%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV352-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:32:15 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV352-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 09:43:56 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.22/0.41 % SZS status Unsatisfiable
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(c_in_type, type, (
% 0.22/0.41 c_in: ( $i * $i * $i ) > $o)).
% 0.22/0.41 tff(tc_Message_Omsg_type, type, (
% 0.22/0.41 tc_Message_Omsg: $i)).
% 0.22/0.41 tff(c_Message_Oparts_type, type, (
% 0.22/0.41 c_Message_Oparts: $i > $i)).
% 0.22/0.41 tff(c_Event_Oknows_type, type, (
% 0.22/0.41 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.22/0.41 tff(v_evso_type, type, (
% 0.22/0.41 v_evso: $i)).
% 0.22/0.41 tff(c_Message_Oagent_OSpy_type, type, (
% 0.22/0.41 c_Message_Oagent_OSpy: $i)).
% 0.22/0.41 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.22/0.41 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.22/0.41 tff(c_Message_Omsg_OMPair_type, type, (
% 0.22/0.41 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.22/0.41 tff(c_Message_Omsg_ONonce_type, type, (
% 0.22/0.41 c_Message_Omsg_ONonce: $i > $i)).
% 0.22/0.41 tff(v_NB_type, type, (
% 0.22/0.41 v_NB: $i)).
% 0.22/0.41 tff(v_NA_type, type, (
% 0.22/0.41 v_NA: $i)).
% 0.22/0.41 tff(c_Message_Omsg_OAgent_type, type, (
% 0.22/0.41 c_Message_Omsg_OAgent: $i > $i)).
% 0.22/0.41 tff(v_A_type, type, (
% 0.22/0.41 v_A: $i)).
% 0.22/0.41 tff(c_Public_OshrK_type, type, (
% 0.22/0.41 c_Public_OshrK: $i > $i)).
% 0.22/0.41 tff(v_B_type, type, (
% 0.22/0.41 v_B: $i)).
% 0.22/0.41 tff(tc_Event_Oevent_type, type, (
% 0.22/0.41 tc_Event_Oevent: $i)).
% 0.22/0.41 tff(c_List_Oset_type, type, (
% 0.22/0.41 c_List_Oset: ( $i * $i ) > $i)).
% 0.22/0.41 tff(c_Event_Oevent_OSays_type, type, (
% 0.22/0.41 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(c_Message_Oagent_OServer_type, type, (
% 0.22/0.41 c_Message_Oagent_OServer: $i)).
% 0.22/0.41 tff(v_NBa_type, type, (
% 0.22/0.41 v_NBa: $i)).
% 0.22/0.41 tff(v_Aa_type, type, (
% 0.22/0.41 v_Aa: $i)).
% 0.22/0.41 tff(v_Ba_type, type, (
% 0.22/0.41 v_Ba: $i)).
% 0.22/0.41 tff(c_Message_Oanalz_type, type, (
% 0.22/0.41 c_Message_Oanalz: $i > $i)).
% 0.22/0.41 tff(c_Event_Oevent_OGets_type, type, (
% 0.22/0.41 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.22/0.41 tff(tc_List_Olist_type, type, (
% 0.22/0.41 tc_List_Olist: $i > $i)).
% 0.22/0.41 tff(c_Yahalom_Oyahalom_type, type, (
% 0.22/0.41 c_Yahalom_Oyahalom: $i)).
% 0.22/0.41 tff(v_X_type, type, (
% 0.22/0.41 v_X: $i)).
% 0.22/0.41 tff(c_Message_Omsg_OKey_type, type, (
% 0.22/0.41 c_Message_Omsg_OKey: $i > $i)).
% 0.22/0.41 tff(v_K_type, type, (
% 0.22/0.41 v_K: $i)).
% 0.22/0.41 tff(1,assumption,(~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)), introduced(assumption)).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 (^[V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : refl(((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) <=> ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(3,plain,
% 0.22/0.41 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) <=> ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.22/0.41 tff(4,plain,
% 0.22/0.41 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) <=> ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(5,axiom,(![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Event_OSays__imp__spies_0')).
