TSTP Solution File: ANA038-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : ANA038-2 : 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 19:15:50 EDT 2022
% Result : Unsatisfiable 8.83s 8.79s
% Output : Proof 8.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA038-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n018.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 05:32:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 8.83/8.79 % SZS status Unsatisfiable
% 8.83/8.79 % SZS output start Proof
% 8.83/8.79 The input problem is unsatisfiable because
% 8.83/8.79
% 8.83/8.79 [1] the following set of Horn clauses is unsatisfiable:
% 8.83/8.79
% 8.83/8.79 c_lessequals(c_0, v_g(v_xa), t_b)
% 8.83/8.79 c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(v_ca, v_g(v_xa), t_b), t_b)
% 8.83/8.79 c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), t_b) ==> \bottom
% 8.83/8.79 class_Ring__and__Field_Oordered__idom(t_b)
% 8.83/8.79 class_Orderings_Olinorder(T_b) ==> c_lessequals(V_y, c_Orderings_Omax(V_x, V_y, T_b), T_b)
% 8.83/8.79 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)
% 8.83/8.79 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)
% 8.83/8.79 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Olinorder(T)
% 8.83/8.79 class_Ring__and__Field_Oordered__idom(T) ==> class_Ring__and__Field_Opordered__semiring(T)
% 8.83/8.79 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Oorder(T)
% 8.83/8.79
% 8.83/8.79 This holds because
% 8.83/8.79
% 8.83/8.79 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.83/8.79
% 8.83/8.79 E:
% 8.83/8.79 c_lessequals(c_0, v_g(v_xa), t_b) = true__
% 8.83/8.79 c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(v_ca, v_g(v_xa), t_b), t_b) = true__
% 8.83/8.79 class_Ring__and__Field_Oordered__idom(t_b) = true__
% 8.83/8.79 f1(c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), t_b)) = true__
% 8.83/8.79 f1(true__) = false__
% 8.83/8.79 f10(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 8.83/8.79 f10(true__, T) = class_Ring__and__Field_Opordered__semiring(T)
% 8.83/8.79 f11(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 8.83/8.79 f11(true__, T) = class_Orderings_Oorder(T)
% 8.83/8.79 f2(class_Orderings_Olinorder(T_b), V_y, V_x, T_b) = true__
% 8.83/8.79 f2(true__, V_y, V_x, T_b) = c_lessequals(V_y, c_Orderings_Omax(V_x, V_y, T_b), T_b)
% 8.83/8.79 f3(true__, V_x, V_z, T_a) = c_lessequals(V_x, V_z, T_a)
% 8.83/8.79 f4(true__, T_a, V_x, V_z) = f3(class_Orderings_Oorder(T_a), V_x, V_z, T_a)
% 8.83/8.79 f5(c_lessequals(V_x, V_y, T_a), V_y, V_z, T_a, V_x) = true__
% 8.83/8.79 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)
% 8.83/8.79 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)
% 8.83/8.79 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)
% 8.83/8.79 f8(c_lessequals(c_0, V_c, T_a), V_a, V_b, T_a, V_c) = true__
% 8.83/8.79 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)
% 8.83/8.79 f9(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 8.83/8.79 f9(true__, T) = class_Orderings_Olinorder(T)
% 8.83/8.79 G:
% 8.83/8.79 true__ = false__
% 8.83/8.79
% 8.83/8.79 This holds because
% 8.83/8.79
% 8.83/8.79 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.83/8.79
% 8.83/8.79
% 8.83/8.79 c_lessequals(V_x, V_z, T_a) -> f3(true__, V_x, V_z, T_a)
% 8.83/8.79 class_Orderings_Olinorder(T) -> f9(true__, T)
% 8.83/8.79 class_Orderings_Oorder(T) -> f11(true__, T)
% 8.83/8.79 class_Ring__and__Field_Oordered__idom(t_b) -> true__
% 8.83/8.79 class_Ring__and__Field_Opordered__semiring(T) -> f10(true__, T)
% 8.83/8.79 f1(f3(true__, c_HOL_Oabs(v_b(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), t_b)) -> true__
% 8.83/8.79 f1(true__) -> false__
% 8.83/8.79 f10(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 8.83/8.79 f10(true__, t_b) -> true__
% 8.83/8.79 f11(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 8.83/8.79 f11(true__, t_b) -> true__
% 8.83/8.79 f2(f9(true__, Y0), Y1, Y2, Y0) -> true__
