%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV277-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n023.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 20:42:38 EDT 2022 % Result : Unsatisfiable 0.58s 0.73s % Output : Proof 0.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.06 % Problem : SWV277-2 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.07 % Command : moca.sh %s % 0.06/0.25 % Computer : n023.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 600 % 0.06/0.25 % DateTime : Tue Jun 14 23:59:05 EDT 2022 % 0.06/0.25 % CPUTime : % 0.58/0.73 % SZS status Unsatisfiable % 0.58/0.73 % SZS output start Proof % 0.58/0.73 The input problem is unsatisfiable because % 0.58/0.73 % 0.58/0.73 [1] the following set of Horn clauses is unsatisfiable: % 0.58/0.73 % 0.58/0.73 c_lessequals(c_Message_Oanalz(V_H), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 0.58/0.73 c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)) ==> c_lessequals(c_Message_OkeysFor(V_G), c_Message_OkeysFor(V_H), tc_set(tc_nat)) % 0.58/0.73 c_in(V_c, V_A, T_a) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> c_in(V_c, V_B, T_a) % 0.58/0.73 c_in(v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat) ==> \bottom % 0.58/0.73 c_in(v_K, c_Message_OkeysFor(c_Message_Oanalz(v_H)), tc_nat) % 0.58/0.73 % 0.58/0.73 This holds because % 0.58/0.73 % 0.58/0.73 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.58/0.73 % 0.58/0.73 E: % 0.58/0.73 c_in(v_K, c_Message_OkeysFor(c_Message_Oanalz(v_H)), tc_nat) = true__ % 0.58/0.73 c_lessequals(c_Message_Oanalz(V_H), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) = true__ % 0.58/0.73 f1(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) = true__ % 0.58/0.73 f1(true__, V_G, V_H) = c_lessequals(c_Message_OkeysFor(V_G), c_Message_OkeysFor(V_H), tc_set(tc_nat)) % 0.58/0.73 f2(true__, V_c, V_B, T_a) = c_in(V_c, V_B, T_a) % 0.58/0.73 f3(c_lessequals(V_A, V_B, tc_set(T_a)), V_c, V_A, T_a, V_B) = true__ % 0.58/0.73 f3(true__, V_c, V_A, T_a, V_B) = f2(c_in(V_c, V_A, T_a), V_c, V_B, T_a) % 0.58/0.73 f4(c_in(v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat)) = true__ % 0.58/0.73 f4(true__) = false__ % 0.58/0.73 G: % 0.58/0.73 true__ = false__ % 0.58/0.73 % 0.58/0.73 This holds because % 0.58/0.73 % 0.58/0.73 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.58/0.73 % 0.58/0.73 % 0.58/0.73 c_in(V_c, V_B, T_a) -> f2(true__, V_c, V_B, T_a) % 0.58/0.73 c_in(v_K, c_Message_OkeysFor(c_Message_Oanalz(v_H)), tc_nat) -> true__ % 0.58/0.73 c_lessequals(c_Message_Oanalz(V_H), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) -> true__ % 0.58/0.73 c_lessequals(c_Message_OkeysFor(V_G), c_Message_OkeysFor(V_H), tc_set(tc_nat)) -> f1(true__, V_G, V_H) % 0.58/0.73 f1(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) -> true__ % 0.58/0.73 f1(true__, c_Message_Oanalz(X0), c_Message_Oparts(X0)) -> true__ % 0.58/0.73 f2(f2(true__, Y2, c_Message_OkeysFor(c_Message_Oanalz(X0)), tc_nat), Y2, c_Message_OkeysFor(c_Message_Oparts(X0)), tc_nat) -> true__ % 0.58/0.73 f2(f2(true__, Y3, c_Message_Oanalz(X0), tc_Message_Omsg), Y3, c_Message_Oparts(X0), tc_Message_Omsg) -> true__ % 0.58/0.73 f2(true__, v_K, c_Message_OkeysFor(c_Message_Oanalz(v_H)), tc_nat) -> true__ % 0.58/0.73 f2(true__, v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat) -> true__ % 0.58/0.73 f3(c_lessequals(V_A, V_B, tc_set(T_a)), V_c, V_A, T_a, V_B) -> true__ % 0.58/0.73 f3(f1(true__, X0, X1), Y3, c_Message_OkeysFor(X0), tc_nat, c_Message_OkeysFor(X1)) -> true__ % 0.58/0.73 f3(true__, V_c, V_A, T_a, V_B) -> f2(c_in(V_c, V_A, T_a), V_c, V_B, T_a) % 0.58/0.73 f4(c_in(v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat)) -> true__ % 0.58/0.73 f4(f2(true__, v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat)) -> true__ % 0.58/0.73 f4(true__) -> false__ % 0.58/0.73 false__ -> true__ % 0.58/0.73 with the LPO induced by % 0.58/0.73 v_H > v_K > f4 > f3 > c_in > f2 > c_Message_Oanalz > c_lessequals > f1 > tc_nat > c_Message_OkeysFor > tc_Message_Omsg > tc_set > c_Message_Oparts > false__ > true__ % 0.58/0.73 % 0.58/0.73 % SZS output end Proof % 0.58/0.73 %------------------------------------------------------------------------------