%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA015-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 19:15:34 EDT 2022 % Result : Unsatisfiable 15.25s 15.16s % Output : Proof 15.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : ANA015-2 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : moca.sh %s % 0.11/0.32 % Computer : n029.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Fri Jul 8 06:18:14 EDT 2022 % 0.11/0.32 % CPUTime : % 15.25/15.16 % SZS status Unsatisfiable % 15.25/15.16 % SZS output start Proof % 15.25/15.16 The input problem is unsatisfiable because % 15.25/15.16 % 15.25/15.16 [1] the following set of Horn clauses is unsatisfiable: % 15.25/15.16 % 15.25/15.16 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 15.25/15.16 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) % 15.25/15.16 class_Ring__and__Field_Oordered__idom(T_a) ==> c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a) % 15.25/15.16 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) % 15.25/15.16 c_lessequals(c_HOL_Oabs(v_g(V_U), t_a), c_times(v_d, c_HOL_Oabs(v_f(V_U), t_a), t_a), t_a) % 15.25/15.16 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(V_U)), t_a), t_a), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_a), t_a), t_a) ==> \bottom % 15.25/15.16 class_Ring__and__Field_Ofield(T) ==> class_OrderedGroup_Osemigroup__mult(T) % 15.25/15.16 class_Ring__and__Field_Oordered__field(T) ==> class_Ring__and__Field_Ofield(T) % 15.25/15.16 class_Ring__and__Field_Oordered__field(T) ==> class_Ring__and__Field_Oordered__idom(T) % 15.25/15.16 class_Ring__and__Field_Oordered__field(T) ==> class_Ring__and__Field_Opordered__semiring(T) % 15.25/15.16 class_Ring__and__Field_Oordered__field(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T) % 15.25/15.16 class_Ring__and__Field_Oordered__field(t_a) % 15.25/15.16 % 15.25/15.16 This holds because % 15.25/15.16 % 15.25/15.16 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 15.25/15.16 % 15.25/15.16 E: % 15.25/15.16 c_lessequals(c_HOL_Oabs(v_g(V_U), t_a), c_times(v_d, c_HOL_Oabs(v_f(V_U), t_a), t_a), t_a) = true__ % 15.25/15.16 class_Ring__and__Field_Oordered__field(t_a) = true__ % 15.25/15.16 f1(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) = true__ % 15.25/15.16 f1(true__, V_a, T_a) = c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 15.25/15.16 f10(class_Ring__and__Field_Oordered__field(T), T) = true__ % 15.25/15.16 f10(true__, T) = class_Ring__and__Field_Oordered__idom(T) % 15.25/15.16 f11(class_Ring__and__Field_Oordered__field(T), T) = true__ % 15.25/15.16 f11(true__, T) = class_Ring__and__Field_Opordered__semiring(T) % 15.25/15.16 f12(class_Ring__and__Field_Oordered__field(T), T) = true__ % 15.25/15.16 f12(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T) % 15.25/15.16 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) % 15.25/15.16 f2(true__, V_a, V_b, T_a, V_c) = c_times(c_times(V_a, V_b, T_a), V_c, T_a) % 15.25/15.16 f3(class_Ring__and__Field_Oordered__idom(T_a), V_a, V_b, T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a) % 15.25/15.16 f3(true__, V_a, V_b, T_a) = c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) % 15.25/15.16 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) % 15.25/15.16 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) % 15.25/15.16 f6(c_lessequals(c_0, V_c, T_a), V_a, V_b, T_a, V_c) = true__ % 15.25/15.16 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) % 15.25/15.16 f7(c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(V_U)), t_a), t_a), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_a), t_a), t_a)) = true__ % 15.25/15.16 f7(true__) = false__ % 