% 0.22/0.41 tff(6,plain,
% 0.22/0.41 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.22/0.41 tff(7,plain,(
% 0.22/0.41 ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.22/0.41 inference(skolemize,[status(sab)],[6])).
% 0.22/0.41 tff(8,plain,
% 0.22/0.41 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (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_evso, 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_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(10,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_evso, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 (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_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), 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_evso, tc_Event_Oevent), tc_Event_Oevent)) | c_in(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_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg))) <=> ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), 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_evso, tc_Event_Oevent), tc_Event_Oevent)) | c_in(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_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), 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_evso, tc_Event_Oevent), tc_Event_Oevent)) | c_in(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_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), 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_evso, tc_Event_Oevent), tc_Event_Oevent)) | c_in(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_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (c_in(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_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[14, 11, 8])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (^[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)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(19,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')).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.22/0.41 tff(21,plain,(
% 0.22/0.41 ![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))),
% 0.22/0.41 inference(skolemize,[status(sab)],[20])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (((~![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_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_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)) | c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_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_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)) | c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 ((~![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_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_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)) | c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[25, 22, 15, 1])).
% 0.22/0.41 tff(27,plain,(c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 (^[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_Y, 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_Y, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 (![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_Y, 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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (![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_Y, 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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(31,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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__parts_0')).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (![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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.42 tff(33,plain,(
% 0.22/0.42 ![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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.22/0.42 inference(skolemize,[status(sab)],[32])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 (![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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 (((~![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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 ((~![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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 ((~![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_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 ((~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 (c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[38, 27])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (^[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)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(43,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')).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.22/0.42 tff(45,plain,(
% 0.22/0.42 ![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.22/0.42 inference(skolemize,[status(sab)],[44])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 ((~![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_evso))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 (c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)) = c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)))),
% 0.22/0.42 inference(symmetry,[status(thm)],[48])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 (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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[49])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.22/0.42 inference(symmetry,[status(thm)],[50])).
% 0.22/0.42 tff(52,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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg)), introduced(assumption)).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (^[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))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (^[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))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.22/0.42 tff(58,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')).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.22/0.42 tff(61,plain,(
% 0.22/0.42 ![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)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[60])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 (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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(64,axiom,(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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 (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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 (c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) <=> c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(67,axiom,(c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 (c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (((~![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(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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, 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(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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (((~c_in(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (((~![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_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, 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(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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[70])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (((~![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_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, 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(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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.22/0.43 inference(transitivity,[status(thm)],[71, 69])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 ((~![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_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 ((~![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(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_NB), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.44 tff(75,plain,
% 0.22/0.44 (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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[74, 68, 65, 62])).
% 0.22/0.44 tff(76,plain,
% 0.22/0.44 (^[V_X: $i, V_B: $i, V_evs: $i] : refl((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)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(77,plain,
% 0.22/0.44 (![V_X: $i, V_B: $i, V_evs: $i] : (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)))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (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))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[76])).
% 0.22/0.44 tff(78,plain,
% 0.22/0.44 (![V_X: $i, V_B: $i, V_evs: $i] : (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)))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (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))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(79,plain,
% 0.22/0.44 (^[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(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_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(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)))), rewrite((((~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(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_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_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))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(80,plain,
% 0.22/0.44 (![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_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))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.22/0.44 tff(81,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')).
% 0.22/0.44 tff(82,plain,
% 0.22/0.44 (![V_X: $i, V_B: $i, V_evs: $i] : (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))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.44 tff(83,plain,
% 0.22/0.44 (![V_X: $i, V_B: $i, V_evs: $i] : (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))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.22/0.44 tff(84,plain,(
% 0.22/0.44 ![V_X: $i, V_B: $i, V_evs: $i] : (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))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[83])).
