%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV354-2 : 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 0.14s 0.41s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SWV354-2 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n015.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 09:44:10 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(c_in_type, type, (
% 0.14/0.41 c_in: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(tc_Event_Oevent_type, type, (
% 0.14/0.41 tc_Event_Oevent: $i)).
% 0.14/0.41 tff(c_List_Oset_type, type, (
% 0.14/0.41 c_List_Oset: ( $i * $i ) > $i)).
% 0.14/0.41 tff(v_evso_type, type, (
% 0.14/0.41 v_evso: $i)).
% 0.14/0.41 tff(c_Event_Oevent_OSays_type, type, (
% 0.14/0.41 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.14/0.41 tff(c_Message_Omsg_OMPair_type, type, (
% 0.14/0.41 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.14/0.41 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.14/0.41 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.14/0.41 tff(c_Message_Omsg_ONonce_type, type, (
% 0.14/0.41 c_Message_Omsg_ONonce: $i > $i)).
% 0.14/0.41 tff(v_NBa_type, type, (
% 0.14/0.41 v_NBa: $i)).
% 0.14/0.41 tff(v_NA_type, type, (
% 0.14/0.41 v_NA: $i)).
% 0.14/0.41 tff(c_Message_Omsg_OAgent_type, type, (
% 0.14/0.41 c_Message_Omsg_OAgent: $i > $i)).
% 0.14/0.41 tff(v_A_type, type, (
% 0.14/0.41 v_A: $i)).
% 0.14/0.41 tff(c_Public_OshrK_type, type, (
% 0.14/0.41 c_Public_OshrK: $i > $i)).
% 0.14/0.41 tff(v_B_type, type, (
% 0.14/0.41 v_B: $i)).
% 0.14/0.41 tff(c_Message_Oagent_OServer_type, type, (
% 0.14/0.41 c_Message_Oagent_OServer: $i)).
% 0.14/0.41 tff(v_NB_type, type, (
% 0.14/0.41 v_NB: $i)).
% 0.14/0.41 tff(v_sko__2VY_type, type, (
% 0.14/0.41 v_sko__2VY: $i > $i)).
% 0.14/0.41 tff(v_K_type, type, (
% 0.14/0.41 v_K: $i)).
% 0.14/0.41 tff(v_X_type, type, (
% 0.14/0.41 v_X: $i)).
% 0.14/0.41 tff(v_NAa_type, type, (
% 0.14/0.41 v_NAa: $i)).
% 0.14/0.41 tff(c_Message_Omsg_OKey_type, type, (
% 0.14/0.41 c_Message_Omsg_OKey: $i > $i)).
% 0.14/0.41 tff(v_Ba_type, type, (
% 0.14/0.41 v_Ba: $i)).
% 0.14/0.41 tff(v_Aa_type, type, (
% 0.14/0.41 v_Aa: $i)).
% 0.14/0.41 tff(tc_List_Olist_type, type, (
% 0.14/0.41 tc_List_Olist: $i > $i)).
% 0.14/0.41 tff(c_Yahalom_Oyahalom_type, type, (
% 0.14/0.41 c_Yahalom_Oyahalom: $i)).
% 0.14/0.41 tff(tc_Message_Omsg_type, type, (
% 0.14/0.41 tc_Message_Omsg: $i)).
% 0.14/0.41 tff(c_Message_Oanalz_type, type, (
% 0.14/0.41 c_Message_Oanalz: $i > $i)).
% 0.14/0.41 tff(c_insert_type, type, (
% 0.14/0.41 c_insert: ( $i * $i * $i ) > $i)).
% 0.14/0.41 tff(c_Event_Oknows_type, type, (
% 0.14/0.41 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.14/0.41 tff(c_Message_Oagent_OSpy_type, type, (
% 0.14/0.41 c_Message_Oagent_OSpy: $i)).
