%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV331-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 20:43:14 EDT 2022 % Result : Unsatisfiable 1.45s 1.61s % Output : Proof 1.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.14 % Problem : SWV331-2 : TPTP v8.1.0. Released v3.2.0. % 0.05/0.15 % Command : moca.sh %s % 0.14/0.36 % Computer : n025.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Wed Jun 15 15:03:10 EDT 2022 % 0.14/0.36 % CPUTime : % 1.45/1.61 % SZS status Unsatisfiable % 1.45/1.61 % SZS output start Proof % 1.45/1.61 The input problem is unsatisfiable because % 1.45/1.61 % 1.45/1.61 [1] the following set of Horn clauses is unsatisfiable: % 1.45/1.61 % 1.45/1.61 c_in(v_evs3, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) % 1.45/1.61 c_in(c_Message_Omsg_OKey(v_K), c_Event_Oused(v_evs3), tc_Message_Omsg) ==> \bottom % 1.45/1.61 c_in(v_K, c_Message_OsymKeys, tc_nat) % 1.45/1.61 c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg) % 1.45/1.61 c_in(V_K, c_Message_OsymKeys, tc_nat) & c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) ==> c_in(V_K, c_Message_OkeysFor(V_H), tc_nat) % 1.45/1.61 c_in(V_K, c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs))), tc_nat) & c_in(V_K, c_Message_OsymKeys, tc_nat) & c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) ==> c_in(c_Message_Omsg_OKey(V_K), c_Event_Oused(V_evs), tc_Message_Omsg) % 1.45/1.61 % 1.45/1.61 This holds because % 1.45/1.61 % 1.45/1.61 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.45/1.61 % 1.45/1.61 E: % 1.45/1.61 c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg) = true__ % 1.45/1.61 c_in(v_K, c_Message_OsymKeys, tc_nat) = true__ % 1.45/1.61 c_in(v_evs3, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) = true__ % 1.45/1.61 f1(c_in(c_Message_Omsg_OKey(v_K), c_Event_Oused(v_evs3), tc_Message_Omsg)) = true__ % 1.45/1.61 f1(true__) = false__ % 1.45/1.61 f2(true__, V_K, V_H) = c_in(V_K, c_Message_OkeysFor(V_H), tc_nat) % 1.45/1.61 f3(c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg), V_K, V_H) = true__ % 1.45/1.61 f3(true__, V_K, V_H) = f2(c_in(V_K, c_Message_OsymKeys, tc_nat), V_K, V_H) % 1.45/1.61 f4(true__, V_K, V_evs) = c_in(c_Message_Omsg_OKey(V_K), c_Event_Oused(V_evs), tc_Message_Omsg) % 1.45/1.61 f5(true__, V_K, V_evs) = f4(c_in(V_K, c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs))), tc_nat), V_K, V_evs) % 1.45/1.61 f6(c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)), V_K, V_evs) = true__ % 1.45/1.61 f6(true__, V_K, V_evs) = f5(c_in(V_K, c_Message_OsymKeys, tc_nat), V_K, V_evs) % 1.45/1.61 G: % 1.45/1.61 true__ = false__ % 1.45/1.61 % 1.45/1.61 This holds because % 1.45/1.61 % 1.45/1.61 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.45/1.61 % 1.45/1.61 % 1.45/1.61 c_in(V_K, c_Message_OkeysFor(V_H), tc_nat) -> f2(true__, V_K, V_H) % 1.45/1.61 c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg) -> true__ % 1.45/1.61 c_in(c_Message_Omsg_OKey(V_K), c_Event_Oused(V_evs), tc_Message_Omsg) -> f4(true__, V_K, V_evs) % 1.45/1.61 c_in(v_K, c_Message_OsymKeys, tc_nat) -> true__ % 1.45/1.61 c_in(v_evs3, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) -> true__ % 1.45/1.61 f1(c_in(c_Message_Omsg_OKey(v_K), c_Event_Oused(v_evs3), tc_Message_Omsg)) -> true__ % 1.45/1.61 f1(f4(true__, v_K, v_evs3)) -> true__ % 1.45/1.61 f1(true__) -> false__ % 1.45/1.61 f2(c_in(V_K, c_Message_OsymKeys, tc_nat), V_K, V_H) -> f3(true__, V_K, V_H) % 1.45/1.61 f2(true__, v_K, Y1) -> f3(true__, v_K, Y1) % 1.45/1.61 f3(c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg), V_K, V_H) -> true__ % 1.45/1.61 f3(true__, v_K, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))) -> true__ % 1.45/1.61 f4(true__, v_K, v_evs3) -> true__ % 1.45/1.61 f5(c_in(V_K, c_Message_OsymKeys, tc_nat), V_K, V_evs) -> f6(true__, V_K, V_evs) % 1.45/1.61 f5(true__, V_K, V_evs) -> f4(c_in(V_K, c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs))), tc_nat), V_K, V_evs) % 1.45/1.61 f6(c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)), V_K, V_evs) -> true__ % 1.45/1.61 f6(true__, Y1, v_evs3) -> true__ % 1.45/1.61 f6(true__, v_K, Y1) -> f4(f2(true__, v_K, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, Y1))), v_K, Y1) % 1.45/1.61 false__ -> true__ % 1.45/1.61 with the LPO induced by % 1.45/1.61 f5 > f6 > c_in > f2 > c_Message_OkeysFor > f3 > c_Message_OsymKeys > tc_nat > c_Message_Oagent_OSpy > f4 > tc_Message_Omsg > c_Event_Oknows > c_Message_Oparts > v_NB > c_Message_Omsg_ONonce > c_Message_Omsg_OCrypt > c_Event_Oused > v_K > c_Message_Omsg_OKey > f1 > tc_Event_Oevent > tc_List_Olist > c_Yahalom_Oyahalom > v_evs3 > false__ > true__ % 1.45/1.61 % 1.45/1.61 % SZS output end Proof % 1.45/1.61 %------------------------------------------------------------------------------