% 8.83/8.79 f2(true__, V_y, V_x, T_b) -> f3(true__, V_y, c_Orderings_Omax(V_x, V_y, T_b), T_b)
% 8.83/8.79 f3(true__, Y1, c_Orderings_Omax(X1, c_Orderings_Omax(X2, c_Orderings_Omax(Y0, Y1, t_b), t_b), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, Y1, c_Orderings_Omax(X1, c_Orderings_Omax(Y0, Y1, t_b), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, Y1, c_Orderings_Omax(Y2, Y1, t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_0, c_Orderings_Omax(X1, c_Orderings_Omax(X2, c_Orderings_Omax(Y0, v_g(v_xa), t_b), t_b), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_0, c_Orderings_Omax(X1, c_Orderings_Omax(X2, v_g(v_xa), t_b), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_0, c_Orderings_Omax(X1, v_g(v_xa), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_0, v_g(v_xa), t_b) -> true__
% 8.83/8.79 f3(true__, c_HOL_Oabs(v_b(v_xa), t_b), c_Orderings_Omax(X1, c_Orderings_Omax(X2, c_times(v_ca, v_g(v_xa), t_b), t_b), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_HOL_Oabs(v_b(v_xa), t_b), c_Orderings_Omax(X1, c_times(v_ca, v_g(v_xa), t_b), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_HOL_Oabs(v_b(v_xa), t_b), c_times(c_Orderings_Omax(X1, v_ca, t_b), v_g(v_xa), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_HOL_Oabs(v_b(v_xa), t_b), c_times(v_ca, v_g(v_xa), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_times(Y0, v_g(v_xa), t_b), c_times(c_Orderings_Omax(X1, Y0, t_b), v_g(v_xa), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_times(c_0, c_Orderings_Omax(Y2, c_0, t_b), t_b), c_times(v_g(v_xa), c_Orderings_Omax(Y2, c_0, t_b), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_times(c_0, v_g(v_xa), t_b), c_Orderings_Omax(X1, c_times(v_g(v_xa), v_g(v_xa), t_b), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_times(c_0, v_g(v_xa), t_b), c_times(c_Orderings_Omax(X0, v_g(v_xa), t_b), v_g(v_xa), t_b), t_b) -> true__
% 8.83/8.79 f3(true__, c_times(c_0, v_g(v_xa), t_b), c_times(v_g(v_xa), v_g(v_xa), t_b), t_b) -> true__
% 8.83/8.79 f4(f3(true__, c_Orderings_Omax(X0, v_g(v_xa), t_b), Y3, t_b), t_b, c_0, Y3) -> true__
% 8.83/8.79 f4(f3(true__, c_Orderings_Omax(X1, Y0, t_b), Y3, t_b), t_b, Y0, Y3) -> true__
% 8.83/8.79 f4(f3(true__, c_Orderings_Omax(X1, c_Orderings_Omax(X2, Y0, t_b), t_b), Y3, t_b), t_b, Y0, Y3) -> true__
% 8.83/8.79 f4(f3(true__, c_times(v_ca, v_g(v_xa), t_b), Y3, t_b), t_b, c_HOL_Oabs(v_b(v_xa), t_b), Y3) -> true__
% 8.83/8.79 f4(f3(true__, c_times(v_g(v_xa), v_g(v_xa), t_b), Y3, t_b), t_b, c_times(c_0, v_g(v_xa), t_b), Y3) -> true__
% 8.83/8.79 f4(f3(true__, v_g(v_xa), Y3, t_b), t_b, c_0, Y3) -> true__
% 8.83/8.79 f4(true__, T_a, V_x, V_z) -> f3(f11(true__, T_a), V_x, V_z, T_a)
% 8.83/8.79 f5(f3(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__
% 8.83/8.79 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)
% 8.83/8.79 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)
% 8.83/8.79 f7(f3(true__, Y2, Y3, t_b), t_b, Y2, c_Orderings_Omax(X0, v_g(v_xa), t_b), Y3) -> true__
% 8.83/8.79 f7(f3(true__, Y2, Y3, t_b), t_b, Y2, c_Orderings_Omax(X1, c_0, t_b), Y3) -> true__
% 8.83/8.79 f7(f3(true__, Y2, Y3, t_b), t_b, Y2, c_Orderings_Omax(X1, c_Orderings_Omax(X2, c_0, t_b), t_b), Y3) -> true__
% 8.83/8.79 f7(f3(true__, Y2, Y3, t_b), t_b, Y2, v_g(v_xa), Y3) -> true__
% 8.83/8.79 f7(true__, T_a, V_a, V_c, V_b) -> f6(f10(true__, T_a), V_a, V_c, T_a, V_b)
% 8.83/8.79 f8(f3(true__, c_0, Y0, Y1), Y2, Y3, Y1, Y0) -> true__
% 8.83/8.79 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)
% 8.83/8.79 f9(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 8.83/8.79 f9(true__, t_b) -> true__
% 8.83/8.79 true__ -> false__
% 8.83/8.79 with the LPO induced by
% 8.83/8.79 v_c > f8 > f7 > f6 > c_times > v_ca > v_b > 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_g > class_Ring__and__Field_Oordered__idom > f1 > true__ > false__
% 8.83/8.79
% 8.83/8.79 % SZS output end Proof
% 8.83/8.79
%------------------------------------------------------------------------------