% 0.14/0.41 tff(c_Event_Oevent_OGets_type, type, (
% 0.14/0.41 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.14/0.41 tff(1,assumption,(v_K = c_Public_OshrK(v_sko__2VY(v_K))), introduced(assumption)).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (c_Public_OshrK(v_sko__2VY(v_K)) = v_K),
% 0.14/0.41 inference(symmetry,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (c_Message_Omsg_OKey(c_Public_OshrK(v_sko__2VY(v_K))) = c_Message_Omsg_OKey(v_K)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[2])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))) = c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa)))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[3])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa)))) = c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[4])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))) = c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa)))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[5])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X) = c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[6])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)) = c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[7])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), 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_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[8])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.14/0.41 inference(symmetry,[status(thm)],[9])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(12,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_NAa), 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')).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (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))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(16,axiom,(c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (^[V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), 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_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(21,axiom,(![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OSays__Server__not__shrK_0')).
% 0.14/0.42 tff(22,plain,
% 0.14/0.42 (![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.42 tff(23,plain,(
% 0.14/0.42 ![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[22])).
% 0.14/0.42 tff(24,plain,
% 0.14/0.42 (![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.42 tff(25,plain,
% 0.14/0.42 (((~![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), 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_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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), 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_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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(26,plain,
% 0.14/0.42 ((~![V_x: $i, V_nb: $i, V_na: $i, V_X: $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_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), 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_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(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(27,plain,
% 0.14/0.42 ((~![V_x: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.14/0.42 tff(28,plain,
% 0.14/0.42 (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(v_sko__2VY(v_K))), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 0.14/0.42 tff(29,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[28, 14])).
% 0.14/0.42 tff(30,plain,(~(v_K = c_Public_OshrK(v_sko__2VY(v_K)))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(31,plain,
% 0.14/0.42 (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(32,axiom,(c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_7')).
% 0.14/0.42 tff(33,plain,
% 0.14/0.42 (c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.42 tff(34,plain,
% 0.14/0.42 ((~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))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(35,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')).
% 0.24/0.42 tff(36,plain,
% 0.24/0.42 (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.24/0.42 tff(37,plain,
% 0.24/0.42 (^[V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : refl(((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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)))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(38,plain,
% 0.24/0.42 (![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.24/0.42 tff(39,plain,
% 0.24/0.42 (![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(40,plain,
% 0.24/0.42 (^[V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), 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(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_ONonce(V_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))), rewrite((((~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_ONonce(V_NB), c_Message_Oanalz(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(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), 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(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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), 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_NB = V_NB_H)) <=> ((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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_NB = V_NB_H)))), rewrite(((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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_NB = V_NB_H)) <=> ((V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), 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_NB = V_NB_H)) <=> ((V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), 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_NB = V_NB_H)) | (V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB)))) <=> (((V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_KAB = c_Public_OshrK(v_sko__2VY(V_KAB)))))), rewrite((((V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_KAB = c_Public_OshrK(v_sko__2VY(V_KAB)))) <=> ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), 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_NB = V_NB_H)) | (V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB)))) <=> ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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))))))),
% 0.24/0.43 inference(bind,[status(th)],[])).
% 0.24/0.43 tff(41,plain,
% 0.24/0.43 (![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), 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_NB = V_NB_H)) | (V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB)))) <=> ![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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))))),
% 0.24/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.24/0.43 tff(42,axiom,(![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), 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_NB = V_NB_H)) | (V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_Osingle__Nonce__secrecy_0')).
% 0.24/0.43 tff(43,plain,
% 0.24/0.43 (![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.24/0.43 tff(44,plain,
% 0.24/0.43 (![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.24/0.43 tff(45,plain,(
% 0.24/0.43 ![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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))))),
% 0.24/0.43 inference(skolemize,[status(sab)],[44])).
% 0.24/0.43 tff(46,plain,
% 0.24/0.43 (![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.24/0.43 tff(47,plain,
% 0.24/0.43 (((~![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (v_NB = v_NBa) | (v_K = c_Public_OshrK(v_sko__2VY(v_K))) | (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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))))) <=> ((~![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (v_NB = v_NBa) | (v_K = c_Public_OshrK(v_sko__2VY(v_K))) | (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(48,plain,
% 0.24/0.43 (((v_K = c_Public_OshrK(v_sko__2VY(v_K))) | (v_NB = v_NBa) | 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_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (v_NB = v_NBa) | (v_K = c_Public_OshrK(v_sko__2VY(v_K))) | (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(49,plain,
% 0.24/0.43 (((~![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_K = c_Public_OshrK(v_sko__2VY(v_K))) | (v_NB = v_NBa) | 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_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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))))) <=> ((~![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (v_NB = v_NBa) | (v_K = c_Public_OshrK(v_sko__2VY(v_K))) | (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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)))))),
% 0.24/0.43 inference(monotonicity,[status(thm)],[48])).
