TSTP Solution File: ANA034-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA034-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 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 : 300s
% DateTime : Wed Aug 30 17:21:10 EDT 2023
% Result : Unsatisfiable 37.20s 5.14s
% Output : Proof 37.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA034-2 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:49:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 37.20/5.14 Command-line arguments: --flatten
% 37.20/5.14
% 37.20/5.14 % SZS status Unsatisfiable
% 37.20/5.14
% 37.20/5.16 % SZS output start Proof
% 37.20/5.16 Take the following subset of the input axioms:
% 37.20/5.17 fof(cls_OrderedGroup_Oabs__ge__zero_0, axiom, ![T_a, V_a]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))).
% 37.20/5.17 fof(cls_Orderings_Oorder__less__imp__le_0, axiom, ![V_x, V_y, T_a2]: (~class_Orderings_Oorder(T_a2) | (~c_less(V_x, V_y, T_a2) | c_lessequals(V_x, V_y, T_a2)))).
% 37.20/5.17 fof(cls_Ring__and__Field_Oabs__mult_0, axiom, ![V_b, T_a2, V_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | c_HOL_Oabs(c_times(V_a2, V_b, T_a2), T_a2)=c_times(c_HOL_Oabs(V_a2, T_a2), c_HOL_Oabs(V_b, T_a2), T_a2))).
% 37.20/5.17 fof(cls_Ring__and__Field_Omult__mono_0, axiom, ![V_c, V_d, T_a2, V_a2, V_b2]: (~class_Ring__and__Field_Opordered__semiring(T_a2) | (~c_lessequals(V_c, V_d, T_a2) | (~c_lessequals(V_a2, V_b2, T_a2) | (~c_lessequals(c_0, V_c, T_a2) | (~c_lessequals(c_0, V_b2, T_a2) | c_lessequals(c_times(V_a2, V_c, T_a2), c_times(V_b2, V_d, T_a2), T_a2))))))).
% 37.20/5.17 fof(cls_Ring__and__Field_Omult__nonneg__nonneg_0, axiom, ![T_a2, V_a2, V_b2]: (~class_Ring__and__Field_Opordered__cancel__semiring(T_a2) | (~c_lessequals(c_0, V_b2, T_a2) | (~c_lessequals(c_0, V_a2, T_a2) | c_lessequals(c_0, c_times(V_a2, V_b2, T_a2), T_a2))))).
% 37.20/5.17 fof(cls_conjecture_0, negated_conjecture, c_less(c_0, v_c, t_b)).
% 37.20/5.17 fof(cls_conjecture_2, negated_conjecture, c_lessequals(c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b)).
% 37.20/5.17 fof(cls_conjecture_3, negated_conjecture, c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b)).
% 37.20/5.17 fof(cls_conjecture_4, negated_conjecture, c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b)=c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b)).
% 37.20/5.17 fof(cls_conjecture_5, negated_conjecture, ~c_lessequals(c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b), c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)).
% 37.20/5.17 fof(clsrel_OrderedGroup_Olordered__ab__group__abs_17, axiom, ![T]: (~class_OrderedGroup_Olordered__ab__group__abs(T) | class_Orderings_Oorder(T))).
% 37.20/5.17 fof(clsrel_Ring__and__Field_Oordered__idom_40, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_Ring__and__Field_Opordered__cancel__semiring(T2))).
% 37.20/5.17 fof(clsrel_Ring__and__Field_Oordered__idom_42, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_Ring__and__Field_Opordered__semiring(T2))).
% 37.20/5.17 fof(clsrel_Ring__and__Field_Oordered__idom_50, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Olordered__ab__group__abs(T2))).
% 37.20/5.17 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 37.20/5.17
% 37.20/5.17 Now clausify the problem and encode Horn clauses using encoding 3 of
% 37.20/5.17 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 37.20/5.17 We repeatedly replace C & s=t => u=v by the two clauses:
% 37.20/5.17 fresh(y, y, x1...xn) = u
% 37.20/5.17 C => fresh(s, t, x1...xn) = v
% 37.20/5.17 where fresh is a fresh function symbol and x1..xn are the free
% 37.20/5.17 variables of u and v.
