TSTP Solution File: SWV879-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV879-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n012.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 : Thu Aug 31 23:06:36 EDT 2023
% Result : Unsatisfiable 150.41s 19.67s
% Output : Proof 150.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV879-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 04:59:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 150.41/19.67 Command-line arguments: --flatten
% 150.41/19.67
% 150.41/19.67 % SZS status Unsatisfiable
% 150.41/19.67
% 150.41/19.76 % SZS output start Proof
% 150.41/19.76 Take the following subset of the input axioms:
% 150.41/19.76 fof(cls_Diff__cancel_0, axiom, ![T_a, V_A]: c_HOL_Ominus__class_Ominus(V_A, V_A, tc_fun(T_a, tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_bool))).
% 150.41/19.76 fof(cls_Diff__insert2_0, axiom, ![V_B, V_a, T_a2, V_A2]: c_HOL_Ominus__class_Ominus(V_A2, c_Set_Oinsert(V_a, V_B, T_a2), tc_fun(T_a2, tc_bool))=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A2, c_Set_Oinsert(V_a, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2), tc_fun(T_a2, tc_bool)), V_B, tc_fun(T_a2, tc_bool))).
% 150.41/19.76 fof(cls_Int__commute_0, axiom, ![T_a2, V_A2, V_B2]: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a2, tc_bool)), V_A2), V_B2)=hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a2, tc_bool)), V_B2), V_A2)).
% 150.41/19.76 fof(cls_Un__Diff__Int_0, axiom, ![T_a2, V_A2, V_B2]: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a2, tc_bool)), c_HOL_Ominus__class_Ominus(V_A2, V_B2, tc_fun(T_a2, tc_bool))), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a2, tc_bool)), V_A2), V_B2))=V_A2).
% 150.41/19.76 fof(cls_Un__commute_0, axiom, ![T_a2, V_A2, V_B2]: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a2, tc_bool)), V_A2), V_B2)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a2, tc_bool)), V_B2), V_A2)).
% 150.41/19.76 fof(cls_assms_I1_J_0, axiom, ![V_G, V_ts]: (hBOOL(hAPP(hAPP(v_P, V_G), V_ts)) | ~c_lessequals(V_ts, V_G, tc_fun(t_a, tc_bool)))).
% 150.41/19.76 fof(cls_conjecture_1, negated_conjecture, v_G=c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a)).
% 150.41/19.76 fof(cls_conjecture_2, negated_conjecture, hBOOL(c_in(v_x, v_U, tc_Com_Opname))).
% 150.41/19.76 fof(cls_conjecture_3, negated_conjecture, ~hBOOL(hAPP(hAPP(v_P, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)))).
% 150.41/19.76 fof(cls_empty__Diff_0, axiom, ![T_a2, V_A2]: c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), V_A2, tc_fun(T_a2, tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool))).
% 150.41/19.76 fof(cls_image__insert_0, axiom, ![T_b, V_f, T_a2, V_a2, V_B2]: c_Set_Oimage(V_f, c_Set_Oinsert(V_a2, V_B2, T_b), T_b, T_a2)=c_Set_Oinsert(hAPP(V_f, V_a2), c_Set_Oimage(V_f, V_B2, T_b, T_a2), T_a2)).
% 150.41/19.76 fof(cls_inf__le1_0, axiom, ![V_x, V_y, T_a2]: (~class_Lattices_Olower__semilattice(T_a2) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a2), V_x), V_y), V_x, T_a2))).
% 150.41/19.76 fof(cls_insert__absorb_0, axiom, ![T_a2, V_A2, V_a2]: (c_Set_Oinsert(V_a2, V_A2, T_a2)=V_A2 | ~hBOOL(c_in(V_a2, V_A2, T_a2)))).
% 150.41/19.76 fof(cls_sup__bot__right_0, axiom, ![T_a2, V_x2]: (~class_Lattices_Obounded__lattice(T_a2) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a2), V_x2), c_Orderings_Obot__class_Obot(T_a2))=V_x2)).
% 150.41/19.76 fof(clsarity_bool__Lattices_Obounded__lattice, axiom, class_Lattices_Obounded__lattice(tc_bool)).
% 150.41/19.76 fof(clsarity_bool__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_bool)).
% 150.41/19.76 fof(clsarity_bool__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_bool)).
