TSTP Solution File: SWV346-2 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SWV346-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:43:24 EDT 2022
% Result : Unsatisfiable 2.60s 2.81s
% Output : Proof 2.60s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV346-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 00:08:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.60/2.81 % SZS status Unsatisfiable
% 2.60/2.81 % SZS output start Proof
% 2.60/2.81 The input problem is unsatisfiable because
% 2.60/2.81
% 2.60/2.81 [1] the following set of Horn clauses is unsatisfiable:
% 2.60/2.81
% 2.60/2.81 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_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) & c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) ==> V_na = V_na_H
% 2.60/2.81 c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))
% 2.60/2.81 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_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)
% 2.60/2.81 c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(v_na, v_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)
% 2.60/2.81 v_na = c_Message_Omsg_ONonce(v_NA) ==> \bottom
% 2.60/2.81
% 2.60/2.81 This holds because
% 2.60/2.81
% 2.60/2.81 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.60/2.81
% 2.60/2.81 E:
% 2.60/2.81 c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(v_na, v_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent) = true__
% 2.60/2.81 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_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent) = true__
% 2.60/2.81 c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) = true__
% 2.60/2.81 f1(true__, V_na, V_na_H) = V_na
% 2.60/2.81 f2(true__, V_evs, V_na, V_na_H) = f1(c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)), V_na, V_na_H)
% 2.60/2.81 f3(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent), V_A_H, V_B_H, V_K, V_na_H, V_nb_H, V_X_H, V_evs, V_na) = V_na_H
% 2.60/2.81 f3(true__, V_A_H, V_B_H, V_K, V_na_H, V_nb_H, V_X_H, V_evs, V_na) = f2(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent), V_evs, V_na, V_na_H)
% 2.60/2.81 f4(c_Message_Omsg_ONonce(v_NA)) = false__
% 2.60/2.81 f4(v_na) = true__
% 2.60/2.81 G:
% 2.60/2.81 true__ = false__
% 2.60/2.81
% 2.60/2.81 This holds because
% 2.60/2.81
% 2.60/2.81 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.60/2.81
% 2.60/2.81 f2(true__, v_evso, Y7, c_Message_Omsg_ONonce(v_NA)) = f3(true__, v_Aa, v_Ba, v_K, c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB), v_X, v_evso, Y7)
% 2.60/2.81 f2(true__, v_evso, Y7, v_na) = f3(true__, v_A, v_B, v_K, v_na, v_nb, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), v_evso, Y7)
% 2.60/2.81 c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), v_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent) -> true__
% 2.60/2.81 c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(v_na, v_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent) -> true__
% 2.60/2.81 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_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent) -> true__
% 2.60/2.81 c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) -> true__
% 2.60/2.81 f1(c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)), V_na, V_na_H) -> f2(true__, V_evs, V_na, V_na_H)
% 2.60/2.81 f1(true__, V_na, V_na_H) -> V_na
% 2.60/2.81 f2(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent), V_evs, V_na, V_na_H) -> f3(true__, V_A_H, V_B_H, V_K, V_na_H, V_nb_H, V_X_H, V_evs, V_na)
% 2.60/2.81 f2(true__, v_evso, Y1, Y2) -> Y1
% 2.60/2.81 f3(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent), V_A_H, V_B_H, V_K, V_na_H, V_nb_H, V_X_H, V_evs, V_na) -> V_na_H
% 2.60/2.81 f3(true__, Y7, Y8, v_K, Y9, Y10, Y11, v_evso, c_Message_Omsg_ONonce(v_NA)) -> Y9
% 2.60/2.81 f3(true__, Y7, Y8, v_K, Y9, Y10, Y11, v_evso, v_na) -> Y9
% 2.60/2.81 f3(true__, v_A, v_B, v_K, c_Message_Omsg_ONonce(v_NA), v_nb, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), v_evso, Y0) -> Y0
% 2.60/2.81 f3(true__, v_A, v_B, v_K, v_na, v_nb, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), v_evso, Y0) -> Y0
% 2.60/2.81 f3(true__, v_Aa, v_Ba, v_K, c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB), v_X, v_evso, Y0) -> Y0
% 2.60/2.81 f4(c_Message_Omsg_ONonce(v_NA)) -> false__
% 2.60/2.81 f4(v_na) -> true__
% 2.60/2.81 false__ -> true__
% 2.60/2.81 v_na -> c_Message_Omsg_ONonce(v_NA)
% 2.60/2.81 with the LPO induced by
% 2.60/2.81 f4 > v_nb > v_na > v_B > v_A > v_X > v_NB > v_NA > c_Message_Omsg_ONonce > v_K > v_Ba > v_Aa > v_evso > f1 > c_List_Oset > c_Message_Omsg_OKey > c_Message_Omsg_OAgent > f2 > f3 > c_Message_Omsg_OMPair > c_Public_OshrK > c_Message_Omsg_OCrypt > c_Message_Oagent_OServer > c_Event_Oevent_OSays > tc_Event_Oevent > tc_List_Olist > c_Yahalom_Oyahalom > c_in > false__ > true__
% 2.60/2.81
% 2.60/2.81 % SZS output end Proof
% 2.60/2.81
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