%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA032-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.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 19:15:46 EDT 2022 % Result : Unsatisfiable 279.94s 279.86s % Output : Proof 279.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : ANA032-2 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.13 % Command : moca.sh %s % 0.13/0.33 % Computer : n003.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Fri Jul 8 05:11:42 EDT 2022 % 0.18/0.34 % CPUTime : % 279.94/279.86 % SZS status Unsatisfiable % 279.94/279.86 % SZS output start Proof % 279.94/279.86 The input problem is unsatisfiable because % 279.94/279.86 % 279.94/279.86 [1] the following set of Horn clauses is unsatisfiable: % 279.94/279.86 % 279.94/279.86 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 279.94/279.86 class_OrderedGroup_Osemigroup__mult(T_a) ==> c_times(c_times(V_a, V_b, T_a), V_c, T_a) = c_times(V_a, c_times(V_b, V_c, T_a), T_a) % 279.94/279.86 class_OrderedGroup_Oab__semigroup__mult(T_a) ==> c_times(V_a, V_b, T_a) = c_times(V_b, V_a, T_a) % 279.94/279.86 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_c, V_a, T_a), c_times(V_c, V_b, T_a), T_a) % 279.94/279.86 c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b) % 279.94/279.86 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_c, c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b) ==> \bottom % 279.94/279.86 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Oab__semigroup__mult(T) % 279.94/279.86 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Osemigroup__mult(T) % 279.94/279.86 class_Ring__and__Field_Oordered__idom(T) ==> class_Ring__and__Field_Opordered__semiring(T) % 279.94/279.86 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T) % 279.94/279.86 class_Ring__and__Field_Oordered__idom(t_b) % 279.94/279.86 % 279.94/279.86 This holds because % 279.94/279.86 % 279.94/279.86 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 279.94/279.86 % 279.94/279.86 E: % 279.94/279.86 c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b) = true__ % 279.94/279.86 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 279.94/279.86 f1(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) = true__ % 279.94/279.86 f1(true__, V_a, T_a) = c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 279.94/279.86 f10(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 279.94/279.86 f10(true__, T) = class_Ring__and__Field_Opordered__semiring(T) % 279.94/279.86 f11(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 279.94/279.86 f11(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T) % 279.94/279.86 f2(class_OrderedGroup_Osemigroup__mult(T_a), V_a, V_b, T_a, V_c) = c_times(V_a, c_times(V_b, V_c, T_a), T_a) % 279.94/279.86 f2(true__, V_a, V_b, T_a, V_c) = c_times(c_times(V_a, V_b, T_a), V_c, T_a) % 279.94/279.86 f3(class_OrderedGroup_Oab__semigroup__mult(T_a), V_a, V_b, T_a) = c_times(V_b, V_a, T_a) % 279.94/279.86 f3(true__, V_a, V_b, T_a) = c_times(V_a, V_b, T_a) % 279.94/279.86 f4(true__, V_c, V_a, T_a, V_b) = c_lessequals(c_times(V_c, V_a, T_a), c_times(V_c, V_b, T_a), T_a) % 279.94/279.86 f5(true__, T_a, V_c, V_a, V_b) = f4(class_Ring__and__Field_Opordered__semiring(T_a), V_c, V_a, T_a, V_b) % 279.94/279.86 f6(c_lessequals(c_0, V_c, T_a), V_a, V_b, T_a, V_c) = true__ % 279.94/279.86 f6(true__, V_a, V_b, T_a, V_c) = f5(c_lessequals(V_a, V_b, T_a), T_a, V_c, V_a, V_b) % 279.94/279.86 f7(c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_c, c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)) = true__ % 279.94/279.86 f7(true__) = false__ % 279.94/279.86 f8(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 279.94/279.86 f8(true__, T) = class_OrderedGroup_Oab__semigroup__mult(T) % 279.94/279.86 f9(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 279.94/279.86 f9(true__, T) = class_OrderedGroup_Osemigroup__mult(T) % 279.94/279.86 G: % 279.94/279.86 true__ = false__ % 279.94/279.86 % 279.94/279.86 This holds because % 279.94/279.86 % 279.94/279.86 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 279.94/279.86 % 279.94/279.86 f3(true__, Y0, f3(true__, Y2, Y1, t_b), t_b) = f3(true__, Y0, f3(true__, Y1, Y2, t_b), t_b) % 279.94/279.86 f3(true__, Y1, Y2, t_b) = f3(true__, Y2, Y1, t_b) % 279.94/279.86 f3(true__, Y1, f3(true__, Y0, Y2, t_b), t_b) = f3(true__, Y0, f3(true__, Y1, Y2, t_b), t_b) % 279.94/279.86 f3(true__, Y2, f3(true__, Y0, Y1, t_b), t_b) = f3(true__, Y0, f3(true__, Y1, Y2, t_b), t_b) % 279.94/279.86 f3(true__, Y2, f3(true__, Y0, Y1, t_b), t_b) = f3(true__, Y1, f3(true__, Y0, Y2, t_b), t_b) % 279.94/279.86 