% 150.41/19.76 fof(clsarity_fun__Lattices_Obounded__lattice, axiom, ![T_2, T_1]: (class_Lattices_Obounded__lattice(tc_fun(T_2, T_1)) | ~class_Lattices_Obounded__lattice(T_1))).
% 150.41/19.76 fof(clsarity_fun__Lattices_Olower__semilattice, axiom, ![T_2_2, T_1_2]: (class_Lattices_Olower__semilattice(tc_fun(T_2_2, T_1_2)) | ~class_Lattices_Olattice(T_1_2))).
% 150.41/19.76 fof(clsarity_nat__OrderedGroup_Oab__semigroup__add, axiom, class_OrderedGroup_Oab__semigroup__add(tc_nat)).
% 150.41/19.76 fof(clsarity_nat__OrderedGroup_Ocomm__monoid__add, axiom, class_OrderedGroup_Ocomm__monoid__add(tc_nat)).
% 150.41/19.76 fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, axiom, class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)).
% 150.41/19.76 fof(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, axiom, class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)).
% 150.41/19.76 fof(clsarity_nat__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_nat)).
% 150.41/19.76
% 150.41/19.76 Now clausify the problem and encode Horn clauses using encoding 3 of
% 150.41/19.76 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 150.41/19.76 We repeatedly replace C & s=t => u=v by the two clauses:
% 150.41/19.76 fresh(y, y, x1...xn) = u
% 150.41/19.76 C => fresh(s, t, x1...xn) = v
% 150.41/19.76 where fresh is a fresh function symbol and x1..xn are the free
% 150.41/19.76 variables of u and v.
% 150.41/19.76 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 150.41/19.76 input problem has no model of domain size 1).
% 150.41/19.76
% 150.41/19.76 The encoding turns the above axioms into the following unit equations and goals:
% 150.41/19.76
% 150.41/19.76 Axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add): class_OrderedGroup_Oab__semigroup__add(tc_nat) = true2.
% 150.41/19.76 Axiom 2 (clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add): class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) = true2.
% 150.41/19.76 Axiom 3 (clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add): class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) = true2.
% 150.41/19.76 Axiom 4 (clsarity_nat__OrderedGroup_Ocomm__monoid__add): class_OrderedGroup_Ocomm__monoid__add(tc_nat) = true2.
% 150.41/19.76 Axiom 5 (clsarity_nat__Orderings_Opreorder): class_Orderings_Opreorder(tc_nat) = true2.
% 150.41/19.76 Axiom 6 (clsarity_bool__Orderings_Opreorder): class_Orderings_Opreorder(tc_bool) = true2.
% 150.41/19.76 Axiom 7 (clsarity_bool__Lattices_Obounded__lattice): class_Lattices_Obounded__lattice(tc_bool) = true2.
% 150.41/19.76 Axiom 8 (clsarity_bool__Lattices_Olattice): class_Lattices_Olattice(tc_bool) = true2.
% 150.41/19.76 Axiom 9 (cls_assms_I1_J_0): fresh606(X, X, Y, Z) = true2.
% 150.41/19.76 Axiom 10 (clsarity_fun__Lattices_Obounded__lattice): fresh117(X, X, Y, Z) = true2.
% 150.41/19.76 Axiom 11 (clsarity_fun__Lattices_Olower__semilattice): fresh114(X, X, Y, Z) = true2.
% 150.41/19.76 Axiom 12 (cls_sup__bot__right_0): fresh55(X, X, Y, Z) = Z.
% 150.41/19.77 Axiom 13 (cls_conjecture_1): v_G = c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a).
% 150.41/19.77 Axiom 14 (cls_conjecture_2): hBOOL(c_in(v_x, v_U, tc_Com_Opname)) = true2.
% 150.41/19.77 Axiom 15 (cls_inf__le1_0): fresh458(X, X, Y, Z, W) = true2.
% 150.41/19.77 Axiom 16 (clsarity_fun__Lattices_Obounded__lattice): fresh117(class_Lattices_Obounded__lattice(X), true2, Y, X) = class_Lattices_Obounded__lattice(tc_fun(Y, X)).
% 150.41/19.77 Axiom 17 (clsarity_fun__Lattices_Olower__semilattice): fresh114(class_Lattices_Olattice(X), true2, Y, X) = class_Lattices_Olower__semilattice(tc_fun(Y, X)).
% 150.41/19.77 Axiom 18 (cls_insert__absorb_0): fresh8(X, X, Y, Z, W) = Z.
