%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA023-2 : 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 : Thu Jul 14 19:15:40 EDT 2022 % Result : Unsatisfiable 13.03s 12.92s % Output : Proof 13.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : ANA023-2 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.14 % Command : moca.sh %s % 0.13/0.35 % Computer : n027.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Fri Jul 8 05:27:30 EDT 2022 % 0.13/0.35 % CPUTime : % 13.03/12.92 % SZS status Unsatisfiable % 13.03/12.92 % SZS output start Proof % 13.03/12.92 The input problem is unsatisfiable because % 13.03/12.92 % 13.03/12.92 [1] the following set of Horn clauses is unsatisfiable: % 13.03/12.92 % 13.03/12.92 class_OrderedGroup_Ocomm__monoid__add(T_a) ==> c_plus(c_0, V_y, T_a) = V_y % 13.03/12.92 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) % 13.03/12.92 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) % 13.03/12.92 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) % 13.03/12.92 c_lessequals(c_0, c_minus(v_k(v_x), v_g(v_x), t_b), t_b) % 13.03/12.92 c_lessequals(v_k(v_x), v_f(v_x), t_b) % 13.03/12.92 c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b) ==> \bottom % 13.03/12.92 class_Orderings_Olinorder(T) ==> class_Orderings_Oorder(T) % 13.03/12.92 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Ocomm__monoid__add(T) % 13.03/12.92 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Olinorder(T) % 13.03/12.92 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Opordered__ab__group__add(T) % 13.03/12.92 class_Ring__and__Field_Oordered__idom(t_b) % 13.03/12.92 % 13.03/12.92 This holds because % 13.03/12.92 % 13.03/12.92 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 13.03/12.92 % 13.03/12.92 E: % 13.03/12.92 c_lessequals(c_0, c_minus(v_k(v_x), v_g(v_x), t_b), t_b) = true__ % 13.03/12.92 c_lessequals(v_k(v_x), v_f(v_x), t_b) = true__ % 13.03/12.92 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 13.03/12.92 f1(class_OrderedGroup_Ocomm__monoid__add(T_a), V_y, T_a) = V_y % 13.03/12.92 f1(true__, V_y, T_a) = c_plus(c_0, V_y, T_a) % 13.03/12.92 f10(class_Orderings_Olinorder(T), T) = true__ % 13.03/12.92 f10(true__, T) = class_Orderings_Oorder(T) % 13.03/12.92 f11(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 13.03/12.92 f11(true__, T) = class_OrderedGroup_Ocomm__monoid__add(T) % 13.03/12.92 f12(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 13.03/12.92 f12(true__, T) = class_Orderings_Olinorder(T) % 13.03/12.92 f13(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 13.03/12.92 f13(true__, T) = class_OrderedGroup_Opordered__ab__group__add(T) % 13.03/12.92 f2(true__, V_a, V_b, T_a, V_c) = c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a) % 13.03/12.92 f3(c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a), T_a, V_a, V_b, V_c) = true__ % 13.03/12.92 f3(true__, T_a, V_a, V_b, V_c) = f2(class_OrderedGroup_Opordered__ab__group__add(T_a), V_a, V_b, T_a, V_c) % 13.03/12.92 f4(true__, V_a, V_c, V_b, T_a) = c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a) % 13.03/12.92 f5(c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a), T_a, V_a, V_c, V_b) = true__ % 13.03/12.92 f5(true__, T_a, V_a, V_c, V_b) = f4(class_OrderedGroup_Opordered__ab__group__add(T_a), V_a, V_c, V_b, T_a) % 13.03/12.92 f6(true__, V_x, V_z, T_a) = c_lessequals(V_x, V_z, T_a) % 13.03/12.92 f7(true__, T_a, V_x, V_z) = f6(class_Orderings_Oorder(T_a), V_x, V_z, T_a) % 13.03/12.92 f8(c_lessequals(V_x, V_y, T_a), V_y, V_z, T_a, V_x) = true__ % 13.03/12.92 f8(true__, V_y, V_z, T_a, V_x) = f7(c_lessequals(V_y, V_z, T_a), T_a, V_x, V_z) % 13.03/12.92 f9(c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) = true__ % 13.03/12.92 f9(true__) = false__ % 13.03/12.92 G: % 13.03/12.92 true__ = false__ % 13.03/12.92 % 13.03/12.92 This holds because % 13.03/12.92 % 13.03/12.92 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 13.03/12.92 % 13.03/12.92 % 13.03/12.92 c_lessequals(V_x, V_z, T_a) -> f6(true__, V_x, V_z, T_a) % 13.03/12.92 c_plus(c_0, V_y, T_a) -> f1(true__, V_y, T_a) % 