%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV355-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n004.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 20:43:30 EDT 2022 % Result : Unsatisfiable 7.19s 7.18s % Output : Proof 7.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWV355-2 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : moca.sh %s % 0.14/0.35 % Computer : n004.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Wed Jun 15 23:47:54 EDT 2022 % 0.14/0.35 % CPUTime : % 7.19/7.18 % SZS status Unsatisfiable % 7.19/7.18 % SZS output start Proof % 7.19/7.18 The input problem is unsatisfiable because % 7.19/7.18 % 7.19/7.18 [1] the following set of Horn clauses is unsatisfiable: % 7.19/7.18 % 7.19/7.18 c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) ==> c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg) % 7.19/7.18 c_in(V_c, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) ==> c_in(V_c, c_Event_Oused(V_evs), tc_Message_Omsg) % 7.19/7.18 c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg) ==> c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg) % 7.19/7.18 c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oparts(V_H), tc_Message_Omsg) ==> c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 7.19/7.18 c_in(V_X, V_H, tc_Message_Omsg) ==> c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 7.19/7.18 c_in(c_Message_Omsg_ONonce(v_NB), c_Event_Oused(v_evs1), tc_Message_Omsg) ==> \bottom % 7.19/7.18 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_evs1, tc_Event_Oevent), tc_Event_Oevent) % 7.19/7.18 % 7.19/7.18 This holds because % 7.19/7.18 % 7.19/7.18 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 7.19/7.18 % 7.19/7.18 E: % 7.19/7.18 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_evs1, tc_Event_Oevent), tc_Event_Oevent) = true__ % 7.19/7.18 f1(c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent), V_X, V_evs) = true__ % 7.19/7.18 f1(true__, V_X, V_evs) = c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg) % 7.19/7.18 f2(c_in(V_c, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg), V_c, V_evs) = true__ % 7.19/7.18 f2(true__, V_c, V_evs) = c_in(V_c, c_Event_Oused(V_evs), tc_Message_Omsg) % 7.19/7.18 f3(c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg), V_Y, V_H) = true__ % 7.19/7.18 f3(true__, V_Y, V_H) = c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg) % 7.19/7.18 f4(c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oparts(V_H), tc_Message_Omsg), V_X, V_H) = true__ % 7.19/7.18 f4(true__, V_X, V_H) = c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 7.19/7.18 f5(c_in(V_X, V_H, tc_Message_Omsg), V_X, V_H) = true__ % 7.19/7.18 f5(true__, V_X, V_H) = c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 7.19/7.18 f6(c_in(c_Message_Omsg_ONonce(v_NB), c_Event_Oused(v_evs1), tc_Message_Omsg)) = true__ % 7.19/7.18 f6(true__) = false__ % 7.19/7.18 G: % 7.19/7.18 true__ = false__ % 7.19/7.18 % 7.19/7.18 This holds because % 7.19/7.18 % 7.19/7.18 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 7.19/7.18 % 7.19/7.18 % 7.19/7.18 c_in(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg) -> f1(true__, V_X, V_evs) % 7.19/7.18 c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg) -> f3(true__, V_Y, V_H) % 7.19/7.18 c_in(V_c, c_Event_Oused(V_evs), tc_Message_Omsg) -> f2(true__, V_c, V_evs) % 7.19/7.18 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_evs1, tc_Event_Oevent), tc_Event_Oevent) -> true__ % 7.19/7.18 f1(c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent), V_X, V_evs) -> true__ % 7.19/7.18 f1(true__, 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))))), v_evs1) -> true__ % 7.19/7.18 f2(c_in(V_c, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg), V_c, V_evs) -> true__ % 7.19/7.18 f2(f3(true__, Y0, c_Event_Oknows(c_Message_Oagent_OSpy, Y1)), Y0, Y1) -> true__ % 7.19/7.18 f2(true__, 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)))), v_evs1) -> true__ % 7.19/7.18 f2(true__, 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))), v_evs1) -> true__ % 7.19/7.18 f2(true__, 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))))), v_evs1) -> true__ % 7.19/7.18 f2(true__, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)), v_evs1) -> true__ % 7.19/7.18 f2(true__, c_Message_Omsg_ONonce(v_NB), v_evs1) -> true__ % 7.19/7.18 f3(c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg), V_Y, V_H) -> true__ % 7.19/7.18 f3(f3(true__, c_Message_Omsg_OMPair(Y0, Y1), Y2), Y1, Y2) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Event_Oused(v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oparts(c_Event_Oused(v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oparts(c_Message_Oparts(c_Event_Oused(v_evs1)))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Event_Oused(v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Event_Oused(v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Message_Oparts(c_Event_Oused(v_evs1)))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)))))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Event_Oused(v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oused(v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)), c_Event_Oused(v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Event_Oused(v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_ONonce(v_NB), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_ONonce(v_NB), c_Event_Oused(v_evs1)) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_ONonce(v_NB), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1))) -> true__ % 7.19/7.18 f3(true__, c_Message_Omsg_ONonce(v_NB), c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs1)))) -> true__ % 7.19/7.18 f4(c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oparts(V_H), tc_Message_Omsg), V_X, V_H) -> true__ % 7.19/7.18 f4(f3(true__, c_Message_Omsg_OCrypt(Y0, Y1), Y2), Y1, Y2) -> true__ % 7.19/7.18 f4(true__, V_X, V_H) -> c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 7.19/7.18 f5(c_in(V_X, V_H, tc_Message_Omsg), V_X, V_H) -> true__ % 7.19/7.18 f5(f1(true__, Y0, X1), Y0, c_Event_Oknows(c_Message_Oagent_OSpy, X1)) -> true__ % 7.19/7.18 f5(f2(true__, Y0, X1), Y0, c_Event_Oused(X1)) -> true__ % 7.19/7.18 f5(f3(true__, Y0, X1), Y0, c_Message_Oparts(X1)) -> true__ % 7.19/7.18 f5(true__, V_X, V_H) -> c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 7.19/7.18 f6(c_in(c_Message_Omsg_ONonce(v_NB), c_Event_Oused(v_evs1), tc_Message_Omsg)) -> true__ % 7.19/7.18 f6(f2(true__, c_Message_Omsg_ONonce(v_NB), v_evs1)) -> true__ % 7.19/7.18 f6(true__) -> false__ % 7.19/7.18 false__ -> true__ % 7.19/7.18 with the LPO induced by % 7.19/7.18 v_NA > v_A > c_Public_OshrK > c_Message_Omsg_OAgent > c_Message_Oagent_OServer > v_NB > f5 > f4 > c_in > f3 > c_Message_Omsg_OMPair > f1 > f2 > tc_Message_Omsg > c_Message_Oagent_OSpy > v_B > v_evs1 > c_Message_Omsg_ONonce > f6 > c_Message_Omsg_OCrypt > c_Message_Oparts > c_Event_Oused > tc_Event_Oevent > c_List_Oset > c_Event_Oevent_OSays > c_Event_Oknows > false__ > true__ % 7.19/7.18 % 7.19/7.18 % SZS output end Proof % 7.19/7.18 %------------------------------------------------------------------------------