%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA024-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 : Thu Jul 14 19:15:40 EDT 2022 % Result : Unsatisfiable 3.17s 3.19s % Output : Proof 3.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : ANA024-2 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Fri Jul 8 05:09:14 EDT 2022 % 0.12/0.34 % CPUTime : % 3.17/3.19 % SZS status Unsatisfiable % 3.17/3.19 % SZS output start Proof % 3.17/3.19 The input problem is unsatisfiable because % 3.17/3.19 % 3.17/3.19 [1] the following set of Horn clauses is unsatisfiable: % 3.17/3.19 % 3.17/3.19 class_OrderedGroup_Oab__group__add(T_a) ==> V_a = c_plus(c_minus(V_a, V_b, T_a), V_b, T_a) % 3.17/3.19 class_OrderedGroup_Opordered__ab__group__add(T_a) & c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a) ==> c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a) % 3.17/3.19 c_lessequals(v_k(V_U), v_f(V_U), t_b) % 3.17/3.19 c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) ==> \bottom % 3.17/3.19 class_OrderedGroup_Opordered__ab__group__add(T) ==> class_OrderedGroup_Oab__group__add(T) % 3.17/3.19 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Opordered__ab__group__add(T) % 3.17/3.19 class_Ring__and__Field_Oordered__idom(t_b) % 3.17/3.19 % 3.17/3.19 This holds because % 3.17/3.19 % 3.17/3.19 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.17/3.19 % 3.17/3.19 E: % 3.17/3.19 c_lessequals(v_k(V_U), v_f(V_U), t_b) = true__ % 3.17/3.19 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 3.17/3.19 f1(class_OrderedGroup_Oab__group__add(T_a), V_a, V_b, T_a) = c_plus(c_minus(V_a, V_b, T_a), V_b, T_a) % 3.17/3.19 f1(true__, V_a, V_b, T_a) = V_a % 3.17/3.19 f2(true__, V_a, V_c, V_b, T_a) = c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a) % 3.17/3.19 f3(c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a), T_a, V_a, V_c, V_b) = true__ % 3.17/3.19 f3(true__, T_a, V_a, V_c, V_b) = f2(class_OrderedGroup_Opordered__ab__group__add(T_a), V_a, V_c, V_b, T_a) % 3.17/3.19 f4(c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) = true__ % 3.17/3.19 f4(true__) = false__ % 3.17/3.19 f5(class_OrderedGroup_Opordered__ab__group__add(T), T) = true__ % 3.17/3.19 f5(true__, T) = class_OrderedGroup_Oab__group__add(T) % 3.17/3.19 f6(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 3.17/3.19 f6(true__, T) = class_OrderedGroup_Opordered__ab__group__add(T) % 3.17/3.19 G: % 3.17/3.19 true__ = false__ % 3.17/3.19 % 3.17/3.19 This holds because % 3.17/3.19 % 3.17/3.19 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.17/3.19 % 3.17/3.19 % 3.17/3.19 c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a) -> f2(true__, V_a, V_c, V_b, T_a) % 3.17/3.19 c_lessequals(v_k(V_U), v_f(V_U), t_b) -> true__ % 3.17/3.19 c_plus(c_minus(V_a, V_b, T_a), V_b, T_a) -> f1(f5(true__, T_a), V_a, V_b, T_a) % 3.17/3.19 class_OrderedGroup_Oab__group__add(T) -> f5(true__, T) % 3.17/3.19 class_OrderedGroup_Opordered__ab__group__add(T) -> f6(true__, T) % 3.17/3.19 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 3.17/3.19 f1(true__, V_a, V_b, T_a) -> V_a % 3.17/3.19 f2(true__, c_minus(c_minus(v_k(X0), Y2, t_b), Y3, t_b), c_minus(v_f(X0), Y2, t_b), Y3, t_b) -> true__ % 3.17/3.19 f2(true__, c_minus(v_k(X0), Y2, t_b), v_f(X0), Y2, t_b) -> true__ % 3.17/3.19 f3(c_lessequals(Y1, Y3, t_b), t_b, c_minus(Y1, Y2, t_b), Y3, Y2) -> true__ % 3.17/3.19 f3(c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a), T_a, V_a, V_c, V_b) -> true__ % 3.17/3.19 f3(c_lessequals(f1(f5(true__, Y2), X0, Y1, Y2), Y3, Y2), Y2, c_minus(X0, Y1, Y2), Y3, Y1) -> true__ % 3.17/3.19 f3(f2(true__, Y0, X1, X2, t_b), t_b, c_minus(Y0, Y2, t_b), c_minus(X1, X2, t_b), Y2) -> true__ % 3.17/3.19 f3(f2(true__, c_plus(Y0, Y1, Y2), X1, X2, Y2), Y2, Y0, c_minus(X1, X2, Y2), Y1) -> true__ % 3.17/3.19 f3(true__, T_a, V_a, V_c, V_b) -> f2(f6(true__, T_a), V_a, V_c, V_b, T_a) % 3.17/3.19 f4(f2(true__, c_minus(v_k(v_x), v_g(v_x), t_b), v_f(v_x), v_g(v_x), t_b)) -> true__ % 3.17/3.19 f4(true__) -> false__ % 3.17/3.19 f5(f6(true__, Y0), Y0) -> true__ % 3.17/3.19 f5(true__, t_b) -> true__ % 3.17/3.19 f6(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 3.17/3.19 f6(true__, t_b) -> true__ % 3.17/3.19 false__ -> true__ % 3.17/3.19 with the LPO induced by % 3.17/3.19 v_g > v_x > f3 > c_lessequals > f2 > class_OrderedGroup_Opordered__ab__group__add > f6 > c_minus > f1 > v_k > class_OrderedGroup_Oab__group__add > f5 > c_plus > v_f > t_b > class_Ring__and__Field_Oordered__idom > f4 > false__ > true__ % 3.17/3.19 % 3.17/3.19 % SZS output end Proof % 3.17/3.19 %------------------------------------------------------------------------------