15.25/15.16 f8(class_Ring__and__Field_Ofield(T), T) = true__ % 15.25/15.16 f8(true__, T) = class_OrderedGroup_Osemigroup__mult(T) % 15.25/15.16 f9(class_Ring__and__Field_Oordered__field(T), T) = true__ % 15.25/15.16 f9(true__, T) = class_Ring__and__Field_Ofield(T) % 15.25/15.16 G: % 15.25/15.16 true__ = false__ % 15.25/15.16 % 15.25/15.16 This holds because % 15.25/15.16 % 15.25/15.16 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 15.25/15.16 % 15.25/15.16 % 15.25/15.16 c_HOL_Oabs(c_times(Y1, Y2, t_a), t_a) -> c_times(c_HOL_Oabs(Y1, t_a), c_HOL_Oabs(Y2, t_a), t_a) % 15.25/15.16 c_lessequals(c_0, c_HOL_Oabs(Y1, t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_0, c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_0, c_times(c_HOL_Oabs(X0, t_a), c_times(c_HOL_Oabs(X1, t_a), c_HOL_Oabs(Y1, t_a), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_0, c_times(c_HOL_Oabs(X0, t_a), c_times(c_HOL_Oabs(X1, t_a), c_times(c_HOL_Oabs(Y1, t_a), c_HOL_Oabs(Y2, t_a), t_a), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_HOL_Oabs(v_g(V_U), t_a), c_times(v_d, c_HOL_Oabs(v_f(V_U), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_times(Y3, c_0, t_a), c_times(Y3, c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a), t_a), t_a) -> f5(true__, t_a, Y3, c_0, c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a)) % 15.25/15.16 c_lessequals(c_times(Y3, c_0, t_a), c_times(Y3, c_times(c_HOL_Oabs(X0, t_a), c_times(c_HOL_Oabs(X1, t_a), c_HOL_Oabs(X2, t_a), t_a), t_a), t_a), t_a) -> f5(true__, t_a, Y3, c_0, c_times(c_HOL_Oabs(X0, t_a), c_times(c_HOL_Oabs(X1, t_a), c_HOL_Oabs(X2, t_a), t_a), t_a)) % 15.25/15.16 c_lessequals(c_times(Y3, c_HOL_Oabs(v_g(X0), t_a), t_a), c_times(Y3, c_times(v_d, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a), t_a) -> f5(true__, t_a, Y3, c_HOL_Oabs(v_g(X0), t_a), c_times(v_d, c_HOL_Oabs(v_f(X0), t_a), t_a)) % 15.25/15.16 c_lessequals(c_times(c_HOL_Oabs(X2, t_a), c_0, t_a), c_times(c_HOL_Oabs(X2, t_a), c_HOL_Oabs(Y0, t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_times(c_HOL_Oabs(Y2, t_a), c_0, t_a), c_times(c_HOL_Oabs(Y2, t_a), c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_times(c_HOL_Oabs(Y2, t_a), c_0, t_a), c_times(c_HOL_Oabs(Y2, t_a), c_times(c_HOL_Oabs(X0, t_a), c_times(c_HOL_Oabs(X1, t_a), c_HOL_Oabs(X2, t_a), t_a), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_times(c_HOL_Oabs(Y2, t_a), c_HOL_Oabs(v_g(X0), t_a), t_a), c_times(c_HOL_Oabs(Y2, t_a), c_times(v_d, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_times(c_HOL_Oabs(Y2, t_a), c_times(c_HOL_Oabs(Y3, t_a), c_0, t_a), t_a), c_times(c_HOL_Oabs(Y2, t_a), c_times(c_HOL_Oabs(Y3, t_a), c_HOL_Oabs(X0, t_a), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_times(c_HOL_Oabs(Y2, t_a), c_times(c_HOL_Oabs(Y3, t_a), c_0, t_a), t_a), c_times(c_HOL_Oabs(Y2, t_a), c_times(c_HOL_Oabs(Y3, t_a), c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_lessequals(c_times(c_HOL_Oabs(Y2, t_a), c_times(c_HOL_Oabs(Y3, t_a), c_HOL_Oabs(v_g(X0), t_a), t_a), t_a), c_times(c_HOL_Oabs(Y2, t_a), c_times(c_HOL_Oabs(Y3, t_a), c_times(v_d, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a), t_a), t_a) -> true__ % 15.25/15.16 c_times(c_times(Y1, Y2, t_a), Y3, t_a) -> c_times(Y1, c_times(Y2, Y3, t_a), t_a) % 15.25/15.16 class_OrderedGroup_Olordered__ab__group__abs(T) -> f12(true__, T) % 15.25/15.16 class_OrderedGroup_Osemigroup__mult(t_a) -> true__ % 15.25/15.16 class_Ring__and__Field_Ofield(T) -> f9(true__, T) % 15.25/15.16 class_Ring__and__Field_Oordered__field(t_a) -> true__ % 15.25/15.16 class_Ring__and__Field_Oordered__idom(T) -> f10(true__, T) % 15.25/15.16 class_Ring__and__Field_Opordered__semiring(T) -> f11(true__, T) % 