TSTP Solution File: ANA039-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 15.15s 15.08s
% Output : Proof 15.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 06:07:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 15.15/15.08 % SZS status Unsatisfiable
% 15.15/15.08 % SZS output start Proof
% 15.15/15.08 The input problem is unsatisfiable because
% 15.15/15.08
% 15.15/15.08 [1] the following set of Horn clauses is unsatisfiable:
% 15.15/15.08
% 15.15/15.08 c_lessequals(c_HOL_Oabs(v_h(V_U), t_a), c_times(v_c, c_HOL_Oabs(v_f(V_U), t_a), t_a), t_a)
% 15.15/15.08 c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a) ==> \bottom
% 15.15/15.08 class_Ring__and__Field_Oordered__idom(t_a)
% 15.15/15.08 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_lessequals(V_a, c_HOL_Oabs(V_a, T_a), T_a)
% 15.15/15.08 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a)
% 15.15/15.08 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)
% 15.15/15.08 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)
% 15.15/15.08 class_Ring__and__Field_Oordered__idom(T) ==> class_Ring__and__Field_Opordered__semiring(T)
% 15.15/15.08 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Oorder(T)
% 15.15/15.08 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T)
% 15.15/15.08
% 15.15/15.08 This holds because
% 15.15/15.08
% 15.15/15.08 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 15.15/15.08
% 15.15/15.08 E:
% 15.15/15.08 c_lessequals(c_HOL_Oabs(v_h(V_U), t_a), c_times(v_c, c_HOL_Oabs(v_f(V_U), t_a), t_a), t_a) = true__
% 15.15/15.08 class_Ring__and__Field_Oordered__idom(t_a) = true__
% 15.15/15.08 f1(c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a)) = true__
% 15.15/15.08 f1(true__) = false__
% 15.15/15.08 f10(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 15.15/15.08 f10(true__, T) = class_Ring__and__Field_Opordered__semiring(T)
% 15.15/15.08 f11(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 15.15/15.08 f11(true__, T) = class_Orderings_Oorder(T)
% 15.15/15.08 f12(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 15.15/15.08 f12(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T)
% 15.15/15.08 f2(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) = true__
% 15.15/15.08 f2(true__, V_a, T_a) = c_lessequals(V_a, c_HOL_Oabs(V_a, T_a), T_a)
% 15.15/15.08 f3(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) = true__
% 15.15/15.08 f3(true__, V_a, T_a) = c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a)
% 15.15/15.08 f4(true__, V_x, V_z, T_a) = c_lessequals(V_x, V_z, T_a)
% 15.15/15.08 f5(true__, T_a, V_x, V_z) = f4(class_Orderings_Oorder(T_a), V_x, V_z, T_a)
% 15.15/15.08 f6(c_lessequals(V_x, V_y, T_a), V_y, V_z, T_a, V_x) = true__
% 15.15/15.08 f6(true__, V_y, V_z, T_a, V_x) = f5(c_lessequals(V_y, V_z, T_a), T_a, V_x, V_z)
% 15.15/15.08 f7(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)
% 15.15/15.08 f8(true__, T_a, V_a, V_c, V_b) = f7(class_Ring__and__Field_Opordered__semiring(T_a), V_a, V_c, T_a, V_b)
% 15.15/15.08 f9(c_lessequals(c_0, V_c, T_a), V_a, V_b, T_a, V_c) = true__
% 15.15/15.08 f9(true__, V_a, V_b, T_a, V_c) = f8(c_lessequals(V_a, V_b, T_a), T_a, V_a, V_c, V_b)
% 15.15/15.08 G:
% 15.15/15.08 true__ = false__
% 15.15/15.08
% 15.15/15.08 This holds because
% 15.15/15.08
% 15.15/15.08 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 15.15/15.08
% 15.15/15.08
% 15.15/15.08 c_lessequals(V_x, V_z, T_a) -> f4(true__, V_x, V_z, T_a)
% 15.15/15.08 class_OrderedGroup_Olordered__ab__group__abs(T) -> f12(true__, T)
% 15.15/15.08 class_Orderings_Oorder(T) -> f11(true__, T)
% 15.15/15.08 class_Ring__and__Field_Oordered__idom(t_a) -> true__
% 15.15/15.08 class_Ring__and__Field_Opordered__semiring(T) -> f10(true__, T)
% 15.15/15.08 f1(f4(true__, c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a)) -> true__
% 15.15/15.08 f1(true__) -> false__
% 15.15/15.08 f10(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 15.15/15.08 f10(true__, t_a) -> true__
% 15.15/15.08 f11(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 15.15/15.08 f11(true__, t_a) -> true__
