, tc_Message_Oagent)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[219, 212])).
% 0.18/0.46 tff(221,plain,
% 0.18/0.46 (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)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(222,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')).
% 0.18/0.46 tff(223,plain,
% 0.18/0.46 (c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.18/0.46 tff(224,plain,
% 0.18/0.46 (^[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))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(225,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[224])).
% 0.18/0.46 tff(226,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(227,plain,
% 0.18/0.46 (^[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)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(228,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[227])).
% 0.18/0.46 tff(229,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')).
% 0.18/0.46 tff(230,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.18/0.46 tff(231,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.18/0.46 tff(232,plain,(
% 0.18/0.46 ![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)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[231])).
% 0.18/0.46 tff(233,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.18/0.46 tff(234,plain,
% 0.18/0.46 (((~![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(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)))) <=> ((~![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(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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(235,plain,
% 0.18/0.46 (((~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(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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(236,plain,
% 0.18/0.46 (((~![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(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))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[235])).
% 0.18/0.47 tff(237,plain,
% 0.18/0.47 (((~![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(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)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[236, 234])).
% 0.18/0.47 tff(238,plain,
% 0.18/0.47 ((~![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)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(239,plain,
% 0.18/0.47 ((~![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(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))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.18/0.47 tff(240,plain,
% 0.18/0.47 (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)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[239, 233, 18, 223, 124, 142])).
% 0.18/0.47 tff(241,plain,
% 0.18/0.47 (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)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[240, 220])).
% 0.18/0.47 tff(242,plain,
% 0.18/0.47 (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)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[241, 186])).
% 0.18/0.47 tff(243,plain,
% 0.18/0.47 (^[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)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(244,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[243])).
% 0.18/0.47 tff(245,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(246,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')).
% 0.18/0.47 tff(247,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.18/0.47 tff(248,plain,(
% 0.18/0.47 ![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))),
% 0.18/0.47 inference(skolemize,[status(sab)],[247])).
% 0.18/0.47 tff(249,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.18/0.47 tff(250,plain,
% 0.18/0.47 ((~![V_U: $i] : (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), V_U))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(251,plain,
% 0.18/0.47 (~c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[250, 249])).
% 0.18/0.47 tff(252,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[251, 242])).
% 0.18/0.47 % SZS output end Proof
% 0.18/0.47 % E exiting
%------------------------------------------------------------------------------