%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV254-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n015.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 20:42:22 EDT 2022 % Result : Unsatisfiable 1.07s 1.20s % Output : Proof 1.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SWV254-2 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.13 % Command : moca.sh %s % 0.15/0.35 % Computer : n015.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 600 % 0.15/0.35 % DateTime : Wed Jun 15 20:02:10 EDT 2022 % 0.21/0.35 % CPUTime : % 1.07/1.20 % SZS status Unsatisfiable % 1.07/1.20 % SZS output start Proof % 1.07/1.20 The input problem is unsatisfiable because % 1.07/1.20 % 1.07/1.20 [1] the following set of Horn clauses is unsatisfiable: % 1.07/1.20 % 1.07/1.20 class_Orderings_Oorder(T_a) & c_lessequals(V_n, V_m, T_a) ==> c_SetInterval_OatLeastLessThan(V_m, V_n, T_a) = c_emptyset % 1.07/1.20 c_SetInterval_OatLeastLessThan(V_m, c_Suc(V_m), tc_nat) = c_insert(V_m, c_emptyset, tc_nat) % 1.07/1.20 c_emptyset = c_insert(V_a, V_A, T_a) ==> \bottom % 1.07/1.20 c_lessequals(V_U, v_x(V_U), tc_nat) % 1.07/1.20 v_x(V_U) = v_nat % 1.07/1.20 class_Orderings_Oorder(tc_nat) % 1.07/1.20 % 1.07/1.20 This holds because % 1.07/1.20 % 1.07/1.20 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.07/1.20 % 1.07/1.20 E: % 1.07/1.20 c_SetInterval_OatLeastLessThan(V_m, c_Suc(V_m), tc_nat) = c_insert(V_m, c_emptyset, tc_nat) % 1.07/1.20 c_lessequals(V_U, v_x(V_U), tc_nat) = true__ % 1.07/1.20 class_Orderings_Oorder(tc_nat) = true__ % 1.07/1.20 f1(true__, V_m, V_n, T_a) = c_SetInterval_OatLeastLessThan(V_m, V_n, T_a) % 1.07/1.20 f2(c_lessequals(V_n, V_m, T_a), T_a, V_m, V_n) = c_emptyset % 1.07/1.20 f2(true__, T_a, V_m, V_n) = f1(class_Orderings_Oorder(T_a), V_m, V_n, T_a) % 1.07/1.20 f3(c_emptyset) = false__ % 1.07/1.20 f3(c_insert(V_a, V_A, T_a)) = true__ % 1.07/1.20 v_x(V_U) = v_nat % 1.07/1.20 G: % 1.07/1.20 true__ = false__ % 1.07/1.20 % 1.07/1.20 This holds because % 1.07/1.20 % 1.07/1.20 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.07/1.20 % 1.07/1.20 % 1.07/1.20 c_SetInterval_OatLeastLessThan(V_m, V_n, T_a) -> f1(true__, V_m, V_n, T_a) % 1.07/1.20 c_insert(V_m, c_emptyset, tc_nat) -> c_SetInterval_OatLeastLessThan(V_m, c_Suc(V_m), tc_nat) % 1.07/1.20 c_lessequals(V_U, v_x(V_U), tc_nat) -> true__ % 1.07/1.20 c_lessequals(Y0, v_nat, tc_nat) -> true__ % 1.07/1.20 class_Orderings_Oorder(tc_nat) -> true__ % 1.07/1.20 f1(class_Orderings_Oorder(T_a), V_m, V_n, T_a) -> f2(true__, T_a, V_m, V_n) % 1.07/1.20 f1(true__, Y1, Y2, tc_nat) -> f2(true__, tc_nat, Y1, Y2) % 1.07/1.20 f2(c_lessequals(V_n, V_m, T_a), T_a, V_m, V_n) -> c_emptyset % 1.07/1.20 f2(true__, tc_nat, v_nat, Y0) -> c_emptyset % 1.07/1.20 f3(c_emptyset) -> false__ % 1.07/1.20 f3(c_insert(V_a, V_A, T_a)) -> true__ % 1.07/1.20 f3(f1(true__, Y0, c_Suc(Y0), tc_nat)) -> true__ % 1.07/1.20 f3(f2(true__, tc_nat, Y0, c_Suc(Y0))) -> true__ % 1.07/1.20 false__ -> true__ % 1.07/1.20 v_x(V_U) -> v_nat % 1.07/1.20 with the LPO induced by % 1.07/1.20 v_x > v_nat > f3 > c_lessequals > c_emptyset > c_insert > c_Suc > c_SetInterval_OatLeastLessThan > f1 > tc_nat > f2 > class_Orderings_Oorder > false__ > true__ % 1.07/1.20 % 1.07/1.20 % SZS output end Proof % 1.07/1.20 %------------------------------------------------------------------------------