% 0.24/0.43 tff(50,plain,
% 0.24/0.43 (((~![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_K = c_Public_OshrK(v_sko__2VY(v_K))) | (v_NB = v_NBa) | 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_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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))))) <=> ((~![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (v_NB = v_NBa) | (v_K = c_Public_OshrK(v_sko__2VY(v_K))) | (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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))))),
% 0.24/0.44 inference(transitivity,[status(thm)],[49, 47])).
% 0.24/0.44 tff(51,plain,
% 0.24/0.44 ((~![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_K = c_Public_OshrK(v_sko__2VY(v_K))) | (v_NB = v_NBa) | 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_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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))))),
% 0.24/0.44 inference(quant_inst,[status(thm)],[])).
% 0.24/0.44 tff(52,plain,
% 0.24/0.44 ((~![V_KAB: $i, V_NB: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_NB_H: $i, V_evs: $i] : ((V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))) | (V_NB = V_NB_H) | 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_ONonce(V_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB), c_Message_Omsg_OMPair(V_na, c_Message_Omsg_ONonce(V_NB_H))))), 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_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (v_NB = v_NBa) | (v_K = c_Public_OshrK(v_sko__2VY(v_K))) | (~c_in(c_Message_Omsg_ONonce(v_NB), c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evso), tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.24/0.44 tff(53,plain,
% 0.24/0.44 ((v_NB = v_NBa) | (v_K = c_Public_OshrK(v_sko__2VY(v_K)))),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[52, 46, 17, 13, 36, 33])).
% 0.24/0.44 tff(54,plain,
% 0.24/0.44 (v_NB = v_NBa),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[53, 30])).
% 0.24/0.44 tff(55,plain,
% 0.24/0.44 (c_Message_Omsg_ONonce(v_NB) = c_Message_Omsg_ONonce(v_NBa)),
% 0.24/0.44 inference(monotonicity,[status(thm)],[54])).
% 0.24/0.44 tff(56,plain,
% 0.24/0.44 (c_Message_Omsg_ONonce(v_NBa) = c_Message_Omsg_ONonce(v_NB)),
% 0.24/0.44 inference(symmetry,[status(thm)],[55])).
% 0.24/0.44 tff(57,plain,
% 0.24/0.44 (c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NBa)) = c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[56])).
% 0.24/0.44 tff(58,plain,
% 0.24/0.44 (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_NBa))) = 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)))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[57])).
% 0.24/0.44 tff(59,plain,
% 0.24/0.44 (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_NBa)))) = 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))))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[58])).
% 0.24/0.44 tff(60,plain,
% 0.24/0.44 (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_NBa))))) = 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)))))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[59])).
% 0.24/0.44 tff(61,plain,
% 0.24/0.44 (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_NBa)))))) = 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))))))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[60])).
% 0.24/0.44 tff(62,plain,
% 0.24/0.44 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NBa)))))), 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)),
% 0.24/0.44 inference(monotonicity,[status(thm)],[61])).
% 0.24/0.44 tff(63,plain,
% 0.24/0.44 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_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_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.24/0.44 inference(symmetry,[status(thm)],[62])).
% 0.24/0.44 tff(64,plain,
% 0.24/0.44 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_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)),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(65,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')).
% 0.24/0.44 tff(66,plain,
% 0.24/0.44 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.24/0.44 tff(67,plain,
% 0.24/0.44 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[66, 63])).
% 0.24/0.44 tff(68,plain,
% 0.24/0.44 (c_in(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_ONonce(v_NB), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.24/0.44 inference(monotonicity,[status(thm)],[56])).
% 0.24/0.44 tff(69,plain,
% 0.24/0.44 (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_NBa), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.24/0.44 inference(symmetry,[status(thm)],[68])).
