%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV259-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 20:42:26 EDT 2022 % Result : Unsatisfiable 3.62s 3.74s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.10 % Problem : SWV259-2 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.11 % Command : moca.sh %s % 0.11/0.30 % Computer : n032.cluster.edu % 0.11/0.30 % Model : x86_64 x86_64 % 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.30 % Memory : 8042.1875MB % 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.30 % CPULimit : 300 % 0.11/0.30 % WCLimit : 600 % 0.11/0.30 % DateTime : Wed Jun 15 10:58:28 EDT 2022 % 0.11/0.31 % CPUTime : % 3.62/3.74 % SZS status Unsatisfiable % 3.62/3.74 % SZS output start Proof % 3.62/3.74 The input problem is unsatisfiable because % 3.62/3.74 % 3.62/3.74 [1] the following set of Horn clauses is unsatisfiable: % 3.62/3.74 % 3.62/3.74 c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) ==> \bottom % 3.62/3.74 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)) % 3.62/3.74 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)) % 3.62/3.74 c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) ==> c_lessequals(V_A, V_B, tc_set(T_a)) % 3.62/3.74 c_lessequals(V_A, V_A, tc_set(T_a)) % 3.62/3.74 % 3.62/3.74 This holds because % 3.62/3.74 % 3.62/3.74 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.62/3.74 % 3.62/3.74 E: % 3.62/3.74 c_lessequals(V_A, V_A, tc_set(T_a)) = true__ % 3.62/3.74 f1(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) = true__ % 3.62/3.74 f1(true__) = false__ % 3.62/3.74 f2(c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)), V_G, V_H) = true__ % 3.62/3.74 f2(true__, V_G, V_H) = c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 3.62/3.74 f3(c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)), V_G, V_H) = true__ % 3.62/3.74 f3(true__, V_G, V_H) = c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) % 3.62/3.74 f4(c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)), V_A, V_B, T_a) = true__ % 3.62/3.74 f4(true__, V_A, V_B, T_a) = c_lessequals(V_A, V_B, tc_set(T_a)) % 3.62/3.74 G: % 3.62/3.74 true__ = false__ % 3.62/3.74 % 3.62/3.74 This holds because % 3.62/3.74 % 3.62/3.74 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.62/3.74 % 3.62/3.74 % 3.62/3.74 c_lessequals(V_A, V_B, tc_set(T_a)) -> f4(true__, V_A, V_B, T_a) % 3.62/3.74 f1(f4(true__, c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) -> true__ % 3.62/3.74 f1(true__) -> false__ % 3.62/3.74 f2(f4(true__, c_Message_Oparts(Y0), c_Message_Oparts(Y1), tc_Message_Omsg), Y0, Y1) -> true__ % 3.62/3.74 f2(true__, V_G, V_H) -> f4(true__, V_G, c_Message_Oparts(V_H), tc_Message_Omsg) % 3.62/3.74 f3(f4(true__, Y0, c_Message_Oparts(Y1), tc_Message_Omsg), Y0, Y1) -> true__ % 3.62/3.74 f3(true__, V_G, V_H) -> f4(true__, c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_Message_Omsg) % 3.62/3.74 f4(f4(true__, c_insert(Y0, Y1, Y2), Y3, Y2), Y1, Y3, Y2) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0)))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0))))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y0)))))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_insert(X1, c_Message_Oparts(Y0), tc_Message_Omsg)))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_Message_Oparts(c_insert(X1, c_Message_Oparts(Y0), tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_insert(X1, c_Message_Oparts(Y0), tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y0, c_Message_Oparts(c_insert(X1, c_Message_Oparts(c_Message_Oparts(Y0)), tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y1, Y1, Y2) -> true__ % 3.62/3.74 f4(true__, Y1, c_Message_Oparts(Y1), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y1, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_insert(Y0, Y1, tc_Message_Omsg))))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y1, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_insert(Y0, Y1, tc_Message_Omsg)))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y1, c_Message_Oparts(c_Message_Oparts(c_insert(Y0, Y1, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y1, c_Message_Oparts(c_insert(X1, c_insert(Y0, Y1, tc_Message_Omsg), tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y1, c_Message_Oparts(c_insert(Y0, Y1, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, Y1, c_insert(X1, c_insert(Y0, Y1, Y2), Y2), Y2) -> true__ % 3.62/3.74 f4(true__, Y1, c_insert(Y0, Y1, Y2), Y2) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(Y0), c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_insert(X1, Y0, tc_Message_Omsg)))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(Y0), c_Message_Oparts(c_Message_Oparts(c_insert(X1, Y0, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(Y0), c_Message_Oparts(c_insert(X1, Y0, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(Y0), c_Message_Oparts(c_insert(X1, c_insert(X2, Y0, tc_Message_Omsg), tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(X0)), c_Message_Oparts(c_Message_Oparts(c_insert(X1, X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(X0)), c_Message_Oparts(c_insert(X1, X0, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(Y1)), c_Message_Oparts(Y1), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(X0))), c_Message_Oparts(c_insert(X1, X0, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1))), c_Message_Oparts(Y1), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1)))), c_Message_Oparts(Y1), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1))))), c_Message_Oparts(Y1), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1)))))), c_Message_Oparts(Y1), tc_Message_Omsg) -> true__ % 3.62/3.74 f4(true__, c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(c_Message_Oparts(Y1))))))), c_Message_Oparts(Y1), tc_Message_Omsg) -> true__ % 3.62/3.74 false__ -> true__ % 3.62/3.74 with the LPO induced by % 3.62/3.74 v_X > v_H > f3 > f2 > tc_Message_Omsg > c_Message_Oparts > c_lessequals > f4 > tc_set > c_insert > f1 > false__ > true__ % 3.62/3.74 % 3.62/3.74 % SZS output end Proof % 3.62/3.74 %------------------------------------------------------------------------------