% 37.20/5.17 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 37.20/5.17 input problem has no model of domain size 1).
% 37.20/5.17
% 37.20/5.17 The encoding turns the above axioms into the following unit equations and goals:
% 37.20/5.17
% 37.20/5.17 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 37.20/5.17 Axiom 2 (clsrel_Ring__and__Field_Oordered__idom_50): fresh(X, X, Y) = true.
% 37.20/5.17 Axiom 3 (clsrel_OrderedGroup_Olordered__ab__group__abs_17): fresh4(X, X, Y) = true.
% 37.20/5.17 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_40): fresh3(X, X, Y) = true.
% 37.20/5.17 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_42): fresh2(X, X, Y) = true.
% 37.20/5.17 Axiom 6 (cls_conjecture_0): c_less(c_0, v_c, t_b) = true.
% 37.20/5.17 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_50): fresh(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Olordered__ab__group__abs(X).
% 37.20/5.17 Axiom 8 (cls_OrderedGroup_Oabs__ge__zero_0): fresh8(X, X, Y, Z) = true.
% 37.20/5.17 Axiom 9 (clsrel_OrderedGroup_Olordered__ab__group__abs_17): fresh4(class_OrderedGroup_Olordered__ab__group__abs(X), true, X) = class_Orderings_Oorder(X).
% 37.20/5.17 Axiom 10 (clsrel_Ring__and__Field_Oordered__idom_40): fresh3(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Ring__and__Field_Opordered__cancel__semiring(X).
% 37.20/5.17 Axiom 11 (clsrel_Ring__and__Field_Oordered__idom_42): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Ring__and__Field_Opordered__semiring(X).
% 37.20/5.17 Axiom 12 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh11(X, X, Y, Z, W) = true.
% 37.20/5.17 Axiom 13 (cls_Orderings_Oorder__less__imp__le_0): fresh9(X, X, Y, Z, W) = c_lessequals(Z, W, Y).
% 37.20/5.17 Axiom 14 (cls_Orderings_Oorder__less__imp__le_0): fresh7(X, X, Y, Z, W) = true.
% 37.20/5.17 Axiom 15 (cls_OrderedGroup_Oabs__ge__zero_0): fresh8(class_OrderedGroup_Olordered__ab__group__abs(X), true, X, Y) = c_lessequals(c_0, c_HOL_Oabs(Y, X), X).
% 37.20/5.17 Axiom 16 (cls_Ring__and__Field_Oabs__mult_0): fresh6(X, X, Y, Z, W) = c_HOL_Oabs(c_times(Z, W, Y), Y).
% 37.20/5.17 Axiom 17 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh5(X, X, Y, Z, W) = c_lessequals(c_0, c_times(W, Z, Y), Y).
% 37.20/5.17 Axiom 18 (cls_Ring__and__Field_Omult__mono_0): fresh16(X, X, Y, Z, W, V, U) = true.
% 37.20/5.17 Axiom 19 (cls_Ring__and__Field_Oabs__mult_0): fresh6(class_Ring__and__Field_Oordered__idom(X), true, X, Y, Z) = c_times(c_HOL_Oabs(Y, X), c_HOL_Oabs(Z, X), X).
% 37.20/5.17 Axiom 20 (cls_Ring__and__Field_Omult__mono_0): fresh15(X, X, Y, Z, W, V, U) = fresh16(class_Ring__and__Field_Opordered__semiring(Y), true, Y, Z, W, V, U).
% 37.20/5.17 Axiom 21 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh10(X, X, Y, Z, W) = fresh11(c_lessequals(c_0, Z, Y), true, Y, Z, W).
% 37.20/5.17 Axiom 22 (cls_Orderings_Oorder__less__imp__le_0): fresh9(c_less(X, Y, Z), true, Z, X, Y) = fresh7(class_Orderings_Oorder(Z), true, Z, X, Y).
% 37.20/5.17 Axiom 23 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh10(class_Ring__and__Field_Opordered__cancel__semiring(X), true, X, Y, Z) = fresh5(c_lessequals(c_0, Z, X), true, X, Y, Z).