% 150.41/19.77 Axiom 19 (cls_Diff__cancel_0): c_HOL_Ominus__class_Ominus(X, X, tc_fun(Y, tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(Y, tc_bool)).
% 150.41/19.77 Axiom 20 (cls_Sup__binary_0): fresh651(X, X, Y, Z, W) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(Y), Z), W).
% 150.41/19.77 Axiom 21 (cls_Inf__binary_0): fresh683(X, X, Y, Z, W) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(Y), Z), W).
% 150.41/19.77 Axiom 22 (cls_sup__bot__right_0): fresh55(class_Lattices_Obounded__lattice(X), true2, X, Y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X), Y), c_Orderings_Obot__class_Obot(X)).
% 150.41/19.77 Axiom 23 (cls_Un__commute_0): hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X, tc_bool)), Y), Z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X, tc_bool)), Z), Y).
% 150.41/19.77 Axiom 24 (cls_Int__commute_0): hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X, tc_bool)), Y), Z) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X, tc_bool)), Z), Y).
% 150.41/19.77 Axiom 25 (cls_empty__Diff_0): c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)), Y, tc_fun(X, tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)).
% 150.41/19.77 Axiom 26 (cls_inf__le1_0): fresh458(class_Lattices_Olower__semilattice(X), true2, X, Y, Z) = c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X), Y), Z), Y, X).
% 150.41/19.77 Axiom 27 (cls_assms_I1_J_0): fresh606(c_lessequals(X, Y, tc_fun(t_a, tc_bool)), true2, Y, X) = hBOOL(hAPP(hAPP(v_P, Y), X)).
% 150.41/19.77 Axiom 28 (cls_insert__absorb_0): fresh8(hBOOL(c_in(X, Y, Z)), true2, X, Y, Z) = c_Set_Oinsert(X, Y, Z).
% 150.41/19.77 Axiom 29 (cls_image__insert_0): c_Set_Oimage(X, c_Set_Oinsert(Y, Z, W), W, V) = c_Set_Oinsert(hAPP(X, Y), c_Set_Oimage(X, Z, W, V), V).
% 150.41/19.77 Axiom 30 (cls_sup__inf__distrib1_0): fresh153(X, X, Y, Z, W, V) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(Y), Z), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(Y), W), V)).
% 150.41/19.77 Axiom 31 (cls_Diff__insert2_0): c_HOL_Ominus__class_Ominus(X, c_Set_Oinsert(Y, Z, W), tc_fun(W, tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X, c_Set_Oinsert(Y, c_Orderings_Obot__class_Obot(tc_fun(W, tc_bool)), W), tc_fun(W, tc_bool)), Z, tc_fun(W, tc_bool)).
% 150.41/19.77 Axiom 32 (cls_Un__Diff__Int_0): hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X, tc_bool)), c_HOL_Ominus__class_Ominus(Y, Z, tc_fun(X, tc_bool))), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X, tc_bool)), Y), Z)) = Y.
% 150.41/19.77
% 150.41/19.77 Lemma 33: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) = class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 150.41/19.77 Proof:
% 150.41/19.77 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
% 150.41/19.77 = { by axiom 2 (clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) }
% 150.41/19.77 true2
% 150.41/19.77 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.77 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 150.41/19.77
% 150.41/19.77 Lemma 34: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) = class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 150.41/19.77 Proof:
% 150.41/19.77 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
% 150.41/19.77 = { by axiom 3 (clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) }
% 150.41/19.77 true2
% 150.41/19.77 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.77 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 33 R->L }
% 150.41/19.77 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
% 150.41/19.77
% 150.41/19.77 Lemma 35: class_OrderedGroup_Ocomm__monoid__add(tc_nat) = class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 150.41/19.77 Proof:
% 150.41/19.77 class_OrderedGroup_Ocomm__monoid__add(tc_nat)
% 150.41/19.77 = { by axiom 4 (clsarity_nat__OrderedGroup_Ocomm__monoid__add) }
% 150.41/19.77 true2
% 150.41/19.77 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.77 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 33 R->L }
% 150.41/19.77 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 34 R->L }
% 150.41/19.77 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
% 150.41/19.77
% 150.41/19.77 Lemma 36: class_Orderings_Opreorder(tc_nat) = class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 150.41/19.77 Proof:
% 150.41/19.77 class_Orderings_Opreorder(tc_nat)
% 150.41/19.77 = { by axiom 5 (clsarity_nat__Orderings_Opreorder) }
% 150.41/19.77 true2
% 150.41/19.77 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.77 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 33 R->L }
% 150.41/19.77 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 34 R->L }
% 150.41/19.77 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 35 R->L }
% 150.41/19.77 class_OrderedGroup_Ocomm__monoid__add(tc_nat)
% 150.41/19.77
% 150.41/19.77 Lemma 37: class_Orderings_Opreorder(tc_bool) = class_Orderings_Opreorder(tc_nat).
