TSTP Solution File: SWV884-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV884-1 : 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 : n010.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 23:06:37 EDT 2023
% Result : Unsatisfiable 275.64s 35.70s
% Output : Proof 275.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWV884-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 03:18:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 275.64/35.70 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 275.64/35.70
% 275.64/35.70 % SZS status Unsatisfiable
% 275.64/35.70
% 275.64/35.71 % SZS output start Proof
% 275.64/35.71 Take the following subset of the input axioms:
% 275.64/35.72 fof(cls_Diff__subset_0, axiom, ![T_a, V_A, V_B]: c_lessequals(c_HOL_Ominus__class_Ominus(V_A, V_B, tc_fun(T_a, tc_bool)), V_A, tc_fun(T_a, tc_bool))).
% 275.64/35.72 fof(cls_conjecture_1, negated_conjecture, c_lessequals(v_G, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))).
% 275.64/35.72 fof(cls_conjecture_4, negated_conjecture, c_in(v_pn, v_U, tc_Com_Opname)).
% 275.64/35.72 fof(cls_conjecture_6, negated_conjecture, ~c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), v_G, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))).
% 275.64/35.72 fof(cls_double__diff_0, axiom, ![V_C, T_a2, V_A2, V_B2]: (c_HOL_Ominus__class_Ominus(V_B2, c_HOL_Ominus__class_Ominus(V_C, V_A2, tc_fun(T_a2, tc_bool)), tc_fun(T_a2, tc_bool))=V_A2 | (~c_lessequals(V_B2, V_C, tc_fun(T_a2, tc_bool)) | ~c_lessequals(V_A2, V_B2, tc_fun(T_a2, tc_bool))))).
% 275.64/35.72 fof(cls_imageI_0, axiom, ![V_x, T_b, V_f, T_a2, V_A2]: (c_in(hAPP(V_f, V_x), c_Set_Oimage(V_f, V_A2, T_a2, T_b), T_b) | ~c_in(V_x, V_A2, T_a2))).
% 275.64/35.72 fof(cls_inf__le2_0, axiom, ![V_y, T_a2, V_x2]: (~class_Lattices_Olower__semilattice(T_a2) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x2, V_y, T_a2), V_y, T_a2))).
% 275.64/35.72 fof(cls_insert__absorb_0, axiom, ![V_a, T_a2, V_A2]: (c_Set_Oinsert(V_a, V_A2, T_a2)=V_A2 | ~c_in(V_a, V_A2, T_a2))).
% 275.64/35.72 fof(cls_insert__code_1, axiom, ![T_a2, V_A2, V_x2]: hBOOL(hAPP(c_Set_Oinsert(V_x2, V_A2, T_a2), V_x2))).
% 275.64/35.72 fof(cls_insert__inter__insert_0, axiom, ![T_a2, V_A2, V_B2, V_a2]: c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a2, V_A2, T_a2), c_Set_Oinsert(V_a2, V_B2, T_a2), tc_fun(T_a2, tc_bool))=c_Set_Oinsert(V_a2, c_Lattices_Olower__semilattice__class_Oinf(V_A2, V_B2, tc_fun(T_a2, tc_bool)), T_a2)).
% 275.64/35.72 fof(cls_le__iff__inf_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Lattices_Olower__semilattice(T_a2) | (c_Lattices_Olower__semilattice__class_Oinf(V_x2, V_y2, T_a2)=V_x2 | ~c_lessequals(V_x2, V_y2, T_a2)))).
% 275.64/35.72 fof(cls_mem__def_1, axiom, ![V_S, T_a2, V_x2]: (c_in(V_x2, V_S, T_a2) | ~hBOOL(hAPP(V_S, V_x2)))).
% 275.64/35.72 fof(cls_subset__insertI2_0, axiom, ![V_b, T_a2, V_A2, V_B2]: (c_lessequals(V_A2, c_Set_Oinsert(V_b, V_B2, T_a2), tc_fun(T_a2, tc_bool)) | ~c_lessequals(V_A2, V_B2, tc_fun(T_a2, tc_bool)))).