% 37.20/5.17 Axiom 24 (cls_Ring__and__Field_Omult__mono_0): fresh13(X, X, Y, Z, W, V, U) = c_lessequals(c_times(W, Z, Y), c_times(V, U, Y), Y).
% 37.20/5.17 Axiom 25 (cls_Ring__and__Field_Omult__mono_0): fresh14(X, X, Y, Z, W, V, U) = fresh15(c_lessequals(Z, U, Y), true, Y, Z, W, V, U).
% 37.20/5.17 Axiom 26 (cls_Ring__and__Field_Omult__mono_0): fresh12(X, X, Y, Z, W, V, U) = fresh13(c_lessequals(W, V, Y), true, Y, Z, W, V, U).
% 37.20/5.17 Axiom 27 (cls_Ring__and__Field_Omult__mono_0): fresh12(c_lessequals(c_0, X, Y), true, Y, Z, W, X, V) = fresh14(c_lessequals(c_0, Z, Y), true, Y, Z, W, X, V).
% 37.20/5.17 Axiom 28 (cls_conjecture_2): c_lessequals(c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b) = true.
% 37.20/5.17 Axiom 29 (cls_conjecture_3): c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b) = true.
% 37.20/5.17 Axiom 30 (cls_conjecture_4): c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b).
% 37.20/5.17
% 37.20/5.17 Lemma 31: class_Ring__and__Field_Oordered__idom(t_b) = class_OrderedGroup_Olordered__ab__group__abs(t_b).
% 37.20/5.17 Proof:
% 37.20/5.17 class_Ring__and__Field_Oordered__idom(t_b)
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 true
% 37.20/5.17 = { by axiom 2 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 37.20/5.17 fresh(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b)
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh(class_Ring__and__Field_Oordered__idom(t_b), true, t_b)
% 37.20/5.17 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 37.20/5.17 class_OrderedGroup_Olordered__ab__group__abs(t_b)
% 37.20/5.17
% 37.20/5.17 Lemma 32: c_lessequals(c_0, c_HOL_Oabs(X, t_b), t_b) = class_Ring__and__Field_Oordered__idom(t_b).
% 37.20/5.17 Proof:
% 37.20/5.17 c_lessequals(c_0, c_HOL_Oabs(X, t_b), t_b)
% 37.20/5.17 = { by axiom 15 (cls_OrderedGroup_Oabs__ge__zero_0) R->L }
% 37.20/5.17 fresh8(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, t_b, X)
% 37.20/5.17 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.17 fresh8(class_OrderedGroup_Olordered__ab__group__abs(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, X)
% 37.20/5.17 = { by lemma 31 R->L }
% 37.20/5.17 fresh8(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, X)
% 37.20/5.17 = { by axiom 8 (cls_OrderedGroup_Oabs__ge__zero_0) }
% 37.20/5.17 true
% 37.20/5.17 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.17 class_Ring__and__Field_Oordered__idom(t_b)
% 37.20/5.17
% 37.20/5.17 Goal 1 (cls_conjecture_5): c_lessequals(c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b), c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = true.