% 150.41/19.77 Proof:
% 150.41/19.77 class_Orderings_Opreorder(tc_bool)
% 150.41/19.77 = { by axiom 6 (clsarity_bool__Orderings_Opreorder) }
% 150.41/19.77 true2
% 150.41/19.77 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.77 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 33 R->L }
% 150.41/19.77 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 34 R->L }
% 150.41/19.77 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
% 150.41/19.77 = { by lemma 35 R->L }
% 150.41/19.77 class_OrderedGroup_Ocomm__monoid__add(tc_nat)
% 150.41/19.77 = { by lemma 36 R->L }
% 150.41/19.77 class_Orderings_Opreorder(tc_nat)
% 150.41/19.77
% 150.41/19.77 Lemma 38: fresh651(X, X, Y, Z, fresh683(W, W, Y, V, U)) = fresh153(T, T, Y, Z, V, U).
% 150.41/19.77 Proof:
% 150.41/19.77 fresh651(X, X, Y, Z, fresh683(W, W, Y, V, U))
% 150.41/19.77 = { by axiom 21 (cls_Inf__binary_0) }
% 150.41/19.77 fresh651(X, X, Y, Z, hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(Y), V), U))
% 150.41/19.77 = { by axiom 20 (cls_Sup__binary_0) }
% 150.41/19.77 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(Y), Z), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(Y), V), U))
% 150.41/19.77 = { by axiom 30 (cls_sup__inf__distrib1_0) R->L }
% 150.41/19.77 fresh153(T, T, Y, Z, V, U)
% 150.41/19.77
% 150.41/19.77 Goal 1 (cls_conjecture_3): hBOOL(hAPP(hAPP(v_P, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))) = true2.
% 150.41/19.77 Proof:
% 150.41/19.77 hBOOL(hAPP(hAPP(v_P, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)))
% 150.41/19.77 = { by axiom 13 (cls_conjecture_1) R->L }
% 150.41/19.77 hBOOL(hAPP(hAPP(v_P, v_G), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)))
% 150.41/19.77 = { by axiom 27 (cls_assms_I1_J_0) R->L }
% 150.41/19.77 fresh606(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.77 fresh606(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), class_OrderedGroup_Oab__semigroup__add(tc_nat), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 33 R->L }
% 150.41/19.77 fresh606(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 34 R->L }
% 150.41/19.77 fresh606(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 35 R->L }
% 150.41/19.77 fresh606(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), class_OrderedGroup_Ocomm__monoid__add(tc_nat), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 36 R->L }
% 150.41/19.77 fresh606(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_nat), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 37 R->L }
% 150.41/19.77 fresh606(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by axiom 32 (cls_Un__Diff__Int_0) R->L }
% 150.41/19.77 fresh606(c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a, tc_bool)), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool))), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), v_G)), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by axiom 20 (cls_Sup__binary_0) R->L }
% 150.41/19.77 fresh606(c_lessequals(fresh651(X, X, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), v_G)), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by axiom 21 (cls_Inf__binary_0) R->L }
% 150.41/19.77 fresh606(c_lessequals(fresh651(X, X, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), fresh683(Y, Y, tc_fun(t_a, tc_bool), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G)), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 38 }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by axiom 13 (cls_conjecture_1) }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by axiom 18 (cls_insert__absorb_0) R->L }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(class_Orderings_Opreorder(tc_bool), class_Orderings_Opreorder(tc_bool), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 37 }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(class_Orderings_Opreorder(tc_nat), class_Orderings_Opreorder(tc_bool), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 36 }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(class_OrderedGroup_Ocomm__monoid__add(tc_nat), class_Orderings_Opreorder(tc_bool), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 35 }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 34 }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by lemma 33 }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(true2, class_Orderings_Opreorder(tc_bool), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.77 = { by axiom 14 (cls_conjecture_2) R->L }
% 150.41/19.77 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(hBOOL(c_in(v_x, v_U, tc_Com_Opname)), class_Orderings_Opreorder(tc_bool), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 37 }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(hBOOL(c_in(v_x, v_U, tc_Com_Opname)), class_Orderings_Opreorder(tc_nat), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 36 }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(hBOOL(c_in(v_x, v_U, tc_Com_Opname)), class_OrderedGroup_Ocomm__monoid__add(tc_nat), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 35 }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(hBOOL(c_in(v_x, v_U, tc_Com_Opname)), class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 34 }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(hBOOL(c_in(v_x, v_U, tc_Com_Opname)), class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 33 }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(hBOOL(c_in(v_x, v_U, tc_Com_Opname)), class_OrderedGroup_Oab__semigroup__add(tc_nat), v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, fresh8(hBOOL(c_in(v_x, v_U, tc_Com_Opname)), true2, v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 28 (cls_insert__absorb_0) }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oimage(v_mgt__call, c_Set_Oinsert(v_x, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 29 (cls_image__insert_0) }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 13 (cls_conjecture_1) R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_x), v_G, t_a), tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 31 (cls_Diff__insert2_0) }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), tc_fun(t_a, tc_bool)), v_G, tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 19 (cls_Diff__cancel_0) }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), v_G, tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 25 (cls_empty__Diff_0) }