% 275.64/35.72 fof(cls_subset__refl_0, axiom, ![T_a2, V_A2]: c_lessequals(V_A2, V_A2, tc_fun(T_a2, tc_bool))).
% 275.64/35.72 fof(clsarity_bool__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_bool)).
% 275.64/35.72 fof(clsarity_fun__Lattices_Olower__semilattice, axiom, ![T_2, T_1]: (class_Lattices_Olower__semilattice(tc_fun(T_2, T_1)) | ~class_Lattices_Olattice(T_1))).
% 275.64/35.72
% 275.64/35.72 Now clausify the problem and encode Horn clauses using encoding 3 of
% 275.64/35.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 275.64/35.72 We repeatedly replace C & s=t => u=v by the two clauses:
% 275.64/35.72 fresh(y, y, x1...xn) = u
% 275.64/35.72 C => fresh(s, t, x1...xn) = v
% 275.64/35.72 where fresh is a fresh function symbol and x1..xn are the free
% 275.64/35.72 variables of u and v.
% 275.64/35.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 275.64/35.72 input problem has no model of domain size 1).
% 275.64/35.72
% 275.64/35.72 The encoding turns the above axioms into the following unit equations and goals:
% 275.64/35.72
% 275.64/35.72 Axiom 1 (clsarity_bool__Lattices_Olattice): class_Lattices_Olattice(tc_bool) = true2.
% 275.64/35.72 Axiom 2 (cls_conjecture_4): c_in(v_pn, v_U, tc_Com_Opname) = true2.
% 275.64/35.72 Axiom 3 (cls_subset__refl_0): c_lessequals(X, X, tc_fun(Y, tc_bool)) = true2.
% 275.64/35.72 Axiom 4 (clsarity_fun__Lattices_Olower__semilattice): fresh165(X, X, Y, Z) = true2.
% 275.64/35.72 Axiom 5 (cls_insert__code_1): hBOOL(hAPP(c_Set_Oinsert(X, Y, Z), X)) = true2.
% 275.64/35.72 Axiom 6 (cls_inf__le2_0): fresh573(X, X, Y, Z, W) = true2.
% 275.64/35.72 Axiom 7 (cls_le__iff__inf_0): fresh510(X, X, Y, Z, W) = c_Lattices_Olower__semilattice__class_Oinf(Z, W, Y).
% 275.64/35.72 Axiom 8 (cls_mem__def_1): fresh449(X, X, Y, Z, W) = true2.
% 275.64/35.72 Axiom 9 (clsarity_fun__Lattices_Olower__semilattice): fresh165(class_Lattices_Olattice(X), true2, Y, X) = class_Lattices_Olower__semilattice(tc_fun(Y, X)).
% 275.64/35.72 Axiom 10 (cls_le__iff__inf_0): fresh77(X, X, Y, Z, W) = Z.
% 275.64/35.72 Axiom 11 (cls_insert__absorb_0): fresh11(X, X, Y, Z, W) = Z.
% 275.64/35.72 Axiom 12 (cls_inf__le2_0): fresh573(class_Lattices_Olower__semilattice(X), true2, X, Y, Z) = c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(Y, Z, X), Z, X).
% 275.64/35.72 Axiom 13 (cls_subset__insertI2_0): fresh237(X, X, Y, Z, W, V) = true2.
% 275.64/35.72 Axiom 14 (cls_double__diff_0): fresh57(X, X, Y, Z, W, V) = W.
% 275.64/35.72 Axiom 15 (cls_conjecture_1): c_lessequals(v_G, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)) = true2.
% 275.64/35.72 Axiom 16 (cls_Diff__subset_0): c_lessequals(c_HOL_Ominus__class_Ominus(X, Y, tc_fun(Z, tc_bool)), X, tc_fun(Z, tc_bool)) = true2.
% 275.64/35.72 Axiom 17 (cls_double__diff_0): fresh697(X, X, Y, Z, W, V) = c_HOL_Ominus__class_Ominus(Y, c_HOL_Ominus__class_Ominus(Z, W, tc_fun(V, tc_bool)), tc_fun(V, tc_bool)).
