%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET846-2 : 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 : Tue Jul 19 03:45:09 EDT 2022 % Result : Unsatisfiable 0.96s 1.16s % Output : Proof 0.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET846-2 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jul 11 04:05:45 EDT 2022 % 0.13/0.34 % CPUTime : % 0.96/1.16 % SZS status Unsatisfiable % 0.96/1.16 % SZS output start Proof % 0.96/1.16 The input problem is unsatisfiable because % 0.96/1.16 % 0.96/1.16 [1] the following set of Horn clauses is unsatisfiable: % 0.96/1.16 % 0.96/1.16 c_in(V_B, V_A, tc_set(T_a)) ==> c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)) % 0.96/1.16 c_lessequals(V_A, V_A, tc_set(T_a)) % 0.96/1.16 c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) ==> c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) % 0.96/1.16 c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a)))) ==> c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) % 0.96/1.16 c_lessequals(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))) ==> \bottom % 0.96/1.16 % 0.96/1.16 This holds because % 0.96/1.16 % 0.96/1.16 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.96/1.16 % 0.96/1.16 E: % 0.96/1.16 c_lessequals(V_A, V_A, tc_set(T_a)) = true__ % 0.96/1.16 f1(c_in(V_B, V_A, tc_set(T_a)), V_B, V_A, T_a) = true__ % 0.96/1.16 f1(true__, V_B, V_A, T_a) = c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)) % 0.96/1.16 f2(c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, V_x, T_a) = true__ % 0.96/1.16 f2(true__, V_S, V_x, T_a) = c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) % 0.96/1.16 f3(c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), V_Y, T_a, V_S) = true__ % 0.96/1.16 f3(true__, V_Y, T_a, V_S) = c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) % 0.96/1.16 f4(c_lessequals(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))) = true__ % 0.96/1.16 f4(true__) = false__ % 0.96/1.16 G: % 0.96/1.16 true__ = false__ % 0.96/1.16 % 0.96/1.16 This holds because % 0.96/1.16 % 0.96/1.16 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.96/1.16 % 0.96/1.16 % 0.96/1.16 c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) -> f3(true__, V_Y, T_a, V_S) % 0.96/1.16 c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) -> f2(true__, V_S, V_x, T_a) % 0.96/1.16 c_lessequals(V_A, V_A, tc_set(T_a)) -> true__ % 0.96/1.16 c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)) -> f1(true__, V_B, V_A, T_a) % 0.96/1.16 f1(c_in(V_B, V_A, tc_set(T_a)), V_B, V_A, T_a) -> true__ % 0.96/1.16 f1(f2(true__, X0, X1, X2), c_Zorn_Osucc(X0, X1, X2), c_Zorn_OTFin(X0, X2), tc_set(X2)) -> true__ % 0.96/1.16 f1(f3(true__, X0, X1, X2), c_Union(X0, tc_set(X1)), c_Zorn_OTFin(X2, X1), tc_set(X1)) -> true__ % 0.96/1.16 f1(true__, c_Union(Y1, Y2), Y1, Y2) -> true__ % 0.96/1.16 f1(true__, c_Zorn_Osucc(Y0, c_Union(c_Zorn_OTFin(Y0, Y2), tc_set(Y2)), Y2), c_Zorn_OTFin(Y0, Y2), tc_set(Y2)) -> true__ % 0.96/1.16 f1(true__, c_Zorn_Osucc(Y0, c_Zorn_Osucc(Y0, c_Union(c_Zorn_OTFin(Y0, Y2), tc_set(Y2)), Y2), Y2), c_Zorn_OTFin(Y0, Y2), tc_set(Y2)) -> true__ % 0.96/1.16 f2(c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, V_x, T_a) -> true__ % 0.96/1.16 f2(f2(true__, Y1, X1, Y2), Y1, c_Zorn_Osucc(Y1, X1, Y2), Y2) -> true__ % 0.96/1.16 f2(f3(true__, X0, Y2, Y1), Y1, c_Union(X0, tc_set(Y2)), Y2) -> true__ % 0.96/1.16 f2(true__, Y0, c_Zorn_Osucc(Y0, c_Union(c_Zorn_OTFin(Y0, Y2), tc_set(Y2)), Y2), Y2) -> true__ % 0.96/1.16 f2(true__, Y0, c_Zorn_Osucc(Y0, c_Zorn_Osucc(Y0, c_Union(c_Zorn_OTFin(Y0, Y2), tc_set(Y2)), Y2), Y2), Y2) -> true__ % 0.96/1.16 f2(true__, Y2, c_Union(c_Zorn_OTFin(Y2, Y1), tc_set(Y1)), Y1) -> true__ % 0.96/1.16 f3(c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), V_Y, T_a, V_S) -> true__ % 0.96/1.16 f3(true__, c_Zorn_OTFin(Y1, Y2), Y2, Y1) -> true__ % 0.96/1.16 f4(c_lessequals(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))) -> true__ % 0.96/1.16 f4(f1(true__, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) -> true__ % 0.96/1.16 f4(true__) -> false__ % 0.96/1.16 false__ -> true__ % 0.96/1.16 with the LPO induced by % 0.96/1.16 t_a > v_S > f4 > c_in > f2 > c_Zorn_Osucc > f3 > c_lessequals > f1 > c_Union > c_Zorn_OTFin > tc_set > false__ > true__ % 0.96/1.16 % 0.96/1.16 % SZS output end Proof % 0.96/1.16 %------------------------------------------------------------------------------