c_lessequals(c_0, c_HOL_Oabs(Y1, t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), f3(true__, v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_0, c_HOL_Oabs(Y0, t_b), t_b), f3(true__, c_HOL_Oabs(Y1, t_b), c_HOL_Oabs(Y0, t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_0, c_HOL_Oabs(Y2, t_b), t_b), f3(true__, c_HOL_Oabs(Y2, t_b), c_HOL_Oabs(X0, t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_0, f3(true__, c_HOL_Oabs(Y0, t_b), c_HOL_Oabs(Y1, t_b), t_b), t_b), f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(Y1, t_b), c_HOL_Oabs(Y0, t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_0, f3(true__, c_HOL_Oabs(Y1, t_b), c_HOL_Oabs(Y0, t_b), t_b), t_b), f3(true__, c_HOL_Oabs(Y0, t_b), f3(true__, c_HOL_Oabs(Y1, t_b), c_HOL_Oabs(Y2, t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_0, f3(true__, c_HOL_Oabs(Y2, t_b), c_HOL_Oabs(X0, t_b), t_b), t_b), f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(X0, t_b), c_HOL_Oabs(X1, t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_0, f3(true__, c_HOL_Oabs(Y2, t_b), c_HOL_Oabs(X0, t_b), t_b), t_b), f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(X1, t_b), c_HOL_Oabs(X0, t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_0, f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(X0, t_b), c_HOL_Oabs(X1, t_b), t_b), t_b), t_b), f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(X0, t_b), f3(true__, c_HOL_Oabs(X1, t_b), c_HOL_Oabs(X2, t_b), t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_0, f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(X0, t_b), c_HOL_Oabs(X1, t_b), t_b), t_b), t_b), f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(X0, t_b), f3(true__, c_HOL_Oabs(X2, t_b), c_HOL_Oabs(X1, t_b), t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_HOL_Oabs(Y0, t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), f3(true__, v_c, f3(true__, c_HOL_Oabs(v_g(v_x), t_b), c_HOL_Oabs(Y0, t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_HOL_Oabs(Y2, t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), f3(true__, v_c, f3(true__, c_HOL_Oabs(Y2, t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(X0, t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), t_b), f3(true__, v_c, f3(true__, c_HOL_Oabs(Y2, t_b), f3(true__, c_HOL_Oabs(X0, t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_lessequals(f3(true__, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(Y0, t_b), t_b), f3(true__, v_c, f3(true__, c_HOL_Oabs(Y0, t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b) -> true__ % 279.94/279.86 c_times(V_a, V_b, T_a) -> f3(true__, V_a, V_b, T_a) % 279.94/279.86 c_times(c_times(Y0, Y2, t_b), Y1, t_b) -> f3(true__, Y2, f3(true__, Y0, Y1, t_b), t_b) % 279.94/279.86 class_OrderedGroup_Oab__semigroup__mult(T) -> f8(true__, T) % 279.94/279.86 class_OrderedGroup_Olordered__ab__group__abs(t_b) -> true__ % 279.94/279.86 class_OrderedGroup_Osemigroup__mult(T) -> f9(true__, T) % 279.94/279.86 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 279.94/279.86 class_Ring__and__Field_Opordered__semiring(T) -> f10(true__, T) % 279.94/279.86 f1(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) -> true__ % 279.94/279.86 f1(true__, V_a, T_a) -> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 279.94/279.86 f10(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 279.94/279.86 f10(true__, t_b) -> true__ % 279.94/279.86 f11(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 279.94/279.86 f11(true__, T) -> class_OrderedGroup_Olordered__ab__group__abs(T) % 279.94/279.86 f2(f9(true__, Y0), Y1, Y2, Y0, Y3) -> f3(true__, Y1, f3(true__, Y2, Y3, Y0), Y0) % 279.94/279.86 f2(true__, Y0, Y1, Y2, Y3) -> f3(true__, f3(true__, Y0, Y1, Y2), Y3, Y2) % 279.94/279.86 f3(f8(true__, T_a), V_a, V_b, T_a) -> f3(true__, V_b, V_a, T_a) % 279.94/279.86 f3(true__, f3(true__, Y1, Y2, t_b), Y3, t_b) -> f3(true__, Y1, f3(true__, Y2, Y3, t_b), t_b) % 279.94/279.86 f4(true__, V_c, V_a, T_a, V_b) -> c_lessequals(f3(true__, V_c, V_a, T_a), f3(true__, V_c, V_b, T_a), T_a) % 279.94/279.86 f5(c_lessequals(Y2, Y3, t_b), t_b, c_HOL_Oabs(X0, t_b), Y2, Y3) -> true__ % 279.94/279.86 f5(true__, T_a, V_c, V_a, V_b) -> f4(f10(true__, T_a), V_c, V_a, T_a, V_b) % 279.94/279.86 f6(c_lessequals(c_0, V_c, T_a), V_a, V_b, T_a, V_c) -> true__ % 279.94/279.86 f6(true__, V_a, V_b, T_a, V_c) -> f5(c_lessequals(V_a, V_b, T_a), T_a, V_c, V_a, V_b) % 279.94/279.86 f7(c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_c, c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)) -> true__ % 279.94/279.86 f7(c_lessequals(f3(true__, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), f3(true__, v_c, f3(true__, c_HOL_Oabs(v_g(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), t_b)) -> true__ % 279.94/279.86 f7(true__) -> false__ % 279.94/279.86 f8(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 279.94/279.86 f8(true__, t_b) -> true__ % 279.94/279.86 f9(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 279.94/279.86 f9(true__, t_b) -> true__ % 279.94/279.86 false__ -> true__ % 279.94/279.86 with the LPO induced by % 279.94/279.86 v_f > class_OrderedGroup_Oab__semigroup__mult > f8 > v_g > v_c > v_x > v_b > f1 > f6 > f5 > f11 > c_HOL_Oabs > class_Ring__and__Field_Opordered__semiring > f10 > class_OrderedGroup_Olordered__ab__group__abs > f7 > f4 > c_times > f2 > class_OrderedGroup_Osemigroup__mult > f9 > f3 > c_lessequals > c_0 > class_Ring__and__Field_Oordered__idom > t_b > false__ > true__ % 279.94/279.86 % 279.94/279.86 % SZS output end Proof % 279.94/279.86 %------------------------------------------------------------------------------