% 0.22/0.44 tff(85,plain,
% 0.22/0.44 (![V_X: $i, V_B: $i, V_evs: $i] : (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))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.22/0.44 tff(86,plain,
% 0.22/0.44 (((~![V_X: $i, V_B: $i, V_evs: $i] : (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_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : (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_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(87,plain,
% 0.22/0.44 ((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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) <=> ((~c_in(v_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(88,plain,
% 0.22/0.44 (((~![V_X: $i, V_B: $i, V_evs: $i] : (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_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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : (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_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[87])).
% 0.22/0.44 tff(89,plain,
% 0.22/0.44 (((~![V_X: $i, V_B: $i, V_evs: $i] : (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_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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : (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_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[88, 86])).
% 0.22/0.44 tff(90,plain,
% 0.22/0.44 ((~![V_X: $i, V_B: $i, V_evs: $i] : (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_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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(91,plain,
% 0.22/0.44 ((~![V_X: $i, V_B: $i, V_evs: $i] : (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_evso, 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.22/0.44 tff(92,plain,
% 0.22/0.44 (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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[91, 68, 85, 75])).
% 0.22/0.44 tff(93,plain,
% 0.22/0.44 (((~![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_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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), 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_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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(94,plain,
% 0.22/0.44 ((~![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_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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(95,plain,
% 0.22/0.44 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.22/0.45 tff(96,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[95, 22, 92, 52])).
% 0.22/0.45 tff(97,plain,(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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(98,plain,
% 0.22/0.45 (((~![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_Y, c_Message_Oparts(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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), 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_Y, c_Message_Oparts(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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(99,plain,
% 0.22/0.45 ((~![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_Y, c_Message_Oparts(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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(100,plain,
% 0.22/0.45 ((~![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_Y, c_Message_Oparts(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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.22/0.45 tff(101,plain,
% 0.22/0.45 ((~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_NB), c_Message_Omsg_ONonce(v_NBa))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[100, 34])).
% 0.22/0.45 tff(102,plain,
% 0.22/0.45 (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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso))), tc_Message_Omsg)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.22/0.45 tff(103,plain,
% 0.22/0.45 (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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[102, 51])).
% 0.22/0.45 tff(104,plain,
% 0.22/0.45 (^[V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(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_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(105,plain,
% 0.22/0.45 (![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[104])).
% 0.22/0.45 tff(106,plain,
% 0.22/0.45 (![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(107,plain,
% 0.22/0.45 (^[V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $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_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(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_NB), V_nb_H))), 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_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(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_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(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_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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(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_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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(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_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(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_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(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_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(108,plain,
% 0.22/0.45 (![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $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_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[107])).
% 0.22/0.45 tff(109,axiom,(![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $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_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_Ono__nonce__YM1__YM2_0')).
% 0.22/0.45 tff(110,plain,
% 0.22/0.45 (![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.22/0.45 tff(111,plain,
% 0.22/0.45 (![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.22/0.45 tff(112,plain,(
% 0.22/0.45 ![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[111])).
% 0.22/0.45 tff(113,plain,
% 0.22/0.45 (![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.22/0.45 tff(114,plain,
% 0.22/0.45 ((~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(115,axiom,(~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_6')).
% 0.22/0.46 tff(116,plain,
% 0.22/0.46 (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.22/0.46 tff(117,plain,
% 0.22/0.46 (((~![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(118,plain,
% 0.22/0.46 (((~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))) <=> (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(119,plain,
% 0.22/0.46 (((~![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[118])).
% 0.22/0.46 tff(120,plain,
% 0.22/0.46 (((~![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[119, 117])).
% 0.22/0.46 tff(121,plain,
% 0.22/0.46 ((~![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(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_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(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, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), 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_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(122,plain,
% 0.22/0.46 ((~![V_B_H: $i, V_A_H: $i, V_nb_H: $i, V_NB: $i, V_na: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB), V_nb_H))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NBa)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.22/0.46 tff(123,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[122, 68, 116, 113, 103, 39])).
% 0.22/0.46 % SZS output end Proof
% 0.22/0.47 % E exiting
%------------------------------------------------------------------------------