%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA037-2 : 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 19:15:49 EDT 2022 % Result : Unsatisfiable 8.75s 8.85s % Output : Proof 8.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ANA037-2 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n025.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 : Fri Jul 8 04:40:59 EDT 2022 % 0.13/0.34 % CPUTime : % 8.75/8.85 % SZS status Unsatisfiable % 8.75/8.85 % SZS output start Proof % 8.75/8.85 The input problem is unsatisfiable because % 8.75/8.85 % 8.75/8.85 [1] the following set of Horn clauses is unsatisfiable: % 8.75/8.85 % 8.75/8.85 c_lessequals(c_0, v_f(v_xa), t_b) % 8.75/8.85 c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(v_c, v_f(v_xa), t_b), t_b) % 8.75/8.85 c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b) ==> \bottom % 8.75/8.85 class_Ring__and__Field_Oordered__idom(t_b) % 8.75/8.85 class_Orderings_Olinorder(T_b) ==> c_lessequals(V_x, c_Orderings_Omax(V_x, V_y, T_b), T_b) % 8.75/8.85 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) % 8.75/8.85 class_Ring__and__Field_Opordered__semiring(T_a) & c_lessequals(V_a, V_b, T_a) & c_lessequals(c_0, V_c, T_a) ==> c_lessequals(c_times(V_a, V_c, T_a), c_times(V_b, V_c, T_a), T_a) % 8.75/8.85 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Olinorder(T) % 8.75/8.85 class_Ring__and__Field_Oordered__idom(T) ==> class_Ring__and__Field_Opordered__semiring(T) % 8.75/8.85 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Oorder(T) % 8.75/8.85 % 8.75/8.85 This holds because % 8.75/8.85 % 8.75/8.85 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 8.75/8.85 % 8.75/8.85 E: % 8.75/8.85 c_lessequals(c_0, v_f(v_xa), t_b) = true__ % 8.75/8.85 c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(v_c, v_f(v_xa), t_b), t_b) = true__ % 8.75/8.85 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 8.75/8.85 f1(c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b)) = true__ % 8.75/8.85 f1(true__) = false__ % 8.75/8.85 f10(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 8.75/8.85 f10(true__, T) = class_Ring__and__Field_Opordered__semiring(T) % 8.75/8.85 f11(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 8.75/8.85 f11(true__, T) = class_Orderings_Oorder(T) % 8.75/8.85 f2(class_Orderings_Olinorder(T_b), V_x, V_y, T_b) = true__ % 8.75/8.85 f2(true__, V_x, V_y, T_b) = c_lessequals(V_x, c_Orderings_Omax(V_x, V_y, T_b), T_b) % 8.75/8.85 f3(true__, V_x, V_z, T_a) = c_lessequals(V_x, V_z, T_a) % 8.75/8.85 f4(true__, T_a, V_x, V_z) = f3(class_Orderings_Oorder(T_a), V_x, V_z, T_a) % 8.75/8.85 f5(c_lessequals(V_x, V_y, T_a), V_y, V_z, T_a, V_x) = true__ % 8.75/8.85 f5(true__, V_y, V_z, T_a, V_x) = f4(c_lessequals(V_y, V_z, T_a), T_a, V_x, V_z) % 8.75/8.85 f6(true__, V_a, V_c, T_a, V_b) = c_lessequals(c_times(V_a, V_c, T_a), c_times(V_b, V_c, T_a), T_a) % 8.75/8.85 f7(true__, T_a, V_a, V_c, V_b) = f6(class_Ring__and__Field_Opordered__semiring(T_a), V_a, V_c, T_a, V_b) % 8.75/8.85 f8(c_lessequals(c_0, V_c, T_a), V_a, V_b, T_a, V_c) = true__ % 8.75/8.85 f8(true__, V_a, V_b, T_a, V_c) = f7(c_lessequals(V_a, V_b, T_a), T_a, V_a, V_c, V_b) % 8.75/8.85 f9(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 8.75/8.85 f9(true__, T) = class_Orderings_Olinorder(T) % 8.75/8.85 G: % 8.75/8.85 true__ = false__ % 8.75/8.85 % 8.75/8.85 This holds because % 8.75/8.85 % 8.75/8.85 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 8.75/8.85 % 8.75/8.85 % 8.75/8.85 c_lessequals(V_x, V_z, T_a) -> f3(true__, V_x, V_z, T_a) % 8.75/8.85 class_Orderings_Olinorder(T) -> f9(true__, T) % 8.75/8.85 class_Orderings_Oorder(T) -> f11(true__, T) % 8.75/8.85 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 8.75/8.85 class_Ring__and__Field_Opordered__semiring(T) -> f10(true__, T) % 8.75/8.85 f1(f3(true__, c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b)) -> true__ % 8.75/8.85 f1(true__) -> false__ % 8.75/8.85 f10(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 8.75/8.85 f10(true__, t_b) -> true__ % 8.75/8.85 f11(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 8.75/8.85 f11(true__, t_b) -> true__ % 8.75/8.85 f2(f9(true__, Y0), Y1, Y2, Y0) -> true__ % 