%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA027-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n018.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 19:15:42 EDT 2022 % Result : Unsatisfiable 12.31s 12.24s % Output : Proof 12.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ANA027-2 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : moca.sh %s % 0.14/0.32 % Computer : n018.cluster.edu % 0.14/0.32 % Model : x86_64 x86_64 % 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.32 % Memory : 8042.1875MB % 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.32 % CPULimit : 300 % 0.14/0.32 % WCLimit : 600 % 0.14/0.32 % DateTime : Fri Jul 8 06:55:40 EDT 2022 % 0.14/0.33 % CPUTime : % 12.31/12.24 % SZS status Unsatisfiable % 12.31/12.24 % SZS output start Proof % 12.31/12.24 The input problem is unsatisfiable because % 12.31/12.24 % 12.31/12.24 [1] the following set of Horn clauses is unsatisfiable: % 12.31/12.24 % 12.31/12.24 c_lessequals(c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b) % 12.31/12.24 c_lessequals(v_g(v_x), v_k(v_x), t_b) % 12.31/12.24 c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b) ==> \bottom % 12.31/12.24 class_Ring__and__Field_Oordered__idom(t_b) % 12.31/12.24 class_OrderedGroup_Ocomm__monoid__add(T_a) ==> c_plus(c_0, V_y, T_a) = V_y % 12.31/12.24 class_OrderedGroup_Opordered__ab__group__add(T_a) & c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a) ==> c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a) % 12.31/12.24 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) % 12.31/12.24 class_Orderings_Oorder(T_a) & c_lessequals(V_y, V_z, T_a) & c_lessequals(V_x, V_y, T_a) ==> c_lessequals(V_x, V_z, T_a) % 12.31/12.24 class_LOrder_Ojoin__semilorder(T) ==> class_Orderings_Oorder(T) % 12.31/12.24 class_OrderedGroup_Olordered__ab__group__abs(T) ==> class_OrderedGroup_Opordered__ab__group__add(T) % 12.31/12.24 class_OrderedGroup_Olordered__ab__group__abs(T) ==> class_LOrder_Ojoin__semilorder(T) % 12.31/12.24 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Ocomm__monoid__add(T) % 12.31/12.24 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T) % 12.31/12.24 % 12.31/12.24 This holds because % 12.31/12.24 % 12.31/12.24 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 12.31/12.24 % 12.31/12.24 E: % 12.31/12.24 c_lessequals(c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b) = true__ % 12.31/12.24 c_lessequals(v_g(v_x), v_k(v_x), t_b) = true__ % 12.31/12.24 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 12.31/12.24 f1(c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) = true__ % 12.31/12.24 f1(true__) = false__ % 12.31/12.24 f10(class_LOrder_Ojoin__semilorder(T), T) = true__ % 12.31/12.24 f10(true__, T) = class_Orderings_Oorder(T) % 12.31/12.24 f11(class_OrderedGroup_Olordered__ab__group__abs(T), T) = true__ % 12.31/12.24 f11(true__, T) = class_OrderedGroup_Opordered__ab__group__add(T) % 12.31/12.24 f12(class_OrderedGroup_Olordered__ab__group__abs(T), T) = true__ % 12.31/12.24 f12(true__, T) = class_LOrder_Ojoin__semilorder(T) % 12.31/12.24 f13(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 12.31/12.24 f13(true__, T) = class_OrderedGroup_Ocomm__monoid__add(T) % 12.31/12.24 f14(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 12.31/12.24 f14(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T) % 12.31/12.24 f2(class_OrderedGroup_Ocomm__monoid__add(T_a), V_y, T_a) = V_y % 12.31/12.24 f2(true__, V_y, T_a) = c_plus(c_0, V_y, T_a) % 12.31/12.24 f3(true__, V_a, V_b, T_a, V_c) = c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a) % 12.31/12.24 f4(c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a), T_a, V_a, V_b, V_c) = true__ % 12.31/12.24 f4(true__, T_a, V_a, V_b, V_c) = f3(class_OrderedGroup_Opordered__ab__group__add(T_a), V_a, V_b, T_a, V_c) % 12.31/12.24 f5(true__, V_a, V_c, V_b, T_a) = c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a) % 12.31/12.24 f6(c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a), T_a, V_a, V_c, V_b) = true__ % 12.31/12.24 f6(true__, T_a, V_a, V_c, V_b) = f5(class_OrderedGroup_Opordered__ab__group__add(T_a), V_a, V_c, V_b, T_a) % 12.31/12.24 f7(true__, V_x, V_z, T_a) = c_lessequals(V_x, V_z, T_a) % 12.31/12.24 f8(true__, T_a, V_x, V_z) = f7(class_Orderings_Oorder(T_a), V_x, V_z, T_a) % 12.31/12.24 f9(c_lessequals(V_x, V_y, T_a), V_y, V_z, T_a, V_x) = true__ % 12.31/12.24 f9(true__, V_y, V_z, T_a, V_x) = f8(c_lessequals(V_y, V_z, T_a), T_a, V_x, V_z) % 12.31/12.24 G: % 12.31/12.24 true__ = false__ % 12.31/12.24 % 12.31/12.24 This holds because % 12.31/12.24 % 12.31/12.24 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 