% 0.24/0.44 tff(70,plain,
% 0.24/0.44 ((~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_NBa), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[69])).
% 0.24/0.44 tff(71,plain,
% 0.24/0.44 (~c_in(c_Message_Omsg_ONonce(v_NBa), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[36, 70])).
% 0.24/0.44 tff(72,plain,
% 0.24/0.44 ((v_NAa = v_NA) <=> (v_NA = v_NAa)),
% 0.24/0.44 inference(commutativity,[status(thm)],[])).
% 0.24/0.44 tff(73,plain,
% 0.24/0.44 ((v_NA = v_NAa) <=> (v_NAa = v_NA)),
% 0.24/0.44 inference(symmetry,[status(thm)],[72])).
% 0.24/0.44 tff(74,plain,
% 0.24/0.44 ((~(v_NA = v_NAa)) <=> (~(v_NAa = v_NA))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[73])).
% 0.24/0.44 tff(75,plain,
% 0.24/0.44 (((~(v_NA = v_NAa)) | (~(v_NB = v_NBa))) <=> ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(76,plain,
% 0.24/0.44 (![V_U: $i] : ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa))) <=> ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)))),
% 0.24/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.24/0.44 tff(77,plain,
% 0.24/0.44 (![V_U: $i] : ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)) | (~(V_U = c_Message_Omsg_OKey(v_K)))) <=> ![V_U: $i] : ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)))),
% 0.24/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.24/0.44 tff(78,plain,
% 0.24/0.44 (![V_U: $i] : ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)) | (~(V_U = c_Message_Omsg_OKey(v_K)))) <=> ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)))),
% 0.24/0.44 inference(transitivity,[status(thm)],[77, 76])).
% 0.24/0.44 tff(79,plain,
% 0.24/0.44 (^[V_U: $i] : trans(monotonicity(rewrite(((~(V_U = c_Message_Omsg_OKey(v_K))) | (~(v_NA = v_NAa))) <=> ((~(v_NA = v_NAa)) | (~(V_U = c_Message_Omsg_OKey(v_K))))), ((((~(V_U = c_Message_Omsg_OKey(v_K))) | (~(v_NA = v_NAa))) | (~(v_NB = v_NBa))) <=> (((~(v_NA = v_NAa)) | (~(V_U = c_Message_Omsg_OKey(v_K)))) | (~(v_NB = v_NBa))))), rewrite((((~(v_NA = v_NAa)) | (~(V_U = c_Message_Omsg_OKey(v_K)))) | (~(v_NB = v_NBa))) <=> ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)) | (~(V_U = c_Message_Omsg_OKey(v_K))))), ((((~(V_U = c_Message_Omsg_OKey(v_K))) | (~(v_NA = v_NAa))) | (~(v_NB = v_NBa))) <=> ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)) | (~(V_U = c_Message_Omsg_OKey(v_K))))))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(80,plain,
% 0.24/0.44 (![V_U: $i] : (((~(V_U = c_Message_Omsg_OKey(v_K))) | (~(v_NA = v_NAa))) | (~(v_NB = v_NBa))) <=> ![V_U: $i] : ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)) | (~(V_U = c_Message_Omsg_OKey(v_K))))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.24/0.44 tff(81,plain,
% 0.24/0.44 (![V_U: $i] : (((~(V_U = c_Message_Omsg_OKey(v_K))) | (~(v_NA = v_NAa))) | (~(v_NB = v_NBa))) <=> ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa)))),
% 0.24/0.44 inference(transitivity,[status(thm)],[80, 78])).
% 0.24/0.44 tff(82,axiom,(![V_U: $i] : (((~(V_U = c_Message_Omsg_OKey(v_K))) | (~(v_NA = v_NAa))) | (~(v_NB = v_NBa)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_9')).
% 0.24/0.44 tff(83,plain,
% 0.24/0.44 ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.24/0.44 tff(84,plain,
% 0.24/0.44 ((~(v_NA = v_NAa)) | (~(v_NB = v_NBa))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[83, 75])).
% 0.24/0.44 tff(85,plain,
% 0.24/0.44 (~(v_NA = v_NAa)),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[84, 54])).
