%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV307-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 20:42:58 EDT 2022 % Result : Unsatisfiable 1.62s 1.78s % Output : Proof 1.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV307-2 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n011.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 16:15:35 EDT 2022 % 0.13/0.34 % CPUTime : % 1.62/1.78 % SZS status Unsatisfiable % 1.62/1.78 % SZS output start Proof % 1.62/1.78 The input problem is unsatisfiable because % 1.62/1.78 % 1.62/1.78 [1] the following set of Horn clauses is unsatisfiable: % 1.62/1.78 % 1.62/1.78 c_in(c_Message_Omsg_ONonce(v_NB), c_Event_Oused(v_evs2), tc_Message_Omsg) ==> \bottom % 1.62/1.78 c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)), tc_Message_Omsg) % 1.62/1.78 v_NA = c_Message_Omsg_ONonce(v_NB) % 1.62/1.78 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) % 1.62/1.78 c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg) ==> c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 1.62/1.78 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) % 1.62/1.78 % 1.62/1.78 This holds because % 1.62/1.78 % 1.62/1.78 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.62/1.78 % 1.62/1.78 E: % 1.62/1.78 c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)), tc_Message_Omsg) = true__ % 1.62/1.78 f1(c_in(c_Message_Omsg_ONonce(v_NB), c_Event_Oused(v_evs2), tc_Message_Omsg)) = true__ % 1.62/1.78 f1(true__) = false__ % 1.62/1.78 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__ % 1.62/1.78 f2(true__, V_c, V_evs) = c_in(V_c, c_Event_Oused(V_evs), tc_Message_Omsg) % 1.62/1.78 f3(c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg), V_X, V_H) = true__ % 1.62/1.78 f3(true__, V_X, V_H) = c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 1.62/1.78 f4(c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oparts(V_H), tc_Message_Omsg), V_X, V_H) = true__ % 1.62/1.78 f4(true__, V_X, V_H) = c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 1.62/1.78 v_NA = c_Message_Omsg_ONonce(v_NB) % 1.62/1.78 G: % 1.62/1.78 true__ = false__ % 1.62/1.78 % 1.62/1.78 This holds because % 1.62/1.78 % 1.62/1.78 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.62/1.78 % 1.62/1.78 % 1.62/1.78 c_Message_Omsg_ONonce(v_NB) -> v_NA % 1.62/1.78 c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) -> f3(true__, V_X, V_H) % 1.62/1.78 c_in(V_c, c_Event_Oused(V_evs), tc_Message_Omsg) -> f2(true__, V_c, V_evs) % 1.62/1.78 c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)), tc_Message_Omsg) -> true__ % 1.62/1.78 f1(c_in(c_Message_Omsg_ONonce(v_NB), c_Event_Oused(v_evs2), tc_Message_Omsg)) -> true__ % 1.62/1.78 f1(f2(true__, v_NA, v_evs2)) -> true__ % 1.62/1.78 f1(true__) -> false__ % 1.62/1.78 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__ % 1.62/1.78 f2(f3(true__, Y0, c_Event_Oknows(c_Message_Oagent_OSpy, Y1)), Y0, Y1) -> true__ % 1.62/1.78 f2(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), v_evs2) -> true__ % 1.62/1.78 f2(true__, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B))), v_evs2) -> true__ % 1.62/1.78 f2(true__, v_NA, v_evs2) -> true__ % 1.62/1.78 f3(c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg), V_X, V_H) -> true__ % 1.62/1.78 f3(f3(true__, c_Message_Omsg_OMPair(Y0, Y1), Y2), Y0, Y2) -> true__ % 1.62/1.78 f3(true__, c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)) -> true__ % 1.62/1.78 f3(true__, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B))), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)) -> true__ % 1.62/1.78 f3(true__, v_NA, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)) -> true__ % 1.62/1.78 f4(c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oparts(V_H), tc_Message_Omsg), V_X, V_H) -> true__ % 1.62/1.78 f4(f3(true__, c_Message_Omsg_OCrypt(Y0, Y1), Y2), Y1, Y2) -> true__ % 1.62/1.78 f4(true__, V_X, V_H) -> c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg) % 1.62/1.78 false__ -> true__ % 1.62/1.78 with the LPO induced by % 1.62/1.78 f4 > c_in > f3 > f2 > tc_Message_Omsg > c_Message_Oagent_OSpy > c_Event_Oknows > c_Message_Oparts > v_B > c_Message_Omsg_OAgent > c_Message_Omsg_ONonce > v_NA > v_NB > c_Message_Omsg_OMPair > v_A > c_Public_OshrK > c_Message_Omsg_OCrypt > v_evs2 > c_Event_Oused > f1 > false__ > true__ % 1.62/1.78 % 1.62/1.78 % SZS output end Proof % 1.62/1.78 %------------------------------------------------------------------------------