15.25/15.16 f1(f12(true__, Y0), Y1, Y0) -> true__ % 15.25/15.16 f1(true__, V_a, T_a) -> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 15.25/15.16 f10(class_Ring__and__Field_Oordered__field(T), T) -> true__ % 15.25/15.16 f10(true__, t_a) -> true__ % 15.25/15.16 f11(class_Ring__and__Field_Oordered__field(T), T) -> true__ % 15.25/15.16 f11(true__, t_a) -> true__ % 15.25/15.16 f12(class_Ring__and__Field_Oordered__field(T), T) -> true__ % 15.25/15.16 f12(true__, t_a) -> true__ % 15.25/15.16 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) % 15.25/15.16 f2(true__, V_a, V_b, T_a, V_c) -> c_times(c_times(V_a, V_b, T_a), V_c, T_a) % 15.25/15.16 f3(f10(true__, Y0), Y1, Y2, Y0) -> c_times(c_HOL_Oabs(Y1, Y0), c_HOL_Oabs(Y2, Y0), Y0) % 15.25/15.16 f3(true__, V_a, V_b, T_a) -> c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) % 15.25/15.16 f4(class_Ring__and__Field_Opordered__semiring(T_a), V_c, V_a, T_a, V_b) -> f5(true__, T_a, V_c, V_a, V_b) % 15.25/15.16 f4(f11(true__, Y0), Y1, Y2, Y0, Y3) -> f5(true__, Y0, Y1, Y2, Y3) % 15.25/15.16 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) % 15.25/15.16 f4(true__, Y3, c_0, t_a, c_HOL_Oabs(X0, t_a)) -> f5(true__, t_a, Y3, c_0, c_HOL_Oabs(X0, t_a)) % 15.25/15.16 f5(c_lessequals(Y0, Y1, t_a), t_a, c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a), Y0, Y1) -> true__ % 15.25/15.16 f5(c_lessequals(Y0, Y1, t_a), t_a, c_times(c_HOL_Oabs(X0, t_a), c_times(c_HOL_Oabs(X1, t_a), c_HOL_Oabs(Y3, t_a), t_a), t_a), Y0, Y1) -> true__ % 15.25/15.16 f5(c_lessequals(Y2, Y3, t_a), t_a, c_HOL_Oabs(X0, t_a), Y2, Y3) -> true__ % 15.25/15.16 f5(true__, t_a, c_HOL_Oabs(Y2, t_a), c_0, c_HOL_Oabs(X0, t_a)) -> true__ % 15.25/15.16 f5(true__, t_a, c_HOL_Oabs(Y2, t_a), c_0, c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a)) -> true__ % 15.25/15.16 f5(true__, t_a, c_HOL_Oabs(Y2, t_a), c_HOL_Oabs(v_g(X0), t_a), c_times(v_d, c_HOL_Oabs(v_f(X0), t_a), t_a)) -> true__ % 15.25/15.16 f5(true__, t_a, c_times(c_HOL_Oabs(Y2, t_a), c_HOL_Oabs(Y3, t_a), t_a), c_0, c_HOL_Oabs(X0, t_a)) -> true__ % 15.25/15.16 f6(c_lessequals(c_0, V_c, T_a), V_a, V_b, T_a, V_c) -> true__ % 15.25/15.16 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) % 15.25/15.16 f6(true__, Y0, Y1, t_a, c_times(c_HOL_Oabs(X0, t_a), c_times(c_HOL_Oabs(X1, t_a), c_times(c_HOL_Oabs(Y3, t_a), c_HOL_Oabs(Y4, t_a), t_a), t_a), t_a)) -> true__ % 15.25/15.16 f7(c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(Y0)), t_a), t_a), c_times(Y0, c_HOL_Oabs(v_f(v_x(Y0)), t_a), t_a), t_a)) -> true__ % 15.25/15.16 f7(c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(X0, X1, t_a))), t_a), t_a), c_times(X0, c_times(X1, c_HOL_Oabs(v_f(v_x(c_times(X0, X1, t_a))), t_a), t_a), t_a), t_a)) -> true__ % 15.25/15.16 f7(true__) -> false__ % 15.25/15.16 f8(f9(true__, Y0), Y0) -> true__ % 15.25/15.16 f8(true__, T) -> class_OrderedGroup_Osemigroup__mult(T) % 15.25/15.16 f9(class_Ring__and__Field_Oordered__field(T), T) -> true__ % 15.25/15.16 f9(true__, t_a) -> true__ % 15.25/15.16 false__ -> true__ % 15.25/15.16 with the LPO induced by % 15.25/15.16 v_x > v_c > c_HOL_Oinverse > v_g > v_f > v_d > t_a > class_Ring__and__Field_Oordered__idom > f1 > f4 > f3 > f2 > c_HOL_Oabs > c_times > f6 > f5 > c_lessequals > f8 > class_OrderedGroup_Osemigroup__mult > f10 > c_0 > f7 > class_Ring__and__Field_Opordered__semiring > f11 > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Ofield > f9 > class_OrderedGroup_Olordered__ab__group__abs > f12 > false__ > true__ % 15.25/15.16 % 15.25/15.16 % SZS output end Proof % 15.25/15.16 %------------------------------------------------------------------------------