TSTP Solution File: ANA030-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA030-2 : 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 : n027.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 17:21:08 EDT 2023
% Result : Unsatisfiable 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA030-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 19:01:04 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.47 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.47
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 Take the following subset of the input axioms:
% 0.21/0.49 fof(cls_OrderedGroup_Oabs__of__nonneg_0, axiom, ![T_a, V_y]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a) | (~c_lessequals(c_0, V_y, T_a) | c_HOL_Oabs(V_y, T_a)=V_y))).
% 0.21/0.49 fof(cls_OrderedGroup_Ocompare__rls__1_0, axiom, ![V_a, V_b, T_a2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_plus(V_a, c_uminus(V_b, T_a2), T_a2)=c_minus(V_a, V_b, T_a2))).
% 0.21/0.49 fof(cls_OrderedGroup_Ocompare__rls__8_0, axiom, ![V_c, T_a2, V_a2, V_b2]: (~class_OrderedGroup_Opordered__ab__group__add(T_a2) | (~c_lessequals(c_minus(V_a2, V_b2, T_a2), V_c, T_a2) | c_lessequals(V_a2, c_plus(V_c, V_b2, T_a2), T_a2)))).
% 0.21/0.49 fof(cls_OrderedGroup_Odiff__minus__eq__add_0, axiom, ![T_a2, V_a2, V_b2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_minus(V_a2, c_uminus(V_b2, T_a2), T_a2)=c_plus(V_a2, V_b2, T_a2))).
% 0.21/0.49 fof(cls_OrderedGroup_Ominus__add__distrib_0, axiom, ![T_a2, V_a2, V_b2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_uminus(c_plus(V_a2, V_b2, T_a2), T_a2)=c_plus(c_uminus(V_a2, T_a2), c_uminus(V_b2, T_a2), T_a2))).
% 0.21/0.49 fof(cls_OrderedGroup_Ominus__diff__eq_0, axiom, ![T_a2, V_a2, V_b2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_uminus(c_minus(V_a2, V_b2, T_a2), T_a2)=c_minus(V_b2, V_a2, T_a2))).
% 0.21/0.49 fof(cls_OrderedGroup_Ominus__minus_0, axiom, ![V_y2, T_a2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_uminus(c_uminus(V_y2, T_a2), T_a2)=V_y2)).
% 0.21/0.49 fof(cls_Orderings_Ole__maxI2_0, axiom, ![T_b, V_x, V_y2]: (~class_Orderings_Olinorder(T_b) | c_lessequals(V_y2, c_Orderings_Omax(V_x, V_y2, T_b), T_b))).
% 0.21/0.49 fof(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, axiom, ![V_z, V_y2, T_b2, V_x2]: (~class_Orderings_Olinorder(T_b2) | (~c_lessequals(c_Orderings_Omax(V_x2, V_y2, T_b2), V_z, T_b2) | c_lessequals(V_x2, V_z, T_b2)))).
% 0.21/0.49 fof(cls_conjecture_1, negated_conjecture, ![V_U]: c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U), v_g(V_U), t_b), c_0, t_b), t_b), c_times(v_c, c_HOL_Oabs(v_h(V_U), t_b), t_b), t_b)).
% 0.21/0.49 fof(cls_conjecture_2, negated_conjecture, ![V_U2]: ~c_lessequals(v_f(v_x(V_U2)), c_plus(v_g(v_x(V_U2)), c_times(V_U2, c_HOL_Oabs(v_h(v_x(V_U2)), t_b), t_b), t_b), t_b)).
% 0.21/0.49 fof(clsrel_OrderedGroup_Olordered__ab__group__abs_1, axiom, ![T]: (~class_OrderedGroup_Olordered__ab__group__abs(T) | class_OrderedGroup_Opordered__ab__group__add(T))).
% 0.21/0.49 fof(clsrel_Ring__and__Field_Oordered__idom_33, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_Orderings_Olinorder(T2))).
% 0.21/0.49 fof(clsrel_Ring__and__Field_Oordered__idom_4, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Oab__group__add(T2))).
% 0.21/0.49 fof(clsrel_Ring__and__Field_Oordered__idom_50, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Olordered__ab__group__abs(T2))).
% 0.21/0.49 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.21/0.49
% 0.21/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.49 fresh(y, y, x1...xn) = u
% 0.21/0.49 C => fresh(s, t, x1...xn) = v
% 0.21/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.49 variables of u and v.
% 0.21/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.49 input problem has no model of domain size 1).
% 0.21/0.49
% 0.21/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.49
% 0.21/0.49 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true2.
% 0.21/0.49 Axiom 2 (clsrel_OrderedGroup_Olordered__ab__group__abs_1): fresh6(X, X, Y) = true2.