% 150.41/19.78 fresh606(c_lessequals(fresh153(Z, Z, tc_fun(t_a, tc_bool), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 38 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh651(W, W, tc_fun(t_a, tc_bool), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), fresh683(V, V, tc_fun(t_a, tc_bool), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G)), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 21 (cls_Inf__binary_0) }
% 150.41/19.78 fresh606(c_lessequals(fresh651(W, W, tc_fun(t_a, tc_bool), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a, tc_bool)), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), v_G)), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 24 (cls_Int__commute_0) }
% 150.41/19.78 fresh606(c_lessequals(fresh651(W, W, tc_fun(t_a, tc_bool), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a, tc_bool)), v_G), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 21 (cls_Inf__binary_0) R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh651(W, W, tc_fun(t_a, tc_bool), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 20 (cls_Sup__binary_0) }
% 150.41/19.78 fresh606(c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a, tc_bool)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool))), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 23 (cls_Un__commute_0) }
% 150.41/19.78 fresh606(c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a, tc_bool)), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 22 (cls_sup__bot__right_0) R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Lattices_Obounded__lattice(tc_fun(t_a, tc_bool)), true2, tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Lattices_Obounded__lattice(tc_fun(t_a, tc_bool)), class_OrderedGroup_Oab__semigroup__add(tc_nat), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 33 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Lattices_Obounded__lattice(tc_fun(t_a, tc_bool)), class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 34 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Lattices_Obounded__lattice(tc_fun(t_a, tc_bool)), class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 35 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Lattices_Obounded__lattice(tc_fun(t_a, tc_bool)), class_OrderedGroup_Ocomm__monoid__add(tc_nat), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 36 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Lattices_Obounded__lattice(tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_nat), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 37 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Lattices_Obounded__lattice(tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 16 (clsarity_fun__Lattices_Obounded__lattice) R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Lattices_Obounded__lattice(tc_bool), true2, t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Lattices_Obounded__lattice(tc_bool), class_OrderedGroup_Oab__semigroup__add(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 33 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Lattices_Obounded__lattice(tc_bool), class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 34 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Lattices_Obounded__lattice(tc_bool), class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 35 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Lattices_Obounded__lattice(tc_bool), class_OrderedGroup_Ocomm__monoid__add(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 36 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Lattices_Obounded__lattice(tc_bool), class_Orderings_Opreorder(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 37 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Lattices_Obounded__lattice(tc_bool), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 7 (clsarity_bool__Lattices_Obounded__lattice) }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(true2, class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 33 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 34 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 35 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_OrderedGroup_Ocomm__monoid__add(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 36 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Orderings_Opreorder(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 37 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(fresh117(class_Orderings_Opreorder(tc_bool), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 10 (clsarity_fun__Lattices_Obounded__lattice) }
% 150.41/19.78 fresh606(c_lessequals(fresh55(true2, class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 33 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 34 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 35 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_OrderedGroup_Ocomm__monoid__add(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 36 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Orderings_Opreorder(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by lemma 37 R->L }