% 15.15/15.08 f12(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 15.15/15.08 f12(true__, t_a) -> true__
% 15.15/15.08 f2(f12(true__, Y0), Y1, Y0) -> true__
% 15.15/15.08 f2(true__, V_a, T_a) -> f4(true__, V_a, c_HOL_Oabs(V_a, T_a), T_a)
% 15.15/15.08 f3(f12(true__, Y0), Y1, Y0) -> true__
% 15.15/15.08 f3(true__, V_a, T_a) -> f4(true__, c_0, c_HOL_Oabs(V_a, T_a), T_a)
% 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, Y1, c_HOL_Oabs(Y1, t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_0, c_HOL_Oabs(Y1, t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_0, c_times(c_HOL_Oabs(c_HOL_Oabs(v_c, t_a), t_a), c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_0, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_0, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_HOL_Oabs(v_h(Y0), t_a), c_HOL_Oabs(c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_HOL_Oabs(v_h(Y0), t_a), c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_HOL_Oabs(v_h(Y0), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_HOL_Oabs(v_h(Y0), t_a), c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_times(Y0, c_HOL_Oabs(Y2, t_a), t_a), c_times(c_HOL_Oabs(Y0, t_a), c_HOL_Oabs(Y2, t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, c_times(c_0, c_HOL_Oabs(Y2, t_a), t_a), c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(Y2, t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, v_h(X0), c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, v_h(X0), c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, v_h(Y0), c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, v_h(Y0), c_HOL_Oabs(c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a), t_a), t_a) -> true__
% 15.15/15.08 f4(true__, v_h(Y0), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__
% 15.15/15.08 f5(f4(true__, c_HOL_Oabs(X0, t_a), Y3, t_a), t_a, c_0, Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_HOL_Oabs(Y0, t_a), Y3, t_a), t_a, Y0, Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), Y3, t_a), t_a, Y0, Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), Y3, t_a), t_a, Y0, Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a), Y3, t_a), t_a, Y0, Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a), Y3, t_a), t_a, v_h(X0), Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, c_0, Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, v_h(X0), Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, c_0, Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, c_HOL_Oabs(v_h(X0), t_a), Y3) -> true__
% 15.15/15.08 f5(f4(true__, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, v_h(X0), Y3) -> true__
% 15.15/15.08 f5(true__, T_a, V_x, V_z) -> f4(f11(true__, T_a), V_x, V_z, T_a)
% 15.15/15.08 f6(f4(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__
% 15.15/15.08 f6(true__, V_y, V_z, T_a, V_x) -> f5(f4(true__, V_y, V_z, T_a), T_a, V_x, V_z)
% 15.15/15.08 f7(true__, V_a, V_c, T_a, V_b) -> f4(true__, c_times(V_a, V_c, T_a), c_times(V_b, V_c, T_a), T_a)
% 15.15/15.08 f8(f4(true__, Y2, Y3, t_a), t_a, Y2, c_HOL_Oabs(X0, t_a), Y3) -> true__
% 15.15/15.08 f8(f4(true__, Y2, Y3, t_a), t_a, Y2, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(X0), t_a), t_a), Y3) -> true__
% 15.15/15.08 f8(f4(true__, Y2, Y3, t_a), t_a, Y2, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), Y3) -> true__
% 15.15/15.08 f8(true__, T_a, V_a, V_c, V_b) -> f7(f10(true__, T_a), V_a, V_c, T_a, V_b)
% 15.15/15.08 f9(f4(true__, c_0, Y0, Y1), Y2, Y3, Y1, Y0) -> true__
% 15.15/15.08 f9(true__, V_a, V_b, T_a, V_c) -> f8(f4(true__, V_a, V_b, T_a), T_a, V_a, V_c, V_b)
% 15.15/15.08 false__ -> true__
% 15.15/15.08 with the LPO induced by
% 15.15/15.08 v_x > v_h > class_OrderedGroup_Olordered__ab__group__abs > f12 > t_a > f3 > c_0 > f9 > f6 > f5 > f2 > f8 > f7 > c_lessequals > class_Orderings_Oorder > class_Ring__and__Field_Opordered__semiring > f10 > f11 > c_times > f1 > f4 > v_f > v_c > class_Ring__and__Field_Oordered__idom > c_HOL_Oabs > false__ > true__
% 15.15/15.08
% 15.15/15.08 % SZS output end Proof
% 15.15/15.08
%------------------------------------------------------------------------------