% 0.21/0.49 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_33): fresh5(X, X, Y) = true2.
% 0.21/0.49 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4): fresh4(X, X, Y) = true2.
% 0.21/0.49 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50): fresh3(X, X, Y) = true2.
% 0.21/0.49 Axiom 6 (cls_OrderedGroup_Ominus__minus_0): fresh(X, X, Y, Z) = Z.
% 0.21/0.49 Axiom 7 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh15(X, X, Y, Z) = c_HOL_Oabs(Z, Y).
% 0.21/0.49 Axiom 8 (clsrel_OrderedGroup_Olordered__ab__group__abs_1): fresh6(class_OrderedGroup_Olordered__ab__group__abs(X), true2, X) = class_OrderedGroup_Opordered__ab__group__add(X).
% 0.21/0.49 Axiom 9 (clsrel_Ring__and__Field_Oordered__idom_33): fresh5(class_Ring__and__Field_Oordered__idom(X), true2, X) = class_Orderings_Olinorder(X).
% 0.21/0.49 Axiom 10 (clsrel_Ring__and__Field_Oordered__idom_4): fresh4(class_Ring__and__Field_Oordered__idom(X), true2, X) = class_OrderedGroup_Oab__group__add(X).
% 0.21/0.49 Axiom 11 (clsrel_Ring__and__Field_Oordered__idom_50): fresh3(class_Ring__and__Field_Oordered__idom(X), true2, X) = class_OrderedGroup_Olordered__ab__group__abs(X).
% 0.21/0.49 Axiom 12 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh2(X, X, Y, Z) = Z.
% 0.21/0.49 Axiom 13 (cls_OrderedGroup_Ominus__minus_0): fresh(class_OrderedGroup_Oab__group__add(X), true2, X, Y) = c_uminus(c_uminus(Y, X), X).
% 0.21/0.49 Axiom 14 (cls_OrderedGroup_Ocompare__rls__1_0): fresh16(X, X, Y, Z, W) = c_minus(Z, W, Y).
% 0.21/0.49 Axiom 15 (cls_OrderedGroup_Odiff__minus__eq__add_0): fresh12(X, X, Y, Z, W) = c_plus(Z, W, Y).
% 0.21/0.49 Axiom 16 (cls_OrderedGroup_Ominus__add__distrib_0): fresh11(X, X, Y, Z, W) = c_uminus(c_plus(Z, W, Y), Y).
% 0.21/0.49 Axiom 17 (cls_OrderedGroup_Ominus__diff__eq_0): fresh10(X, X, Y, Z, W) = c_minus(W, Z, Y).
% 0.21/0.49 Axiom 18 (cls_Orderings_Ole__maxI2_0): fresh9(X, X, Y, Z, W) = true2.
% 0.21/0.49 Axiom 19 (cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0): fresh7(X, X, Y, Z, W) = true2.
% 0.21/0.49 Axiom 20 (cls_OrderedGroup_Ocompare__rls__1_0): fresh16(class_OrderedGroup_Oab__group__add(X), true2, X, Y, Z) = c_plus(Y, c_uminus(Z, X), X).
% 0.21/0.49 Axiom 21 (cls_OrderedGroup_Ocompare__rls__8_0): fresh14(X, X, Y, Z, W, V) = c_lessequals(Z, c_plus(V, W, Y), Y).
% 0.21/0.49 Axiom 22 (cls_OrderedGroup_Ocompare__rls__8_0): fresh13(X, X, Y, Z, W, V) = true2.
% 0.21/0.49 Axiom 23 (cls_OrderedGroup_Odiff__minus__eq__add_0): fresh12(class_OrderedGroup_Oab__group__add(X), true2, X, Y, Z) = c_minus(Y, c_uminus(Z, X), X).
% 0.21/0.49 Axiom 24 (cls_OrderedGroup_Ominus__diff__eq_0): fresh10(class_OrderedGroup_Oab__group__add(X), true2, X, Y, Z) = c_uminus(c_minus(Y, Z, X), X).
% 0.21/0.49 Axiom 25 (cls_Orderings_Ole__maxI2_0): fresh9(class_Orderings_Olinorder(X), true2, X, Y, Z) = c_lessequals(Y, c_Orderings_Omax(Z, Y, X), X).
% 0.21/0.49 Axiom 26 (cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0): fresh8(X, X, Y, Z, W, V) = c_lessequals(Z, V, Y).
% 0.21/0.49 Axiom 27 (cls_OrderedGroup_Ominus__add__distrib_0): fresh11(class_OrderedGroup_Oab__group__add(X), true2, X, Y, Z) = c_plus(c_uminus(Y, X), c_uminus(Z, X), X).
