%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET849-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n008.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 03:45:11 EDT 2022 % Result : Unsatisfiable 0.13s 0.40s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET849-2 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n008.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 : Sun Jul 10 14:46:23 EDT 2022 % 0.13/0.34 % CPUTime : % 0.13/0.40 % SZS status Unsatisfiable % 0.13/0.40 % SZS output start Proof % 0.13/0.40 The input problem is unsatisfiable because % 0.13/0.40 % 0.13/0.40 [1] the following set of Horn clauses is unsatisfiable: % 0.13/0.40 % 0.13/0.40 c_lessequals(V_A, V_A, tc_set(T_a)) % 0.13/0.40 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))) % 0.13/0.40 c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) ==> c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a) % 0.13/0.40 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)) ==> \bottom % 0.13/0.40 % 0.13/0.40 This holds because % 0.13/0.40 % 0.13/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.13/0.40 % 0.13/0.40 E: % 0.13/0.40 c_lessequals(V_A, V_A, tc_set(T_a)) = true__ % 0.13/0.40 f1(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__ % 0.13/0.40 f1(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))) % 0.13/0.40 f2(c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, T_a) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a) % 0.13/0.40 f2(true__, V_S, T_a) = c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) % 0.13/0.40 f3(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) = false__ % 0.13/0.40 f3(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)) = true__ % 0.13/0.40 G: % 0.13/0.40 true__ = false__ % 0.13/0.40 % 0.13/0.40 This holds because % 0.13/0.40 % 0.13/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.13/0.40 % 0.13/0.40 f2(c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, T_a) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a) % 0.13/0.40 c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) -> f2(true__, V_S, T_a) % 0.13/0.40 c_Zorn_Osucc(Y0, f2(true__, Y0, Y1), Y1) -> f2(true__, Y0, Y1) % 0.13/0.40 c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) -> f1(true__, V_Y, T_a, V_S) % 0.13/0.40 c_in(f2(true__, X0, Y1), c_Zorn_OTFin(Y2, Y1), tc_set(tc_set(Y1))) -> f1(true__, c_Zorn_OTFin(X0, Y1), Y1, Y2) % 0.13/0.40 c_lessequals(V_A, V_A, tc_set(T_a)) -> true__ % 0.13/0.40 f1(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__ % 0.13/0.40 f1(true__, c_Zorn_OTFin(Y1, Y2), Y2, Y1) -> true__ % 0.13/0.40 f3(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) -> false__ % 0.13/0.40 f3(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)) -> true__ % 0.13/0.40 f3(c_Zorn_Osucc(v_S, f2(true__, v_S, t_a), t_a)) -> true__ % 0.13/0.40 f3(f2(f1(true__, c_Zorn_OTFin(v_S, t_a), t_a, v_S), v_S, t_a)) -> true__ % 0.13/0.40 f3(f2(true__, v_S, t_a)) -> false__ % 0.13/0.40 false__ -> true__ % 0.13/0.40 with the LPO induced by % 0.13/0.40 t_a > v_S > f3 > tc_set > c_Zorn_Osucc > c_Union > f2 > c_Zorn_OTFin > c_in > f1 > c_lessequals > false__ > true__ % 0.13/0.40 % 0.13/0.40 % SZS output end Proof % 0.13/0.40 %------------------------------------------------------------------------------