13.03/12.92 class_OrderedGroup_Ocomm__monoid__add(T) -> f11(true__, T) % 13.03/12.92 class_OrderedGroup_Opordered__ab__group__add(T) -> f13(true__, T) % 13.03/12.92 class_Orderings_Olinorder(T) -> f12(true__, T) % 13.03/12.92 class_Orderings_Oorder(T) -> f10(true__, T) % 13.03/12.92 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 13.03/12.92 f1(f11(true__, Y0), Y1, Y0) -> Y1 % 13.03/12.92 f1(true__, Y1, t_b) -> Y1 % 13.03/12.92 f10(f12(true__, Y0), Y0) -> true__ % 13.03/12.92 f10(true__, t_b) -> true__ % 13.03/12.92 f11(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 13.03/12.92 f11(true__, t_b) -> true__ % 13.03/12.92 f12(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 13.03/12.92 f12(true__, t_b) -> true__ % 13.03/12.92 f13(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 13.03/12.92 f13(true__, t_b) -> true__ % 13.03/12.92 f2(true__, V_a, V_b, T_a, V_c) -> f6(true__, c_plus(V_a, V_b, T_a), V_c, T_a) % 13.03/12.92 f3(f6(true__, Y0, c_minus(Y1, Y2, Y3), Y3), Y3, Y0, Y2, Y1) -> true__ % 13.03/12.92 f3(true__, T_a, V_a, V_b, V_c) -> f2(f13(true__, T_a), V_a, V_b, T_a, V_c) % 13.03/12.92 f4(true__, V_a, V_c, V_b, T_a) -> f6(true__, V_a, c_minus(V_c, V_b, T_a), T_a) % 13.03/12.92 f5(f6(true__, Y0, Y2, t_b), t_b, c_0, Y2, Y0) -> true__ % 13.03/12.92 f5(f6(true__, c_plus(Y0, Y1, Y2), Y3, Y2), Y2, Y0, Y3, Y1) -> true__ % 13.03/12.92 f5(f6(true__, f1(true__, Y1, Y2), Y3, Y2), Y2, c_0, Y3, Y1) -> true__ % 13.03/12.92 f5(true__, T_a, V_a, V_c, V_b) -> f4(f13(true__, T_a), V_a, V_c, V_b, T_a) % 13.03/12.92 f6(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__ % 13.03/12.92 f6(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__ % 13.03/12.92 f6(true__, c_0, c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b), t_b) -> true__ % 13.03/12.92 f6(true__, c_0, c_minus(c_minus(v_f(v_x), v_k(v_x), t_b), c_0, t_b), t_b) -> true__ % 13.03/12.92 f6(true__, c_0, c_minus(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), t_b) -> true__ % 13.03/12.92 f6(true__, c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b) -> true__ % 13.03/12.92 f6(true__, c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b) -> true__ % 13.03/12.92 f6(true__, c_0, c_minus(v_k(v_x), v_g(v_x), t_b), t_b) -> true__ % 13.03/12.92 f6(true__, v_g(v_x), v_f(v_x), t_b) -> true__ % 13.03/12.92 f6(true__, v_g(v_x), v_k(v_x), t_b) -> true__ % 13.03/12.92 f6(true__, v_k(v_x), v_f(v_x), t_b) -> true__ % 13.03/12.92 f7(f6(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__ % 13.03/12.92 f7(f6(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__ % 13.03/12.92 f7(f6(true__, c_minus(v_f(v_x), v_g(v_x), t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 13.03/12.92 f7(f6(true__, c_minus(v_f(v_x), v_k(v_x), t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 13.03/12.92 f7(f6(true__, c_minus(v_k(v_x), v_g(v_x), t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 13.03/12.92 f7(f6(true__, v_f(v_x), Y3, t_b), t_b, v_g(v_x), Y3) -> true__ % 13.03/12.92 f7(f6(true__, v_f(v_x), Y3, t_b), t_b, v_k(v_x), Y3) -> true__ % 13.03/12.92 f7(f6(true__, v_k(v_x), Y3, t_b), t_b, v_g(v_x), Y3) -> true__ % 13.03/12.92 f7(true__, T_a, V_x, V_z) -> f6(f10(true__, T_a), V_x, V_z, T_a) % 13.03/12.92 f8(f6(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__ % 13.03/12.92 f8(true__, V_y, V_z, T_a, V_x) -> f7(f6(true__, V_y, V_z, T_a), T_a, V_x, V_z) % 13.03/12.92 f9(f6(true__, c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) -> true__ % 13.03/12.92 f9(true__) -> false__ % 13.03/12.92 false__ -> true__ % 13.03/12.92 with the LPO induced by % 13.03/12.92 f3 > f2 > c_plus > f1 > c_0 > f5 > f4 > t_b > class_OrderedGroup_Opordered__ab__group__add > f13 > c_minus > f8 > c_lessequals > f7 > f6 > class_Orderings_Oorder > f10 > v_g > v_f > v_x > v_k > class_Orderings_Olinorder > f12 > class_OrderedGroup_Ocomm__monoid__add > f11 > class_Ring__and__Field_Oordered__idom > f9 > false__ > true__ % 13.03/12.92 % 13.03/12.92 % SZS output end Proof % 13.03/12.92 %------------------------------------------------------------------------------