%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV273-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n005.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 20:42:35 EDT 2022 % Result : Unsatisfiable 9.94s 9.81s % Output : Proof 9.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV273-2 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n005.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 : Thu Jun 16 06:30:08 EDT 2022 % 0.12/0.33 % CPUTime : % 9.94/9.81 % SZS status Unsatisfiable % 9.94/9.81 % SZS output start Proof % 9.94/9.81 The input problem is unsatisfiable because % 9.94/9.81 % 9.94/9.81 [1] the following set of Horn clauses is unsatisfiable: % 9.94/9.81 % 9.94/9.81 c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)) ==> \bottom % 9.94/9.81 c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)) ==> c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 9.94/9.81 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)) % 9.94/9.81 c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)) % 9.94/9.81 c_lessequals(V_B, V_C, tc_set(T_a)) & c_lessequals(V_A, V_C, tc_set(T_a)) ==> c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) % 9.94/9.81 c_lessequals(V_A, V_A, tc_set(T_a)) % 9.94/9.81 % 9.94/9.81 This holds because % 9.94/9.81 % 9.94/9.81 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 9.94/9.81 % 9.94/9.81 E: % 9.94/9.81 c_lessequals(V_A, V_A, tc_set(T_a)) = true__ % 9.94/9.81 c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)) = true__ % 9.94/9.81 f1(c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) = true__ % 9.94/9.81 f1(true__) = false__ % 9.94/9.81 f2(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) = true__ % 9.94/9.81 f2(true__, V_G, V_H) = c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 9.94/9.81 f3(c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)), V_G, V_H) = true__ % 9.94/9.81 f3(true__, V_G, V_H) = c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 9.94/9.81 f4(true__, V_A, V_B, T_a, V_C) = c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) % 9.94/9.81 f5(c_lessequals(V_A, V_C, tc_set(T_a)), V_B, V_C, T_a, V_A) = true__ % 9.94/9.81 f5(true__, V_B, V_C, T_a, V_A) = f4(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_B, T_a, V_C) % 9.94/9.81 G: % 9.94/9.81 true__ = false__ % 9.94/9.81 % 9.94/9.81 This holds because % 9.94/9.81 % 9.94/9.81 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 9.94/9.81 % 9.94/9.81 % 9.94/9.81 c_lessequals(V_A, V_A, tc_set(T_a)) -> true__ % 9.94/9.81 c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) -> f3(true__, V_G, V_H) % 9.94/9.81 c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(Y1, Y1, tc_Message_Omsg), c_Message_Osynth(Y1), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(Y1, c_union(Y1, Y1, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y1), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(Y1, c_union(Y1, c_Message_Osynth(Y1), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y1), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(Y1, c_union(c_Message_Osynth(Y1), Y1, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y1), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(Y2, Y2, Y1), Y2, tc_set(Y1)) -> true__ % 9.94/9.81 c_lessequals(c_union(Y2, c_Message_Osynth(Y2), tc_Message_Omsg), c_Message_Osynth(Y2), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(Y2, c_union(Y2, Y2, Y1), Y1), Y2, tc_set(Y1)) -> true__ % 9.94/9.81 c_lessequals(c_union(Y2, c_union(c_Message_Osynth(Y2), c_Message_Osynth(Y2), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y2), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_Message_Osynth(Y0), Y0, tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_Message_Osynth(Y0), c_union(Y0, Y0, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_Message_Osynth(Y0), c_union(Y0, c_Message_Osynth(Y0), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_Message_Osynth(Y0), c_union(c_Message_Osynth(Y0), Y0, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(X1, X1, tc_Message_Omsg), c_Message_Osynth(X1), tc_Message_Omsg), c_Message_Osynth(X1), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(X1, X1, tc_Message_Omsg), c_union(c_Message_Osynth(X1), c_Message_Osynth(X1), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X1), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(X1, c_Message_Osynth(X1), tc_Message_Omsg), c_Message_Osynth(X1), tc_Message_Omsg), c_Message_Osynth(X1), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(Y0, Y0, Y1), Y0, Y1), Y0, tc_set(Y1)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(Y0, Y0, Y1), c_union(Y0, Y0, Y1), Y1), Y0, tc_set(Y1)