12.31/12.24 % 12.31/12.24 % 12.31/12.24 c_lessequals(V_x, V_z, T_a) -> f7(true__, V_x, V_z, T_a) % 12.31/12.24 c_plus(c_0, V_y, T_a) -> f2(true__, V_y, T_a) % 12.31/12.24 class_LOrder_Ojoin__semilorder(T) -> f12(true__, T) % 12.31/12.24 class_OrderedGroup_Ocomm__monoid__add(T) -> f13(true__, T) % 12.31/12.24 class_OrderedGroup_Olordered__ab__group__abs(T) -> f14(true__, T) % 12.31/12.24 class_OrderedGroup_Opordered__ab__group__add(T) -> f11(true__, T) % 12.31/12.24 class_Orderings_Oorder(T) -> f10(true__, T) % 12.31/12.24 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 12.31/12.24 f1(f7(true__, c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) -> true__ % 12.31/12.24 f1(true__) -> false__ % 12.31/12.24 f10(f12(true__, Y0), Y0) -> true__ % 12.31/12.24 f10(true__, t_b) -> true__ % 12.31/12.24 f11(f14(true__, Y0), Y0) -> true__ % 12.31/12.24 f11(true__, t_b) -> true__ % 12.31/12.24 f12(f14(true__, Y0), Y0) -> true__ % 12.31/12.24 f12(true__, t_b) -> true__ % 12.31/12.24 f13(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 12.31/12.24 f13(true__, t_b) -> true__ % 12.31/12.24 f14(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 12.31/12.24 f14(true__, t_b) -> true__ % 12.31/12.24 f2(f13(true__, Y0), Y1, Y0) -> Y1 % 12.31/12.24 f2(true__, Y1, t_b) -> Y1 % 12.31/12.24 f3(true__, V_a, V_b, T_a, V_c) -> f7(true__, c_plus(V_a, V_b, T_a), V_c, T_a) % 12.31/12.24 f4(f7(true__, Y0, c_minus(Y1, Y2, Y3), Y3), Y3, Y0, Y2, Y1) -> true__ % 12.31/12.24 f4(true__, T_a, V_a, V_b, V_c) -> f3(f11(true__, T_a), V_a, V_b, T_a, V_c) % 12.31/12.24 f5(true__, V_a, V_c, V_b, T_a) -> f7(true__, V_a, c_minus(V_c, V_b, T_a), T_a) % 12.31/12.24 f6(f7(true__, Y0, Y2, t_b), t_b, c_0, Y2, Y0) -> true__ % 12.31/12.24 f6(f7(true__, c_plus(Y0, Y1, Y2), Y3, Y2), Y2, Y0, Y3, Y1) -> true__ % 12.31/12.24 f6(f7(true__, f2(true__, Y1, Y2), Y3, Y2), Y2, c_0, Y3, Y1) -> true__ % 12.31/12.24 f6(true__, T_a, V_a, V_c, V_b) -> f5(f11(true__, T_a), V_a, V_c, V_b, T_a) % 12.31/12.24 f7(true__, c_0, c_minus(c_minus(c_minus(v_f(v_x), v_k(v_x), t_b), c_0, t_b), c_0, t_b), t_b) -> true__ % 12.31/12.24 f7(true__, c_0, c_minus(c_minus(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_0, t_b), t_b) -> true__ % 12.31/12.24 f7(true__, c_0, c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b), t_b) -> true__ % 12.31/12.24 f7(true__, c_0, c_minus(c_minus(v_f(v_x), v_k(v_x), t_b), c_0, t_b), t_b) -> true__ % 12.31/12.24 f7(true__, c_0, c_minus(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), t_b) -> true__ % 12.31/12.24 f7(true__, c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b) -> true__ % 12.31/12.24 f7(true__, c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b) -> true__ % 12.31/12.24 f7(true__, c_0, c_minus(v_k(v_x), v_g(v_x), t_b), t_b) -> true__ % 12.31/12.24 f7(true__, v_g(v_x), v_f(v_x), t_b) -> true__ % 12.31/12.24 f7(true__, v_g(v_x), v_k(v_x), t_b) -> true__ % 12.31/12.24 f7(true__, v_k(v_x), v_f(v_x), t_b) -> true__ % 12.31/12.24 f8(f7(true__, c_minus(c_minus(v_f(v_x), v_k(v_x), t_b), c_0, t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 12.31/12.24 f8(f7(true__, c_minus(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 12.31/12.24 f8(f7(true__, c_minus(v_f(v_x), v_g(v_x), t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 12.31/12.24 f8(f7(true__, c_minus(v_f(v_x), v_k(v_x), t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 12.31/12.24 f8(f7(true__, c_minus(v_k(v_x), v_g(v_x), t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 12.31/12.24 f8(f7(true__, v_f(v_x), Y3, t_b), t_b, v_g(v_x), Y3) -> true__ % 12.31/12.24 f8(f7(true__, v_f(v_x), Y3, t_b), t_b, v_k(v_x), Y3) -> true__ % 12.31/12.24 f8(f7(true__, v_k(v_x), Y3, t_b), t_b, v_g(v_x), Y3) -> true__ % 12.31/12.24 f8(true__, T_a, V_x, V_z) -> f7(f10(true__, T_a), V_x, V_z, T_a) % 12.31/12.24 f9(f7(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__ % 12.31/12.24 f9(true__, V_y, V_z, T_a, V_x) -> f8(f7(true__, V_y, V_z, T_a), T_a, V_x, V_z) % 12.31/12.24 false__ -> true__ % 12.31/12.24 with the LPO induced by % 12.31/12.24 f6 > f5 > c_minus > f4 > f3 > c_plus > class_OrderedGroup_Opordered__ab__group__add > f11 > f2 > c_0 > f9 > f8 > v_f > c_lessequals > f7 > v_k > v_x > v_g > class_Orderings_Oorder > f10 > class_OrderedGroup_Ocomm__monoid__add > f13 > class_OrderedGroup_Olordered__ab__group__abs > f14 > class_LOrder_Ojoin__semilorder > f12 > t_b > class_Ring__and__Field_Oordered__idom > f1 > false__ > true__ % 12.31/12.24 % 12.31/12.24 % SZS output end Proof % 12.31/12.24 %------------------------------------------------------------------------------