% 275.64/35.72 Axiom 18 (cls_imageI_0): fresh599(X, X, Y, Z, W, V, U) = true2.
% 275.64/35.72 Axiom 19 (cls_mem__def_1): fresh449(hBOOL(hAPP(X, Y)), true2, Y, X, Z) = c_in(Y, X, Z).
% 275.64/35.72 Axiom 20 (cls_le__iff__inf_0): fresh510(class_Lattices_Olower__semilattice(X), true2, X, Y, Z) = fresh77(c_lessequals(Y, Z, X), true2, X, Y, Z).
% 275.64/35.72 Axiom 21 (cls_insert__absorb_0): fresh11(c_in(X, Y, Z), true2, X, Y, Z) = c_Set_Oinsert(X, Y, Z).
% 275.64/35.72 Axiom 22 (cls_insert__inter__insert_0): c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X, Y, Z), c_Set_Oinsert(X, W, Z), tc_fun(Z, tc_bool)) = c_Set_Oinsert(X, c_Lattices_Olower__semilattice__class_Oinf(Y, W, tc_fun(Z, tc_bool)), Z).
% 275.64/35.72 Axiom 23 (cls_imageI_0): fresh599(c_in(X, Y, Z), true2, W, X, Y, Z, V) = c_in(hAPP(W, X), c_Set_Oimage(W, Y, Z, V), V).
% 275.64/35.72 Axiom 24 (cls_subset__insertI2_0): fresh237(c_lessequals(X, Y, tc_fun(Z, tc_bool)), true2, X, W, Y, Z) = c_lessequals(X, c_Set_Oinsert(W, Y, Z), tc_fun(Z, tc_bool)).
% 275.64/35.72 Axiom 25 (cls_double__diff_0): fresh697(c_lessequals(X, Y, tc_fun(Z, tc_bool)), true2, Y, W, X, Z) = fresh57(c_lessequals(Y, W, tc_fun(Z, tc_bool)), true2, Y, W, X, Z).
% 275.64/35.72
% 275.64/35.72 Lemma 26: class_Lattices_Olower__semilattice(tc_fun(X, tc_bool)) = true2.
% 275.64/35.72 Proof:
% 275.64/35.72 class_Lattices_Olower__semilattice(tc_fun(X, tc_bool))
% 275.64/35.72 = { by axiom 9 (clsarity_fun__Lattices_Olower__semilattice) R->L }
% 275.64/35.72 fresh165(class_Lattices_Olattice(tc_bool), true2, X, tc_bool)
% 275.64/35.72 = { by axiom 1 (clsarity_bool__Lattices_Olattice) }
% 275.64/35.72 fresh165(true2, true2, X, tc_bool)
% 275.64/35.72 = { by axiom 4 (clsarity_fun__Lattices_Olower__semilattice) }
% 275.64/35.72 true2
% 275.64/35.72
% 275.64/35.72 Lemma 27: c_Set_Oinsert(hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z) = c_Set_Oimage(X, v_U, tc_Com_Opname, Y).