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(Y0, Y0, tc_Message_Omsg), Y0, tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(Y0, Y0, tc_Message_Omsg), c_union(Y0, Y0, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(Y0, Y0, tc_Message_Omsg), c_union(Y0, c_Message_Osynth(Y0), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(Y0, Y0, tc_Message_Omsg), c_union(c_Message_Osynth(Y0), Y0, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(Y0, c_Message_Osynth(Y0), tc_Message_Omsg), Y0, tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(c_Message_Osynth(X1), X1, tc_Message_Omsg), c_Message_Osynth(X1), tc_Message_Omsg), c_Message_Osynth(X1), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(c_Message_Osynth(Y0), c_Message_Osynth(Y0), tc_Message_Omsg), Y0, tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(c_Message_Osynth(Y0), c_Message_Osynth(Y0), tc_Message_Omsg), c_union(Y0, Y0, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(c_Message_Osynth(Y0), c_Message_Osynth(Y0), tc_Message_Omsg), c_union(Y0, c_Message_Osynth(Y0), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 c_lessequals(c_union(c_union(c_Message_Osynth(Y0), c_Message_Osynth(Y0), tc_Message_Omsg), c_union(c_Message_Osynth(Y0), Y0, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) -> true__ % 9.94/9.81 f1(c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) -> true__ % 9.94/9.81 f1(f3(true__, c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(v_H))) -> true__ % 9.94/9.81 f1(true__) -> false__ % 9.94/9.81 f2(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) -> true__ % 9.94/9.81 f2(f3(true__, Y0, X1), Y0, c_Message_Oparts(X1)) -> true__ % 9.94/9.81 f2(true__, V_G, V_H) -> c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 9.94/9.81 f3(c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)), V_G, V_H) -> true__ % 9.94/9.81 f3(f3(true__, c_Message_Oparts(Y0), Y1), Y0, Y1) -> true__ % 9.94/9.81 f3(true__, Y0, c_Message_Oparts(Y0)) -> true__ % 9.94/9.81 f3(true__, Y0, c_Message_Oparts(c_Message_Oparts(Y0))) -> true__ % 9.94/9.81 f3(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0)))) -> true__ % 9.94/9.81 f3(true__, Y0, c_Message_Oparts(c_Message_Osynth(Y0))) -> true__ % 9.94/9.81 f3(true__, Y0, c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f3(true__, Y0, c_Message_Osynth(c_Message_Oparts(Y0))) -> true__ % 9.94/9.81 f3(true__, Y0, c_Message_Osynth(c_Message_Oparts(c_Message_Oparts(Y0)))) -> true__ % 9.94/9.81 f3(true__, Y1, Y1) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(Y0), c_Message_Oparts(c_Message_Osynth(Y0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(Y0), c_Message_Oparts(c_Message_Osynth(c_Message_Oparts(Y0)))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(Y0), c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(Y1), Y1) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_Message_Oparts(X0)), c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0)))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_Message_Oparts(X0)), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(X0))), c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0)))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(X0)))), c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0))))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_Message_Oparts(c_union(X0, X0, tc_Message_Omsg))), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_Message_Oparts(c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg))), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_Message_Oparts(c_union(Y1, Y1, tc_Message_Omsg))), c_Message_Oparts(Y1)) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_Message_Oparts(c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg))), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(X0, X0, tc_Message_Omsg)), c_Message_Osynth(X0)) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg)), c_Message_Osynth(X0)) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(Y1, Y1, tc_Message_Omsg)), Y1) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(Y1, Y1, tc_Message_Omsg)), c_Message_Oparts(Y1)) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(Y1, c_Message_Oparts(Y1), tc_Message_Omsg)), c_Message_Oparts(Y1)) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(c_Message_Oparts(X0), c_Message_Oparts(X0), tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(c_Message_Oparts(X0), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(c_Message_Oparts(X0), c_Message_Osynth(X0), tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(c_Message_Oparts(Y1), Y1, tc_Message_Omsg)), c_Message_Oparts(Y1)) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(c_Message_Oparts(c_Message_Osynth(X0)), c_Message_Oparts(X0), tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg)), c_Message_Osynth(X0)) -> true__ % 9.94/9.81 f3(true__, c_Message_Oparts(c_union(c_Message_Osynth(X0), c_Message_Oparts(X0), tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(X0))) -> true__ % 9.94/9.81 f3(true__, c_union(X0, X0, tc_Message_Omsg), c_Message_Osynth(X0)) -> true__ % 9.94/9.81 f3(true__, c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg), c_Message_Osynth(X0)) -> true__ % 9.94/9.81 f3(true__, c_union(Y1, Y1, tc_Message_Omsg), Y1) -> true__ % 9.94/9.81 f3(true__, c_union(Y1, Y1, tc_Message_Omsg), c_Message_Oparts(Y1)) -> true__ % 9.94/9.81 f3(true__, c_union(Y1, c_Message_Oparts(Y1), tc_Message_Omsg), c_Message_Oparts(Y1)) -> true__ % 9.94/9.81 f3(true__, c_union(Y1, c_Message_Oparts(Y1), tc_Message_Omsg), c_Message_Osynth(Y1)) -> true__ % 9.94/9.81 f3(true__, c_union(Y2, c_Message_Oparts(Y2), tc_Message_Omsg), Y2) -> true__ % 9.94/9.81 f3(true__, c_union(Y2, c_Message_Oparts(c_Message_Oparts(Y2)), tc_Message_Omsg), c_Message_Oparts(Y2)) -> true__ % 9.94/9.81 f3(true__, c_union(Y2, c_Message_Oparts(c_Message_Osynth(Y2)), tc_Message_Omsg), c_Message_Osynth(Y2)) -> true__ % 9.94/9.81 f3(true__, c_union(Y2, c_union(c_Message_Oparts(Y2), c_Message_Oparts(Y2), tc_Message_Omsg), tc_Message_Omsg), Y2) -> true__ % 9.94/9.81 f3(true__, c_union(Y2, c_union(c_Message_Oparts(c_Message_Oparts(Y2)), c_Message_Oparts(c_Message_Oparts(Y2)), tc_Message_Omsg), tc_Message_Omsg), c_Message_Oparts(Y2)) -> true__ % 9.94/9.81 f3(true__, c_union(Y2, c_union(c_Message_Oparts(c_Message_Osynth(Y2)), c_Message_Oparts(c_Message_Osynth(Y2)), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(Y2)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(X1), c_Message_Oparts(c_Message_Osynth(X1)), tc_Message_Omsg), c_Message_Osynth(X1)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(X1), c_Message_Osynth(X1), tc_Message_Omsg), c_Message_Osynth(X1)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(X1), c_union(c_Message_Oparts(c_Message_Osynth(X1)), c_Message_Oparts(c_Message_Osynth(X1)), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X1)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(Y0), Y0, tc_Message_Omsg), Y0) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(Y0), Y0, tc_Message_Omsg), c_Message_Oparts(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(Y0), Y0, tc_Message_Omsg), c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(Y0), c_Message_Oparts(Y0), tc_Message_Omsg), c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(Y1), c_Message_Oparts(Y1), tc_Message_Omsg), Y1) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(c_Message_Oparts(X1)), c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X1))), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X1))) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(c_Message_Oparts(X1)), c_Message_Oparts(c_Message_Osynth(X1)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X1))) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(c_Message_Oparts(X1)), c_Message_Osynth(X1), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X1))) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(c_Message_Oparts(Y0)), Y0, tc_Message_Omsg), c_Message_Oparts(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(Y0))), c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(Y0))) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(c_Message_Osynth(Y0)), Y0, tc_Message_Omsg), c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(c_Message_Osynth(Y0)), c_Message_Oparts(Y0), tc_Message_Omsg), c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Oparts(c_Message_Osynth(Y0)), c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(Y0))) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg), c_Message_Osynth(X0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Osynth(Y0), c_Message_Oparts(Y0), tc_Message_Omsg), c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_Message_Osynth(Y0), c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(Y0))) -> true__ % 9.94/9.81 f3(true__, c_union(c_union(c_Message_Oparts(Y0), c_Message_Oparts(Y0), tc_Message_Omsg), Y0, tc_Message_Omsg), Y0) -> true__ % 9.94/9.81 f3(true__, c_union(c_union(c_Message_Oparts(c_Message_Oparts(Y0)), c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg), Y0, tc_Message_Omsg), c_Message_Oparts(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_union(c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(Y0))), c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(Y0))), tc_Message_Omsg), c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(Y0))) -> true__ % 9.94/9.81 f3(true__, c_union(c_union(c_Message_Oparts(c_Message_Osynth(Y0)), c_Message_Oparts(c_Message_Osynth(Y0)), tc_Message_Omsg), Y0, tc_Message_Omsg), c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f3(true__, c_union(c_union(c_Message_Oparts(c_Message_Osynth(Y0)), c_Message_Oparts(c_Message_Osynth(Y0)), tc_Message_Omsg), c_Message_Oparts(Y0), tc_Message_Omsg), c_Message_Osynth(Y0)) -> true__ % 9.94/9.81 f4(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_B, T_a, V_C) -> f5(true__, V_B, V_C, T_a, V_A) % 9.94/9.81 f4(f3(true__, Y0, X1), Y3, Y0, tc_Message_Omsg, c_Message_Oparts(X1)) -> f5(true__, Y0, c_Message_Oparts(X1), tc_Message_Omsg, Y3) % 9.94/9.81 f4(true__, V_A, V_B, T_a, V_C) -> c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) % 9.94/9.81 f5(c_lessequals(V_A, V_C, tc_set(T_a)), V_B, V_C, T_a, V_A) -> true__ % 9.94/9.81 f5(f3(true__, Y0, X1), Y3, c_Message_Oparts(X1), tc_Message_Omsg, Y0) -> true__ % 9.94/9.81 f5(true__, Y0, c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, Y0, tc_Message_Omsg), c_Message_Oparts(Y0)) % 9.94/9.81 f5(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0))), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, Y0, tc_Message_Omsg), c_Message_Oparts(c_Message_Oparts(Y0))) % 9.94/9.81 f5(true__, Y0, c_Message_Oparts(c_Message_Osynth(Y0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, Y0, tc_Message_Omsg), c_Message_Osynth(Y0)) % 9.94/9.81 f5(true__, Y0, c_Message_Oparts(c_Message_Osynth(c_Message_Oparts(Y0))), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, Y0, tc_Message_Omsg), c_Message_Osynth(c_Message_Oparts(Y0))) % 9.94/9.81 f5(true__, Y0, c_Message_Osynth(Y0), tc_Message_Omsg, Y3) -> c_lessequals(c_union(Y3, Y0, tc_Message_Omsg), c_Message_Osynth(Y0), tc_set(tc_Message_Omsg)) % 9.94/9.81 f5(true__, Y1, Y1, Y2, Y3) -> c_lessequals(c_union(Y3, Y1, Y2), Y1, tc_set(Y2)) % 9.94/9.81 f5(true__, Y1, c_Message_Oparts(Y1), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, Y1, tc_Message_Omsg), Y1) % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(Y1), tc_Message_Omsg, Y1) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(Y1), tc_Message_Omsg, c_Message_Oparts(c_union(Y1, Y1, tc_Message_Omsg))) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(Y1), tc_Message_Omsg, c_union(Y1, Y1, tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(Y1), tc_Message_Omsg, c_union(Y1, c_Message_Oparts(Y1), tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(Y1), tc_Message_Omsg, c_union(c_Message_Oparts(Y1), Y1, tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg, Y0) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0))), tc_Message_Omsg, Y0) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0)))), tc_Message_Omsg, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(X0)))) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0))), tc_Message_Omsg, c_Message_Oparts(X0)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0))), tc_Message_Omsg, c_Message_Oparts(c_Message_Oparts(X0))) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_Message_Oparts(X0)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_Message_Oparts(c_union(X0, X0, tc_Message_Omsg))) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_Message_Oparts(c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg))) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_Message_Oparts(c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg))) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_union(c_Message_Oparts(X0), c_Message_Oparts(X0), tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_union(c_Message_Oparts(X0), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_union(c_Message_Oparts(X0), c_Message_Osynth(X0), tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_union(c_Message_Oparts(c_Message_Osynth(X0)), c_Message_Oparts(X0), tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, c_union(c_Message_Osynth(X0), c_Message_Oparts(X0), tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(Y0)), tc_Message_Omsg, Y0) -> true__ % 9.94/9.81 f5(true__, Y2, c_Message_Oparts(c_Message_Osynth(c_Message_Oparts(Y0))), tc_Message_Omsg, Y0) -> true__ % 9.94/9.81 f5(true__, Y3, Y1, Y2, Y1) -> true__ % 9.94/9.81 f5(true__, Y3, Y1, Y2, c_union(Y1, Y1, Y2)) -> true__ % 9.94/9.81 f5(true__, Y3, c_Message_Osynth(X0), tc_Message_Omsg, c_union(X0, X0, tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y3, c_Message_Osynth(X0), tc_Message_Omsg, c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y3, c_Message_Osynth(X0), tc_Message_Omsg, c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg)) -> true__ % 9.94/9.81 