% 0.21/0.49 Axiom 28 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh15(class_OrderedGroup_Olordered__ab__group__abs(X), true2, X, Y) = fresh2(c_lessequals(c_0, Y, X), true2, X, Y).
% 0.21/0.49 Axiom 29 (cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0): fresh8(class_Orderings_Olinorder(X), true2, X, Y, Z, W) = fresh7(c_lessequals(c_Orderings_Omax(Y, Z, X), W, X), true2, X, Y, W).
% 0.21/0.49 Axiom 30 (cls_OrderedGroup_Ocompare__rls__8_0): fresh14(class_OrderedGroup_Opordered__ab__group__add(X), true2, X, Y, Z, W) = fresh13(c_lessequals(c_minus(Y, Z, X), W, X), true2, X, Y, Z, W).
% 0.21/0.49 Axiom 31 (cls_conjecture_1): c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(X), v_g(X), t_b), c_0, t_b), t_b), c_times(v_c, c_HOL_Oabs(v_h(X), t_b), t_b), t_b) = true2.
% 0.21/0.49
% 0.21/0.49 Lemma 32: class_OrderedGroup_Olordered__ab__group__abs(t_b) = true2.
% 0.21/0.49 Proof:
% 0.21/0.49 class_OrderedGroup_Olordered__ab__group__abs(t_b)
% 0.21/0.49 = { by axiom 11 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.21/0.49 fresh3(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b)
% 0.21/0.49 = { by axiom 1 (tfree_tcs) }
% 0.21/0.49 fresh3(true2, true2, t_b)
% 0.21/0.49 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.21/0.49 true2
% 0.21/0.49
% 0.21/0.49 Lemma 33: class_OrderedGroup_Oab__group__add(t_b) = true2.
% 0.21/0.49 Proof:
% 0.21/0.49 class_OrderedGroup_Oab__group__add(t_b)
% 0.21/0.49 = { by axiom 10 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 0.21/0.49 fresh4(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b)
% 0.21/0.49 = { by axiom 1 (tfree_tcs) }
% 0.21/0.49 fresh4(true2, true2, t_b)
% 0.21/0.49 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 0.21/0.49 true2
% 0.21/0.49
% 0.21/0.49 Lemma 34: class_Orderings_Olinorder(t_b) = true2.
% 0.21/0.49 Proof:
% 0.21/0.49 class_Orderings_Olinorder(t_b)
% 0.21/0.49 = { by axiom 9 (clsrel_Ring__and__Field_Oordered__idom_33) R->L }
% 0.21/0.49 fresh5(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b)
% 0.21/0.49 = { by axiom 1 (tfree_tcs) }
% 0.21/0.49 fresh5(true2, true2, t_b)
% 0.21/0.49 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_33) }
% 0.21/0.49 true2
% 0.21/0.49
% 0.21/0.49 Goal 1 (cls_conjecture_2): c_lessequals(v_f(v_x(X)), c_plus(v_g(v_x(X)), c_times(X, c_HOL_Oabs(v_h(v_x(X)), t_b), t_b), t_b), t_b) = true2.
% 0.21/0.49 The goal is true when:
% 0.21/0.49 X = v_c
% 0.21/0.49
% 0.21/0.49 Proof:
% 0.21/0.49 c_lessequals(v_f(v_x(v_c)), c_plus(v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)
% 0.21/0.49 = { by axiom 6 (cls_OrderedGroup_Ominus__minus_0) R->L }
% 0.21/0.49 c_lessequals(v_f(v_x(v_c)), fresh(true2, true2, t_b, c_plus(v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b)), t_b)
% 0.21/0.49 = { by lemma 33 R->L }
% 0.21/0.49 c_lessequals(v_f(v_x(v_c)), fresh(class_OrderedGroup_Oab__group__add(t_b), true2, t_b, c_plus(v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b)), t_b)
% 0.21/0.49 = { by axiom 13 (cls_OrderedGroup_Ominus__minus_0) }
% 0.21/0.49 c_lessequals(v_f(v_x(v_c)), c_uminus(c_uminus(c_plus(v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), t_b)
% 0.21/0.50 = { by axiom 16 (cls_OrderedGroup_Ominus__add__distrib_0) R->L }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), c_uminus(fresh11(true2, true2, t_b, v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), t_b), t_b)
% 0.21/0.50 = { by lemma 33 R->L }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), c_uminus(fresh11(class_OrderedGroup_Oab__group__add(t_b), true2, t_b, v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), t_b), t_b)
% 0.21/0.50 = { by axiom 27 (cls_OrderedGroup_Ominus__add__distrib_0) }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), c_uminus(c_plus(c_uminus(v_g(v_x(v_c)), t_b), c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), t_b)
% 0.21/0.50 = { by axiom 20 (cls_OrderedGroup_Ocompare__rls__1_0) R->L }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), c_uminus(fresh16(class_OrderedGroup_Oab__group__add(t_b), true2, t_b, c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), t_b), t_b)
% 0.21/0.50 = { by lemma 33 }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), c_uminus(fresh16(true2, true2, t_b, c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), t_b), t_b)
% 0.21/0.50 = { by axiom 14 (cls_OrderedGroup_Ocompare__rls__1_0) }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b)
