%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV345-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 20:43:23 EDT 2022 % Result : Unsatisfiable 2.82s 3.02s % Output : Proof 2.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWV345-2 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 15 21:55:34 EDT 2022 % 0.13/0.34 % CPUTime : % 2.82/3.02 % SZS status Unsatisfiable % 2.82/3.02 % SZS output start Proof % 2.82/3.02 The input problem is unsatisfiable because % 2.82/3.02 % 2.82/3.02 [1] the following set of Horn clauses is unsatisfiable: % 2.82/3.02 % 2.82/3.02 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_nb = V_nb_H % 2.82/3.02 c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) % 2.82/3.02 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) % 2.82/3.02 c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_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) % 2.82/3.02 v_nb = c_Message_Omsg_ONonce(v_NB) ==> \bottom % 2.82/3.02 % 2.82/3.02 This holds because % 2.82/3.02 % 2.82/3.02 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.82/3.02 % 2.82/3.02 E: % 2.82/3.02 c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_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__ % 2.82/3.02 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__ % 2.82/3.02 c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) = true__ % 2.82/3.02 f1(true__, V_nb, V_nb_H) = V_nb % 2.82/3.02 f2(true__, V_evs, V_nb, V_nb_H) = f1(c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)), V_nb, V_nb_H) % 2.82/3.02 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_nb) = V_nb_H % 2.82/3.02 f3(true__, V_A_H, V_B_H, V_K, V_na_H, V_nb_H, V_X_H, V_evs, V_nb) = 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_nb, V_nb_H) % 2.82/3.02 f4(c_Message_Omsg_ONonce(v_NB)) = false__ % 2.82/3.02 f4(v_nb) = true__ % 2.82/3.02 G: % 2.82/3.02 true__ = false__ % 2.82/3.02 % 2.82/3.02 This holds because % 2.82/3.02 % 2.82/3.02 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.82/3.02 % 2.82/3.02 f2(true__, v_evso, Y7, c_Message_Omsg_ONonce(v_NB)) = 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) % 2.82/3.02 c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_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, c_Message_Omsg_ONonce(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__ % 2.82/3.02 c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_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__ % 2.82/3.02 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__ % 2.82/3.02 c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) -> true__ % 2.82/3.02 f1(c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)), V_nb, V_nb_H) -> f2(true__, V_evs, V_nb, V_nb_H) % 2.82/3.02 f1(true__, V_nb, V_nb_H) -> V_nb % 2.82/3.02 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_nb, V_nb_H) -> f3(true__, V_A_H, V_B_H, V_K, V_na_H, V_nb_H, V_X_H, V_evs, V_nb) % 2.82/3.02 f2(true__, v_evso, Y1, Y2) -> Y1 % 2.82/3.02 f2(true__, v_evso, Y7, v_nb) -> 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) % 2.82/3.02 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_nb) -> V_nb_H % 2.82/3.02 f3(true__, Y7, Y8, v_K, Y9, Y10, Y11, v_evso, c_Message_Omsg_ONonce(v_NB)) -> Y10 % 2.82/3.02 f3(true__, Y7, Y8, v_K, Y9, Y10, Y11, v_evso, v_nb) -> Y10 % 2.82/3.02 f3(true__, v_A, v_B, v_K, v_na, c_Message_Omsg_ONonce(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 % 2.82/3.02 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 % 2.82/3.02 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 % 2.82/3.02 f4(c_Message_Omsg_ONonce(v_NB)) -> false__ % 2.82/3.02 f4(v_nb) -> true__ % 2.82/3.02 false__ -> true__ % 2.82/3.02 v_nb -> c_Message_Omsg_ONonce(v_NB) % 2.82/3.02 with the LPO induced by % 2.82/3.02 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__ % 2.82/3.02 % 2.82/3.02 % SZS output end Proof % 2.82/3.02 %------------------------------------------------------------------------------