% 0.24/0.44 tff(86,plain,
% 0.24/0.44 (~(v_NAa = v_NA)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[85, 74])).
% 0.24/0.44 tff(87,plain,
% 0.24/0.44 (^[V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : refl((c_in(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_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_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))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(88,plain,
% 0.24/0.45 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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(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_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)))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[87])).
% 0.24/0.45 tff(89,plain,
% 0.24/0.45 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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(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_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)))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(90,plain,
% 0.24/0.45 (^[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(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_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))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(91,plain,
% 0.24/0.45 (![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(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_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)))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[90])).
% 0.24/0.45 tff(92,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')).
% 0.24/0.45 tff(93,plain,
% 0.24/0.45 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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)))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.24/0.45 tff(94,plain,
% 0.24/0.45 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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)))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.24/0.45 tff(95,plain,(
% 0.24/0.45 ![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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)))),
% 0.24/0.45 inference(skolemize,[status(sab)],[94])).
% 0.24/0.45 tff(96,plain,
% 0.24/0.45 (![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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)))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.24/0.45 tff(97,plain,
% 0.24/0.45 (((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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_NAa), 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_NAa), 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(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_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_NAa), 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_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(98,plain,
% 0.24/0.45 ((c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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_NAa), 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_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(99,plain,
% 0.24/0.45 (((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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(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_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_NAa), 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_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.45 inference(monotonicity,[status(thm)],[98])).
% 0.24/0.45 tff(100,plain,
% 0.24/0.45 (((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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(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_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_NAa), 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_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.24/0.46 inference(transitivity,[status(thm)],[99, 97])).
% 0.24/0.46 tff(101,plain,
% 0.24/0.46 ((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_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(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(102,plain,
% 0.24/0.46 ((~![V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_k: $i, V_evs: $i] : (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_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_NAa), 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_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.24/0.46 tff(103,plain,
% 0.24/0.46 (c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[102, 96, 17, 13])).
% 0.24/0.46 tff(104,plain,
% 0.24/0.46 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(105,plain,
% 0.24/0.46 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[104])).
% 0.24/0.46 tff(106,plain,
% 0.24/0.46 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(107,plain,
% 0.24/0.46 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))), ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_NA_H = V_NA)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_NA_H = V_NA)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_NA_H = V_NA)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), ((((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_NA_H = V_NA)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(108,plain,
% 0.24/0.46 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_NA_H = V_NA)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[107])).
% 0.24/0.46 tff(109,axiom,(![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (V_NA_H = V_NA))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_OSays__unique__NB_0')).
% 0.24/0.46 tff(110,plain,
% 0.24/0.46 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.24/0.46 tff(111,plain,
% 0.24/0.46 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.24/0.47 tff(112,plain,(
% 0.24/0.47 ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.47 inference(skolemize,[status(sab)],[111])).
% 0.24/0.47 tff(113,plain,
% 0.24/0.47 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.24/0.47 tff(114,plain,
% 0.24/0.47 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_NAa = v_NA) | c_in(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_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_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_NAa = v_NA) | c_in(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_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_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(115,plain,
% 0.24/0.47 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_NAa = v_NA) | c_in(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_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_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.24/0.47 inference(quant_inst,[status(thm)],[])).
% 0.24/0.47 tff(116,plain,
% 0.24/0.47 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_NA: $i, V_nb: $i, V_S: $i, V_X: $i, V_NA_H: $i, V_B: $i, V_A: $i, V_S_H: $i, V_C: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_NA_H = V_NA) | c_in(V_nb, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(V_C, V_S, c_Message_Omsg_OMPair(V_X, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(V_S_H, c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H), V_nb))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (~c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_NAa = v_NA) | c_in(c_Message_Omsg_ONonce(v_NBa), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evso)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_ONonce(v_NBa)))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.24/0.47 tff(117,plain,
% 0.24/0.47 ($false),
% 0.24/0.47 inference(unit_resolution,[status(thm)],[116, 113, 17, 103, 86, 71, 67])).
% 0.24/0.47 % SZS output end Proof
% 0.24/0.47 % E exiting
%------------------------------------------------------------------------------