%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET844-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n027.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 03:45:07 EDT 2022 % Result : Unsatisfiable 0.93s 1.10s % Output : Proof 0.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET844-2 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n027.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 23:26:18 EDT 2022 % 0.13/0.35 % CPUTime : % 0.93/1.10 % SZS status Unsatisfiable % 0.93/1.10 % SZS output start Proof % 0.93/1.10 The input problem is unsatisfiable because % 0.93/1.10 % 0.93/1.10 [1] the following set of Horn clauses is unsatisfiable: % 0.93/1.10 % 0.93/1.10 c_lessequals(V_A, V_A, tc_set(T_a)) % 0.93/1.10 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))) % 0.93/1.10 c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) & c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) & V_m = c_Zorn_Osucc(V_S, V_m, T_a) ==> c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) % 0.93/1.10 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) % 0.93/1.10 v_m = c_Zorn_Osucc(v_S, v_m, t_a) % 0.93/1.10 c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a))) ==> \bottom % 0.93/1.10 % 0.93/1.10 This holds because % 0.93/1.10 % 0.93/1.10 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.93/1.10 % 0.93/1.10 E: % 0.93/1.10 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) = true__ % 0.93/1.10 c_lessequals(V_A, V_A, tc_set(T_a)) = true__ % 0.93/1.10 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__ % 0.93/1.10 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))) % 0.93/1.10 f2(true__, V_n, V_m, T_a) = c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) % 0.93/1.10 f3(true__, V_m, V_S, T_a, V_n) = f2(c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_n, V_m, T_a) % 0.93/1.10 f4(V_m, V_m, V_n, V_S, T_a) = f3(c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_m, V_S, T_a, V_n) % 0.93/1.10 f4(c_Zorn_Osucc(V_S, V_m, T_a), V_m, V_n, V_S, T_a) = true__ % 0.93/1.10 f5(c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))) = true__ % 0.93/1.10 f5(true__) = false__ % 0.93/1.10 v_m = c_Zorn_Osucc(v_S, v_m, t_a) % 0.93/1.10 G: % 0.93/1.10 true__ = false__ % 0.93/1.10 % 0.93/1.10 This holds because % 0.93/1.10 % 0.93/1.10 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.93/1.10 % 0.93/1.10 % 0.93/1.10 c_Zorn_Osucc(v_S, v_m, t_a) -> v_m % 0.93/1.10 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) % 0.93/1.10 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) -> true__ % 0.93/1.10 c_lessequals(V_A, V_A, tc_set(T_a)) -> true__ % 0.93/1.10 c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) -> f2(true__, V_n, V_m, T_a) % 0.93/1.10 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__ % 0.93/1.10 f1(f2(true__, Y0, c_Zorn_OTFin(Y1, Y2), tc_set(Y2)), Y0, Y2, Y1) -> true__ % 0.93/1.10 f1(true__, c_Zorn_OTFin(Y1, Y2), Y2, Y1) -> true__ % 0.93/1.10 f2(c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_n, V_m, T_a) -> f3(true__, V_m, V_S, T_a, V_n) % 0.93/1.10 f2(f1(true__, X0, Y2, Y1), Y3, c_Union(X0, tc_set(Y2)), Y2) -> f3(true__, c_Union(X0, tc_set(Y2)), Y1, Y2, Y3) % 0.93/1.10 f2(true__, Y1, Y1, Y2) -> true__ % 0.93/1.10 f2(true__, Y3, c_Union(c_Zorn_OTFin(Y2, Y1), tc_set(Y1)), Y1) -> f3(true__, c_Union(c_Zorn_OTFin(Y2, Y1), tc_set(Y1)), Y2, Y1, Y3) % 0.93/1.10 f2(true__, Y3, v_m, t_a) -> f3(true__, v_m, v_S, t_a, Y3) % 0.93/1.10 f3(c_in(Y3, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))), v_m, v_S, t_a, Y3) -> true__ % 0.93/1.10 f3(f1(true__, X0, t_a, v_S), v_m, v_S, t_a, c_Union(X0, tc_set(t_a))) -> true__ % 0.93/1.10 f3(true__, c_Union(c_Zorn_OTFin(Y1, Y2), tc_set(Y2)), Y1, Y2, c_Union(c_Zorn_OTFin(Y1, Y2), tc_set(Y2))) -> true__ % 0.93/1.10 f3(true__, v_m, v_S, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) -> true__ % 0.93/1.10 f3(true__, v_m, v_S, t_a, v_m) -> true__ % 0.93/1.10 f4(V_m, V_m, V_n, V_S, T_a) -> f3(c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_m, V_S, T_a, V_n) % 0.93/1.10 f4(c_Zorn_Osucc(V_S, V_m, T_a), V_m, V_n, V_S, T_a) -> true__ % 0.93/1.10 f5(c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))) -> true__ % 0.93/1.10 f5(f2(true__, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, t_a)) -> true__ % 0.93/1.10 f5(f3(true__, v_m, v_S, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) -> true__ % 0.93/1.10 f5(true__) -> false__ % 0.93/1.10 false__ -> true__ % 0.93/1.10 with the LPO induced by % 0.93/1.10 f5 > t_a > v_S > v_m > c_Zorn_Osucc > f4 > c_in > f1 > c_lessequals > f2 > f3 > c_Union > c_Zorn_OTFin > tc_set > false__ > true__ % 0.93/1.10 % 0.93/1.10 % SZS output end Proof % 0.93/1.10 %------------------------------------------------------------------------------