% 275.64/35.72 Proof:
% 275.64/35.72 c_Set_Oinsert(hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 21 (cls_insert__absorb_0) R->L }
% 275.64/35.72 fresh11(c_in(hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 11 (cls_insert__absorb_0) R->L }
% 275.64/35.72 fresh11(c_in(hAPP(X, v_pn), fresh11(true2, true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), Z), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 18 (cls_imageI_0) R->L }
% 275.64/35.72 fresh11(c_in(hAPP(X, v_pn), fresh11(fresh599(true2, true2, X, v_pn, v_U, tc_Com_Opname, Y), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), Z), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 2 (cls_conjecture_4) R->L }
% 275.64/35.72 fresh11(c_in(hAPP(X, v_pn), fresh11(fresh599(c_in(v_pn, v_U, tc_Com_Opname), true2, X, v_pn, v_U, tc_Com_Opname, Y), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), Z), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 23 (cls_imageI_0) }
% 275.64/35.72 fresh11(c_in(hAPP(X, v_pn), fresh11(c_in(hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), Z), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 21 (cls_insert__absorb_0) }
% 275.64/35.72 fresh11(c_in(hAPP(X, v_pn), c_Set_Oinsert(hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), Z), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 19 (cls_mem__def_1) R->L }
% 275.64/35.72 fresh11(fresh449(hBOOL(hAPP(c_Set_Oinsert(hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), hAPP(X, v_pn))), true2, hAPP(X, v_pn), c_Set_Oinsert(hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), Z), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 5 (cls_insert__code_1) }
% 275.64/35.72 fresh11(fresh449(true2, true2, hAPP(X, v_pn), c_Set_Oinsert(hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Y), Z), true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 8 (cls_mem__def_1) }
% 275.64/35.72 fresh11(true2, true2, hAPP(X, v_pn), c_Set_Oimage(X, v_U, tc_Com_Opname, Y), Z)
% 275.64/35.72 = { by axiom 11 (cls_insert__absorb_0) }
% 275.64/35.72 c_Set_Oimage(X, v_U, tc_Com_Opname, Y)
% 275.64/35.72
% 275.64/35.72 Goal 1 (cls_conjecture_6): c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), v_G, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)) = true2.
% 275.64/35.72 Proof:
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), v_G, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 10 (cls_le__iff__inf_0) R->L }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(true2, true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 13 (cls_subset__insertI2_0) R->L }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(fresh237(true2, true2, fresh697(true2, true2, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, t_a), hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 16 (cls_Diff__subset_0) R->L }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(fresh237(c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, tc_fun(t_a, tc_bool)), tc_fun(t_a, tc_bool)), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), true2, fresh697(true2, true2, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, t_a), hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 17 (cls_double__diff_0) R->L }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(fresh237(c_lessequals(fresh697(true2, true2, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), true2, fresh697(true2, true2, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, t_a), hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 24 (cls_subset__insertI2_0) }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(c_lessequals(fresh697(true2, true2, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), tc_fun(t_a, tc_bool)), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 15 (cls_conjecture_1) R->L }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(c_lessequals(fresh697(c_lessequals(v_G, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), true2, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), tc_fun(t_a, tc_bool)), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 25 (cls_double__diff_0) }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(c_lessequals(fresh57(c_lessequals(c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), true2, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), tc_fun(t_a, tc_bool)), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 3 (cls_subset__refl_0) }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(c_lessequals(fresh57(true2, true2, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), v_G, t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), tc_fun(t_a, tc_bool)), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 14 (cls_double__diff_0) }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh77(c_lessequals(v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), tc_fun(t_a, tc_bool)), true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 20 (cls_le__iff__inf_0) R->L }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh510(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_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by lemma 26 }
% 275.64/35.72 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), fresh510(true2, true2, tc_fun(t_a, tc_bool), v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a)), t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.72 = { by axiom 7 (cls_le__iff__inf_0) }
% 275.64/35.73 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Lattices_Olower__semilattice__class_Oinf(v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), 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))
% 275.64/35.73 = { by lemma 27 }
% 275.64/35.73 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Lattices_Olower__semilattice__class_Oinf(v_G, c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), 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))
% 275.64/35.73 = { by axiom 22 (cls_insert__inter__insert_0) R->L }
% 275.64/35.73 c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), v_G, t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), tc_fun(t_a, tc_bool)), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.73 = { by lemma 27 }
% 275.64/35.73 c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), v_G, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 275.64/35.73 = { by axiom 12 (cls_inf__le2_0) R->L }
% 275.64/35.73 fresh573(class_Lattices_Olower__semilattice(tc_fun(t_a, tc_bool)), true2, tc_fun(t_a, tc_bool), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), v_G, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a))
% 275.64/35.73 = { by lemma 26 }
% 275.64/35.73 fresh573(true2, true2, tc_fun(t_a, tc_bool), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), v_G, t_a), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a))
% 275.64/35.73 = { by axiom 6 (cls_inf__le2_0) }
% 275.64/35.73 true2
% 275.64/35.73 % SZS output end Proof
% 275.64/35.73
% 275.64/35.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------