% 150.41/19.78 fresh606(c_lessequals(fresh55(class_Orderings_Opreorder(tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 12 (cls_sup__bot__right_0) }
% 150.41/19.78 fresh606(c_lessequals(fresh683(U, U, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 21 (cls_Inf__binary_0) }
% 150.41/19.78 fresh606(c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a, tc_bool)), v_G), c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), v_G, tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.78 = { by axiom 26 (cls_inf__le1_0) R->L }
% 150.41/19.78 fresh606(fresh458(class_Lattices_Olower__semilattice(tc_fun(t_a, tc_bool)), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.79 fresh606(fresh458(class_Lattices_Olower__semilattice(tc_fun(t_a, tc_bool)), class_OrderedGroup_Oab__semigroup__add(tc_nat), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 33 R->L }
% 150.41/19.79 fresh606(fresh458(class_Lattices_Olower__semilattice(tc_fun(t_a, tc_bool)), class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 34 R->L }
% 150.41/19.79 fresh606(fresh458(class_Lattices_Olower__semilattice(tc_fun(t_a, tc_bool)), class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 35 R->L }
% 150.41/19.79 fresh606(fresh458(class_Lattices_Olower__semilattice(tc_fun(t_a, tc_bool)), class_OrderedGroup_Ocomm__monoid__add(tc_nat), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 36 R->L }
% 150.41/19.79 fresh606(fresh458(class_Lattices_Olower__semilattice(tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_nat), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 37 R->L }
% 150.41/19.79 fresh606(fresh458(class_Lattices_Olower__semilattice(tc_fun(t_a, tc_bool)), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 17 (clsarity_fun__Lattices_Olower__semilattice) R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Lattices_Olattice(tc_bool), true2, t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Lattices_Olattice(tc_bool), class_OrderedGroup_Oab__semigroup__add(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 33 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Lattices_Olattice(tc_bool), class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 34 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Lattices_Olattice(tc_bool), class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 35 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Lattices_Olattice(tc_bool), class_OrderedGroup_Ocomm__monoid__add(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 36 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Lattices_Olattice(tc_bool), class_Orderings_Opreorder(tc_nat), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 37 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Lattices_Olattice(tc_bool), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 8 (clsarity_bool__Lattices_Olattice) }
% 150.41/19.79 fresh606(fresh458(fresh114(true2, class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 33 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 34 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 35 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_OrderedGroup_Ocomm__monoid__add(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 36 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Orderings_Opreorder(tc_nat), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 37 R->L }
% 150.41/19.79 fresh606(fresh458(fresh114(class_Orderings_Opreorder(tc_bool), class_Orderings_Opreorder(tc_bool), t_a, tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 11 (clsarity_fun__Lattices_Olower__semilattice) }
% 150.41/19.79 fresh606(fresh458(true2, class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.79 fresh606(fresh458(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 33 R->L }
% 150.41/19.79 fresh606(fresh458(class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 34 R->L }
% 150.41/19.79 fresh606(fresh458(class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 35 R->L }
% 150.41/19.79 fresh606(fresh458(class_OrderedGroup_Ocomm__monoid__add(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 36 R->L }
% 150.41/19.79 fresh606(fresh458(class_Orderings_Opreorder(tc_nat), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 37 R->L }
% 150.41/19.79 fresh606(fresh458(class_Orderings_Opreorder(tc_bool), class_Orderings_Opreorder(tc_bool), tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 15 (cls_inf__le1_0) }
% 150.41/19.79 fresh606(true2, class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 1 (clsarity_nat__OrderedGroup_Oab__semigroup__add) R->L }
% 150.41/19.79 fresh606(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 33 R->L }
% 150.41/19.79 fresh606(class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 34 R->L }
% 150.41/19.79 fresh606(class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 35 R->L }
% 150.41/19.79 fresh606(class_OrderedGroup_Ocomm__monoid__add(tc_nat), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 36 R->L }
% 150.41/19.79 fresh606(class_Orderings_Opreorder(tc_nat), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by lemma 37 R->L }
% 150.41/19.79 fresh606(class_Orderings_Opreorder(tc_bool), class_Orderings_Opreorder(tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_x), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 150.41/19.79 = { by axiom 9 (cls_assms_I1_J_0) }
% 150.41/19.79 true2
% 150.41/19.79 % SZS output end Proof
% 150.41/19.79
% 150.41/19.79 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------