% 0.21/0.50 = { by axiom 24 (cls_OrderedGroup_Ominus__diff__eq_0) R->L }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), fresh10(class_OrderedGroup_Oab__group__add(t_b), true2, t_b, c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), t_b)
% 0.21/0.50 = { by lemma 33 }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), fresh10(true2, true2, t_b, c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), t_b)
% 0.21/0.50 = { by axiom 17 (cls_OrderedGroup_Ominus__diff__eq_0) }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), c_minus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), c_uminus(v_g(v_x(v_c)), t_b), t_b), t_b)
% 0.21/0.50 = { by axiom 23 (cls_OrderedGroup_Odiff__minus__eq__add_0) R->L }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), fresh12(class_OrderedGroup_Oab__group__add(t_b), true2, t_b, c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c))), t_b)
% 0.21/0.50 = { by lemma 33 }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), fresh12(true2, true2, t_b, c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c))), t_b)
% 0.21/0.50 = { by axiom 15 (cls_OrderedGroup_Odiff__minus__eq__add_0) }
% 0.21/0.50 c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b)
% 0.21/0.50 = { by axiom 21 (cls_OrderedGroup_Ocompare__rls__8_0) R->L }
% 0.21/0.50 fresh14(true2, true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 2 (clsrel_OrderedGroup_Olordered__ab__group__abs_1) R->L }
% 0.21/0.50 fresh14(fresh6(true2, true2, t_b), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by lemma 32 R->L }
% 0.21/0.50 fresh14(fresh6(class_OrderedGroup_Olordered__ab__group__abs(t_b), true2, t_b), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 8 (clsrel_OrderedGroup_Olordered__ab__group__abs_1) }
% 0.21/0.50 fresh14(class_OrderedGroup_Opordered__ab__group__add(t_b), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 30 (cls_OrderedGroup_Ocompare__rls__8_0) }
% 0.21/0.50 fresh13(c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 26 (cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) R->L }
% 0.21/0.50 fresh13(fresh8(true2, true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by lemma 34 R->L }
% 0.21/0.50 fresh13(fresh8(class_Orderings_Olinorder(t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 29 (cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) }
% 0.21/0.50 fresh13(fresh7(c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 12 (cls_OrderedGroup_Oabs__of__nonneg_0) R->L }
% 0.21/0.50 fresh13(fresh7(c_lessequals(fresh2(true2, true2, t_b, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 18 (cls_Orderings_Ole__maxI2_0) R->L }
% 0.21/0.50 fresh13(fresh7(c_lessequals(fresh2(fresh9(true2, true2, t_b, c_0, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b)), true2, t_b, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by lemma 34 R->L }
% 0.21/0.50 fresh13(fresh7(c_lessequals(fresh2(fresh9(class_Orderings_Olinorder(t_b), true2, t_b, c_0, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b)), true2, t_b, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 25 (cls_Orderings_Ole__maxI2_0) }
% 0.21/0.50 fresh13(fresh7(c_lessequals(fresh2(c_lessequals(c_0, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), true2, t_b, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 28 (cls_OrderedGroup_Oabs__of__nonneg_0) R->L }
% 0.21/0.50 fresh13(fresh7(c_lessequals(fresh15(class_OrderedGroup_Olordered__ab__group__abs(t_b), true2, t_b, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by lemma 32 }
% 0.21/0.50 fresh13(fresh7(c_lessequals(fresh15(true2, true2, t_b, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 7 (cls_OrderedGroup_Oabs__of__nonneg_0) }
% 0.21/0.50 fresh13(fresh7(c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 31 (cls_conjecture_1) }
% 0.21/0.50 fresh13(fresh7(true2, true2, t_b, c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b)), true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.50 = { by axiom 19 (cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) }
% 0.21/0.50 fresh13(true2, true2, t_b, v_f(v_x(v_c)), v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b))
% 0.21/0.51 = { by axiom 22 (cls_OrderedGroup_Ocompare__rls__8_0) }
% 0.21/0.51 true2
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51
% 0.21/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------