% 37.20/5.17 Proof:
% 37.20/5.17 c_lessequals(c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b), c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)
% 37.20/5.17 = { by axiom 30 (cls_conjecture_4) }
% 37.20/5.17 c_lessequals(c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 37.20/5.17 = { by axiom 16 (cls_Ring__and__Field_Oabs__mult_0) R->L }
% 37.20/5.17 c_lessequals(fresh6(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, v_a(v_x), v_b(v_x)), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 c_lessequals(fresh6(class_Ring__and__Field_Oordered__idom(t_b), true, t_b, v_a(v_x), v_b(v_x)), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 37.20/5.17 = { by axiom 19 (cls_Ring__and__Field_Oabs__mult_0) }
% 37.20/5.17 c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 37.20/5.17 = { by axiom 24 (cls_Ring__and__Field_Omult__mono_0) R->L }
% 37.20/5.17 fresh13(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh13(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 28 (cls_conjecture_2) R->L }
% 37.20/5.17 fresh13(c_lessequals(c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh13(c_lessequals(c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true, t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 26 (cls_Ring__and__Field_Omult__mono_0) R->L }
% 37.20/5.17 fresh12(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh12(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 12 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) R->L }
% 37.20/5.17 fresh12(fresh11(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by lemma 32 R->L }
% 37.20/5.17 fresh12(fresh11(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh12(fresh11(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_b), t_b), true, t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 21 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) R->L }
% 37.20/5.17 fresh12(fresh10(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh12(fresh10(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_40) R->L }
% 37.20/5.17 fresh12(fresh10(fresh3(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh12(fresh10(fresh3(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 10 (clsrel_Ring__and__Field_Oordered__idom_40) }
% 37.20/5.17 fresh12(fresh10(class_Ring__and__Field_Opordered__cancel__semiring(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh12(fresh10(class_Ring__and__Field_Opordered__cancel__semiring(t_b), true, t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 23 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) }
% 37.20/5.17 fresh12(fresh5(c_lessequals(c_0, v_c, t_b), true, t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.17 fresh12(fresh5(c_lessequals(c_0, v_c, t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 13 (cls_Orderings_Oorder__less__imp__le_0) R->L }
% 37.20/5.17 fresh12(fresh5(fresh9(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh12(fresh5(fresh9(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 6 (cls_conjecture_0) R->L }
% 37.20/5.17 fresh12(fresh5(fresh9(c_less(c_0, v_c, t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) }
% 37.20/5.17 fresh12(fresh5(fresh9(c_less(c_0, v_c, t_b), true, t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 22 (cls_Orderings_Oorder__less__imp__le_0) }
% 37.20/5.17 fresh12(fresh5(fresh7(class_Orderings_Oorder(t_b), true, t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.17 fresh12(fresh5(fresh7(class_Orderings_Oorder(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 9 (clsrel_OrderedGroup_Olordered__ab__group__abs_17) R->L }
% 37.20/5.17 fresh12(fresh5(fresh7(fresh4(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.17 fresh12(fresh5(fresh7(fresh4(class_OrderedGroup_Olordered__ab__group__abs(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by lemma 31 R->L }
% 37.20/5.17 fresh12(fresh5(fresh7(fresh4(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 3 (clsrel_OrderedGroup_Olordered__ab__group__abs_17) }
% 37.20/5.17 fresh12(fresh5(fresh7(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.17 fresh12(fresh5(fresh7(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_0, v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 14 (cls_Orderings_Oorder__less__imp__le_0) }
% 37.20/5.17 fresh12(fresh5(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.17 fresh12(fresh5(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_f(v_x), t_b), v_c), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.17 = { by axiom 17 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) }
% 37.20/5.18 fresh12(c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 1 (tfree_tcs) }
% 37.20/5.18 fresh12(c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true, t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 27 (cls_Ring__and__Field_Omult__mono_0) }
% 37.20/5.18 fresh14(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.18 fresh14(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by lemma 32 }
% 37.20/5.18 fresh14(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 25 (cls_Ring__and__Field_Omult__mono_0) }
% 37.20/5.18 fresh15(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.18 fresh15(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 29 (cls_conjecture_3) }
% 37.20/5.18 fresh15(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.18 fresh15(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 20 (cls_Ring__and__Field_Omult__mono_0) }
% 37.20/5.18 fresh16(class_Ring__and__Field_Opordered__semiring(t_b), true, t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.18 fresh16(class_Ring__and__Field_Opordered__semiring(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 11 (clsrel_Ring__and__Field_Oordered__idom_42) R->L }
% 37.20/5.18 fresh16(fresh2(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.18 fresh16(fresh2(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_42) }
% 37.20/5.18 fresh16(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 1 (tfree_tcs) R->L }
% 37.20/5.18 fresh16(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b))
% 37.20/5.18 = { by axiom 18 (cls_Ring__and__Field_Omult__mono_0) }
% 37.20/5.18 true
% 37.20/5.18 % SZS output end Proof
% 37.20/5.18
% 37.20/5.18 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------