%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV258-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n010.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 20:42:25 EDT 2022 % Result : Unsatisfiable 4.26s 4.32s % Output : Proof 4.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV258-2 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n010.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 14 17:21:24 EDT 2022 % 0.12/0.33 % CPUTime : % 4.26/4.32 % SZS status Unsatisfiable % 4.26/4.32 % SZS output start Proof % 4.26/4.32 The input problem is unsatisfiable because % 4.26/4.32 % 4.26/4.32 [1] the following set of Horn clauses is unsatisfiable: % 4.26/4.32 % 4.26/4.32 c_in(v_X, c_Message_Oparts(v_H), tc_Message_Omsg) % 4.26/4.32 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(v_H), tc_set(tc_Message_Omsg)) ==> \bottom % 4.26/4.32 c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) ==> c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 4.26/4.32 c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) ==> c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 4.26/4.32 c_in(V_x, V_B, T_a) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) % 4.26/4.32 c_lessequals(V_A, V_A, tc_set(T_a)) % 4.26/4.32 % 4.26/4.32 This holds because % 4.26/4.32 % 4.26/4.32 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.26/4.32 % 4.26/4.32 E: % 4.26/4.32 c_in(v_X, c_Message_Oparts(v_H), tc_Message_Omsg) = true__ % 4.26/4.32 c_lessequals(V_A, V_A, tc_set(T_a)) = true__ % 4.26/4.32 f1(c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(v_H), tc_set(tc_Message_Omsg))) = true__ % 4.26/4.32 f1(true__) = false__ % 4.26/4.32 f2(c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)), V_G, V_H) = true__ % 4.26/4.32 f2(true__, V_G, V_H) = c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 4.26/4.32 f3(c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)), V_G, V_H) = true__ % 4.26/4.32 f3(true__, V_G, V_H) = c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 4.26/4.32 f4(true__, V_x, V_A, T_a, V_B) = c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) % 4.26/4.32 f5(c_lessequals(V_A, V_B, tc_set(T_a)), V_x, V_B, T_a, V_A) = true__ % 4.26/4.32 f5(true__, V_x, V_B, T_a, V_A) = f4(c_in(V_x, V_B, T_a), V_x, V_A, T_a, V_B) % 4.26/4.32 G: % 4.26/4.32 true__ = false__ % 4.26/4.32 % 4.26/4.32 This holds because % 4.26/4.32 % 4.26/4.32 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.26/4.32 % 4.26/4.32 % 4.26/4.32 c_in(v_X, c_Message_Oparts(v_H), tc_Message_Omsg) -> true__ % 4.26/4.32 c_lessequals(V_A, V_A, tc_set(T_a)) -> true__ % 4.26/4.32 c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) -> f2(true__, V_G, V_H) % 4.26/4.32 f1(f2(true__, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), v_H)) -> true__ % 4.26/4.32 f1(true__) -> false__ % 4.26/4.32 f2(f2(true__, c_Message_Oparts(Y0), Y1), Y0, Y1) -> true__ % 4.26/4.32 f2(true__, Y0, c_Message_Oparts(Y0)) -> true__ % 4.26/4.32 f2(true__, Y0, c_Message_Oparts(c_Message_Oparts(Y0))) -> true__ % 4.26/4.32 f2(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0)))) -> true__ % 4.26/4.32 f2(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0))))) -> true__ % 4.26/4.32 f2(true__, Y1, Y1) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(Y1), Y1) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(Y1)), Y1) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1))), Y1) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1)))), Y1) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1))))), Y1) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1)))))), Y1) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1))))))), Y1) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_insert(v_X, c_Message_Oparts(v_H), tc_Message_Omsg)))), v_H) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(c_insert(v_X, c_Message_Oparts(v_H), tc_Message_Omsg))), v_H) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg))), v_H) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_insert(v_X, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(v_H))), tc_Message_Omsg)), v_H) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_insert(v_X, c_Message_Oparts(c_Message_Oparts(v_H)), tc_Message_Omsg)), v_H) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_insert(v_X, c_Message_Oparts(v_H), tc_Message_Omsg)), v_H) -> true__ % 4.26/4.32 f2(true__, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), v_H) -> true__ % 4.26/4.32 f2(true__, c_insert(v_X, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(v_H))), tc_Message_Omsg), v_H) -> true__ % 4.26/4.32 f2(true__, c_insert(v_X, c_Message_Oparts(c_Message_Oparts(v_H)), tc_Message_Omsg), v_H) -> true__ % 4.26/4.32 f2(true__, c_insert(v_X, c_Message_Oparts(v_H), tc_Message_Omsg), v_H) -> true__ % 4.26/4.32 f2(true__, c_insert(v_X, v_H, tc_Message_Omsg), v_H) -> true__ % 4.26/4.32 f3(f2(true__, Y0, Y1), Y0, Y1) -> true__ % 4.26/4.32 f3(true__, V_G, V_H) -> f2(true__, c_Message_Oparts(V_G), V_H) % 4.26/4.32 f4(c_in(Y2, c_Message_Oparts(Y1), tc_Message_Omsg), Y2, Y1, tc_Message_Omsg, c_Message_Oparts(Y1)) -> true__ % 4.26/4.32 f4(c_in(Y2, c_Message_Oparts(Y1), tc_Message_Omsg), Y2, c_Message_Oparts(c_Message_Oparts(Y1)), tc_Message_Omsg, c_Message_Oparts(Y1)) -> true__ % 4.26/4.32 f4(c_in(Y2, c_Message_Oparts(Y1), tc_Message_Omsg), Y2, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1))), tc_Message_Omsg, c_Message_Oparts(Y1)) -> true__ % 4.26/4.32 f4(c_in(Y2, c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg), Y2, Y0, tc_Message_Omsg, c_Message_Oparts(c_Message_Oparts(Y0))) -> true__ % 4.26/4.32 f4(c_in(Y2, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0))), tc_Message_Omsg), Y2, Y0, tc_Message_Omsg, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0)))) -> true__ % 4.26/4.32 f4(c_in(Y2, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0)))), tc_Message_Omsg), Y2, Y0, tc_Message_Omsg, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0))))) -> true__ % 4.26/4.32 f4(c_in(Y2, c_Message_Oparts(v_H), tc_Message_Omsg), Y2, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(v_H)) -> true__ % 4.26/4.32 f4(c_in(Y3, Y1, Y2), Y3, Y1, Y2, Y1) -> true__ % 4.26/4.32 f4(true__, V_x, V_A, T_a, V_B) -> c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) % 4.26/4.32 f5(c_lessequals(V_A, V_B, tc_set(T_a)), V_x, V_B, T_a, V_A) -> true__ % 4.26/4.32 f5(f2(true__, Y0, X1), Y3, c_Message_Oparts(X1), tc_Message_Omsg, Y0) -> true__ % 4.26/4.32 f5(true__, V_x, V_B, T_a, V_A) -> f4(c_in(V_x, V_B, T_a), V_x, V_A, T_a, V_B) % 4.26/4.32 false__ -> true__ % 4.26/4.32 with the LPO induced by % 4.26/4.32 f3 > f5 > c_in > f4 > c_lessequals > f2 > c_insert > tc_Message_Omsg > tc_set > v_H > c_Message_Oparts > v_X > f1 > false__ > true__ % 4.26/4.32 % 4.26/4.32 % SZS output end Proof % 4.26/4.32 %------------------------------------------------------------------------------