%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET850-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n004.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 : Tue Jul 19 03:45:12 EDT 2022 % Result : Unsatisfiable 0.67s 0.83s % Output : Proof 0.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET850-2 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n004.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 : Mon Jul 11 02:12:52 EDT 2022 % 0.12/0.33 % CPUTime : % 0.67/0.83 % SZS status Unsatisfiable % 0.67/0.83 % SZS output start Proof % 0.67/0.83 The input problem is unsatisfiable because % 0.67/0.83 % 0.67/0.83 [1] the following set of Horn clauses is unsatisfiable: % 0.67/0.83 % 0.67/0.83 c_lessequals(V_B, V_C, tc_set(T_a)) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> c_lessequals(V_A, V_C, tc_set(T_a)) % 0.67/0.83 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) % 0.67/0.83 c_lessequals(v_x, v_y, tc_set(tc_set(t_a))) % 0.67/0.83 c_lessequals(v_x, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(tc_set(t_a))) ==> \bottom % 0.67/0.83 % 0.67/0.83 This holds because % 0.67/0.83 % 0.67/0.83 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.67/0.83 % 0.67/0.83 E: % 0.67/0.83 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) = true__ % 0.67/0.83 c_lessequals(v_x, v_y, tc_set(tc_set(t_a))) = true__ % 0.67/0.83 f1(true__, V_A, V_C, T_a) = c_lessequals(V_A, V_C, tc_set(T_a)) % 0.67/0.83 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_C, T_a, V_A) = true__ % 0.67/0.83 f2(true__, V_B, V_C, T_a, V_A) = f1(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_C, T_a) % 0.67/0.83 f3(c_lessequals(v_x, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(tc_set(t_a)))) = true__ % 0.67/0.83 f3(true__) = false__ % 0.67/0.83 G: % 0.67/0.83 true__ = false__ % 0.67/0.83 % 0.67/0.83 This holds because % 0.67/0.83 % 0.67/0.83 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.67/0.83 % 0.67/0.83 % 0.67/0.83 c_lessequals(V_A, V_C, tc_set(T_a)) -> f1(true__, V_A, V_C, T_a) % 0.67/0.83 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) -> true__ % 0.67/0.83 c_lessequals(v_x, v_y, tc_set(tc_set(t_a))) -> true__ % 0.67/0.83 f1(f1(true__, c_Zorn_Osucc(X0, v_y, t_a), Y3, tc_set(t_a)), v_x, Y3, tc_set(t_a)) -> true__ % 0.67/0.83 f1(f1(true__, c_Zorn_Osucc(X1, Y0, X2), Y3, tc_set(X2)), Y0, Y3, tc_set(X2)) -> true__ % 0.67/0.83 f1(f1(true__, c_Zorn_Osucc(X1, c_Zorn_Osucc(X2, Y0, X3), X3), Y3, tc_set(X3)), Y0, Y3, tc_set(X3)) -> true__ % 0.67/0.83 f1(f1(true__, v_y, Y3, tc_set(t_a)), v_x, Y3, tc_set(t_a)) -> true__ % 0.67/0.83 f1(true__, Y0, c_Zorn_Osucc(X1, Y0, X2), tc_set(X2)) -> true__ % 0.67/0.83 f1(true__, Y1, c_Zorn_Osucc(X1, c_Zorn_Osucc(X2, c_Zorn_Osucc(Y0, Y1, Y2), Y2), Y2), tc_set(Y2)) -> true__ % 0.67/0.83 f1(true__, Y1, c_Zorn_Osucc(X1, c_Zorn_Osucc(Y0, Y1, Y2), Y2), tc_set(Y2)) -> true__ % 0.67/0.83 f1(true__, v_x, c_Zorn_Osucc(X1, c_Zorn_Osucc(X2, v_y, t_a), t_a), tc_set(t_a)) -> true__ % 0.67/0.83 f1(true__, v_x, c_Zorn_Osucc(X1, v_y, t_a), tc_set(t_a)) -> true__ % 0.67/0.83 f1(true__, v_x, v_y, tc_set(t_a)) -> true__ % 0.67/0.83 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_C, T_a, V_A) -> true__ % 0.67/0.83 f2(f1(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__ % 0.67/0.83 f2(true__, V_B, V_C, T_a, V_A) -> f1(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_C, T_a) % 0.67/0.83 f3(c_lessequals(v_x, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(tc_set(t_a)))) -> true__ % 0.67/0.83 f3(f1(true__, v_x, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(t_a))) -> true__ % 0.67/0.83 f3(true__) -> false__ % 0.67/0.83 false__ -> true__ % 0.67/0.83 with the LPO induced by % 0.67/0.83 v_S > f3 > t_a > v_y > v_x > c_Zorn_Osucc > f2 > c_lessequals > f1 > tc_set > false__ > true__ % 0.67/0.83 % 0.67/0.83 % SZS output end Proof % 0.67/0.83 %------------------------------------------------------------------------------