f5(true__, Y3, c_Message_Osynth(Y0), tc_Message_Omsg, Y0) -> true__ % 9.94/9.81 f5(true__, c_Message_Oparts(X0), c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0))), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_Message_Oparts(X0), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X0))) % 9.94/9.81 f5(true__, c_Message_Oparts(X0), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_Message_Oparts(X0), tc_Message_Omsg), c_Message_Osynth(X0)) % 9.94/9.81 f5(true__, c_Message_Oparts(c_Message_Oparts(X0)), c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0))), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_Message_Oparts(c_Message_Oparts(X0)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X0))) % 9.94/9.81 f5(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(X0))), c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0)))), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(X0))), tc_Message_Omsg), c_Message_Oparts(c_Message_Oparts(c_Message_Osynth(X0)))) % 9.94/9.81 f5(true__, c_Message_Oparts(c_union(X0, X0, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_Message_Oparts(c_union(X0, X0, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(X0)) % 9.94/9.81 f5(true__, c_Message_Oparts(c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_Message_Oparts(c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(X0)) % 9.94/9.81 f5(true__, c_Message_Oparts(c_union(Y1, Y1, tc_Message_Omsg)), c_Message_Oparts(Y1), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_Message_Oparts(c_union(Y1, Y1, tc_Message_Omsg)), tc_Message_Omsg), Y1) % 9.94/9.81 f5(true__, c_Message_Oparts(c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_Message_Oparts(c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(X0)) % 9.94/9.81 f5(true__, c_union(X0, X0, tc_Message_Omsg), c_Message_Osynth(X0), tc_Message_Omsg, Y3) -> c_lessequals(c_union(Y3, c_union(X0, X0, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X0), tc_set(tc_Message_Omsg)) % 9.94/9.81 f5(true__, c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg), c_Message_Osynth(X0), tc_Message_Omsg, Y3) -> c_lessequals(c_union(Y3, c_union(X0, c_Message_Osynth(X0), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X0), tc_set(tc_Message_Omsg)) % 9.94/9.81 f5(true__, c_union(Y1, Y1, Y2), Y1, Y2, Y3) -> c_lessequals(c_union(Y3, c_union(Y1, Y1, Y2), Y2), Y1, tc_set(Y2)) % 9.94/9.81 f5(true__, c_union(Y1, Y1, tc_Message_Omsg), c_Message_Oparts(Y1), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_union(Y1, Y1, tc_Message_Omsg), tc_Message_Omsg), Y1) % 9.94/9.81 f5(true__, c_union(Y1, c_Message_Oparts(Y1), tc_Message_Omsg), c_Message_Oparts(Y1), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_union(Y1, c_Message_Oparts(Y1), tc_Message_Omsg), tc_Message_Omsg), Y1) % 9.94/9.81 f5(true__, c_union(c_Message_Oparts(X0), c_Message_Oparts(X0), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_union(c_Message_Oparts(X0), c_Message_Oparts(X0), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X0)) % 9.94/9.81 f5(true__, c_union(c_Message_Oparts(X0), c_Message_Osynth(X0), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_union(c_Message_Oparts(X0), c_Message_Osynth(X0), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X0)) % 9.94/9.81 f5(true__, c_union(c_Message_Oparts(Y1), Y1, tc_Message_Omsg), c_Message_Oparts(Y1), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_union(c_Message_Oparts(Y1), Y1, tc_Message_Omsg), tc_Message_Omsg), Y1) % 9.94/9.81 f5(true__, c_union(c_Message_Oparts(c_Message_Osynth(X0)), c_Message_Oparts(X0), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_union(c_Message_Oparts(c_Message_Osynth(X0)), c_Message_Oparts(X0), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X0)) % 9.94/9.81 f5(true__, c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg), c_Message_Osynth(X0), tc_Message_Omsg, Y3) -> c_lessequals(c_union(Y3, c_union(c_Message_Osynth(X0), X0, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X0), tc_set(tc_Message_Omsg)) % 9.94/9.81 f5(true__, c_union(c_Message_Osynth(X0), c_Message_Oparts(X0), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(X0)), tc_Message_Omsg, Y2) -> f3(true__, c_union(Y2, c_union(c_Message_Osynth(X0), c_Message_Oparts(X0), tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(X0)) % 9.94/9.81 false__ -> true__ % 9.94/9.81 with the LPO induced by % 9.94/9.81 f4 > f5 > f2 > c_lessequals > f3 > tc_set > tc_Message_Omsg > c_Message_Osynth > v_H > c_Message_Oparts > c_union > f1 > false__ > true__ % 9.94/9.81 % 9.94/9.81 % SZS output end Proof % 9.94/9.81 %------------------------------------------------------------------------------