8.75/8.85 f2(true__, V_x, V_y, T_b) -> f3(true__, V_x, c_Orderings_Omax(V_x, V_y, T_b), T_b) % 8.75/8.85 f3(true__, Y0, c_Orderings_Omax(c_Orderings_Omax(Y0, Y1, t_b), X1, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, Y0, c_Orderings_Omax(c_Orderings_Omax(c_Orderings_Omax(Y0, Y1, t_b), X1, t_b), X2, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, Y1, c_Orderings_Omax(Y1, Y2, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_0, c_Orderings_Omax(c_Orderings_Omax(c_Orderings_Omax(v_f(v_xa), Y0, t_b), X1, t_b), X2, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_0, c_Orderings_Omax(c_Orderings_Omax(v_f(v_xa), X1, t_b), X2, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_0, c_Orderings_Omax(v_f(v_xa), X1, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_0, v_f(v_xa), t_b) -> true__ % 8.75/8.85 f3(true__, c_HOL_Oabs(v_a(v_xa), t_b), c_Orderings_Omax(c_Orderings_Omax(c_times(v_c, v_f(v_xa), t_b), X1, t_b), X2, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_HOL_Oabs(v_a(v_xa), t_b), c_Orderings_Omax(c_times(v_c, v_f(v_xa), t_b), X1, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, X1, t_b), v_f(v_xa), t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_HOL_Oabs(v_a(v_xa), t_b), c_times(v_c, v_f(v_xa), t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_times(Y0, v_f(v_xa), t_b), c_times(c_Orderings_Omax(Y0, X1, t_b), v_f(v_xa), t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_times(c_0, c_Orderings_Omax(c_0, Y2, t_b), t_b), c_times(v_f(v_xa), c_Orderings_Omax(c_0, Y2, t_b), t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_times(c_0, v_f(v_xa), t_b), c_Orderings_Omax(c_times(v_f(v_xa), v_f(v_xa), t_b), X1, t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_times(c_0, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_f(v_xa), X0, t_b), v_f(v_xa), t_b), t_b) -> true__ % 8.75/8.85 f3(true__, c_times(c_0, v_f(v_xa), t_b), c_times(v_f(v_xa), v_f(v_xa), t_b), t_b) -> true__ % 8.75/8.85 f4(f3(true__, c_Orderings_Omax(Y0, X1, t_b), Y3, t_b), t_b, Y0, Y3) -> true__ % 8.75/8.85 f4(f3(true__, c_Orderings_Omax(c_Orderings_Omax(Y0, X1, t_b), X2, t_b), Y3, t_b), t_b, Y0, Y3) -> true__ % 8.75/8.85 f4(f3(true__, c_Orderings_Omax(v_f(v_xa), X0, t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 8.75/8.85 f4(f3(true__, c_times(v_c, v_f(v_xa), t_b), Y3, t_b), t_b, c_HOL_Oabs(v_a(v_xa), t_b), Y3) -> true__ % 8.75/8.85 f4(f3(true__, c_times(v_f(v_xa), v_f(v_xa), t_b), Y3, t_b), t_b, c_times(c_0, v_f(v_xa), t_b), Y3) -> true__ % 8.75/8.85 f4(f3(true__, v_f(v_xa), Y3, t_b), t_b, c_0, Y3) -> true__ % 8.75/8.85 f4(true__, T_a, V_x, V_z) -> f3(f11(true__, T_a), V_x, V_z, T_a) % 8.75/8.85 f5(f3(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__ % 8.75/8.85 f5(true__, V_y, V_z, T_a, V_x) -> f4(f3(true__, V_y, V_z, T_a), T_a, V_x, V_z) % 8.75/8.85 f6(true__, V_a, V_c, T_a, V_b) -> f3(true__, c_times(V_a, V_c, T_a), c_times(V_b, V_c, T_a), T_a) % 8.75/8.85 f7(f3(true__, Y2, Y3, t_b), t_b, Y2, c_Orderings_Omax(c_0, X1, t_b), Y3) -> true__ % 8.75/8.85 f7(f3(true__, Y2, Y3, t_b), t_b, Y2, c_Orderings_Omax(c_Orderings_Omax(c_0, X1, t_b), X2, t_b), Y3) -> true__ % 8.75/8.85 f7(f3(true__, Y2, Y3, t_b), t_b, Y2, c_Orderings_Omax(v_f(v_xa), X0, t_b), Y3) -> true__ % 8.75/8.85 f7(f3(true__, Y2, Y3, t_b), t_b, Y2, v_f(v_xa), Y3) -> true__ % 8.75/8.85 f7(true__, T_a, V_a, V_c, V_b) -> f6(f10(true__, T_a), V_a, V_c, T_a, V_b) % 8.75/8.85 f8(f3(true__, c_0, Y0, Y1), Y2, Y3, Y1, Y0) -> true__ % 8.75/8.85 f8(true__, V_a, V_b, T_a, V_c) -> f7(f3(true__, V_a, V_b, T_a), T_a, V_a, V_c, V_b) % 8.75/8.85 f9(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 8.75/8.85 f9(true__, t_b) -> true__ % 8.75/8.85 true__ -> false__ % 8.75/8.85 with the LPO induced by % 8.75/8.85 v_ca > f8 > f7 > f6 > c_times > v_c > v_a > c_HOL_Oabs > f5 > f4 > f2 > c_lessequals > c_0 > class_Orderings_Olinorder > f9 > t_b > c_Orderings_Omax > f3 > v_xa > class_Ring__and__Field_Opordered__semiring > f10 > class_Orderings_Oorder > f11 > v_f > class_Ring__and__Field_Oordered__idom > f1 > true__ > false__ % 8.75/8.85 % 8.75/8.85 % SZS output end Proof % 8.75/8.85 %------------------------------------------------------------------------------