TSTP Solution File: SWV841-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV841-1 : 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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 23:06:29 EDT 2023
% Result : Unsatisfiable 50.42s 6.78s
% Output : Proof 51.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV841-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 07:12:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 50.42/6.78 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 50.42/6.78
% 50.42/6.78 % SZS status Unsatisfiable
% 50.42/6.78
% 50.42/6.79 % SZS output start Proof
% 50.42/6.79 Take the following subset of the input axioms:
% 51.09/6.80 fof(cls_Int__commute_0, axiom, ![T_a, V_A, V_B]: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a, tc_bool)), V_A), V_B)=hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a, tc_bool)), V_B), V_A)).
% 51.09/6.80 fof(cls_Int__lower1_0, axiom, ![T_a2, V_B2, V_A2]: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a2, tc_bool)), V_A2), V_B2), V_A2, tc_fun(T_a2, tc_bool))).
% 51.09/6.80 fof(cls_asm_0, axiom, ![V_G, V_ts, T_a2]: (c_Hoare__Mirabelle_Ohoare__derivs(V_G, V_ts, T_a2) | ~c_lessequals(V_ts, V_G, tc_fun(tc_Hoare__Mirabelle_Otriple(T_a2), tc_bool)))).
% 51.09/6.80 fof(cls_conjecture_0, negated_conjecture, c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), t_a)).
% 51.09/6.80 fof(cls_conjecture_1, negated_conjecture, ~c_Hoare__Mirabelle_Ohoare__derivs(v_G, v_ts, t_a) | ~c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a)).
% 51.09/6.80 fof(cls_cut_0, axiom, ![V_G_H, T_a2, V_G2, V_ts2]: (c_Hoare__Mirabelle_Ohoare__derivs(V_G2, V_ts2, T_a2) | (~c_Hoare__Mirabelle_Ohoare__derivs(V_G2, V_G_H, T_a2) | ~c_Hoare__Mirabelle_Ohoare__derivs(V_G_H, V_ts2, T_a2)))).
% 51.09/6.80 fof(cls_empty__subsetI_0, axiom, ![T_a2, V_A2]: c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), V_A2, tc_fun(T_a2, tc_bool))).
% 51.09/6.80 fof(cls_insert__mono_0, axiom, ![V_a, V_C, V_D, T_a2]: (c_lessequals(hAPP(hAPP(c_Set_Oinsert(T_a2), V_a), V_C), hAPP(hAPP(c_Set_Oinsert(T_a2), V_a), V_D), tc_fun(T_a2, tc_bool)) | ~c_lessequals(V_C, V_D, tc_fun(T_a2, tc_bool)))).
% 51.09/6.80 fof(cls_le__iff__inf_0, axiom, ![V_x, V_y, T_a2]: (~class_Lattices_Olower__semilattice(T_a2) | (hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a2), V_x), V_y)=V_x | ~c_lessequals(V_x, V_y, T_a2)))).
% 51.09/6.80 fof(cls_subset__insertI_0, axiom, ![T_a2, V_B2, V_a2]: c_lessequals(V_B2, hAPP(hAPP(c_Set_Oinsert(T_a2), V_a2), V_B2), tc_fun(T_a2, tc_bool))).
% 51.09/6.80 fof(clsarity_bool__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_bool)).
% 51.09/6.80 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))).
% 51.09/6.80
% 51.09/6.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 51.09/6.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 51.09/6.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 51.09/6.80 fresh(y, y, x1...xn) = u
% 51.09/6.80 C => fresh(s, t, x1...xn) = v
% 51.09/6.80 where fresh is a fresh function symbol and x1..xn are the free
% 51.09/6.80 variables of u and v.
% 51.09/6.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 51.09/6.80 input problem has no model of domain size 1).
% 51.09/6.80
% 51.09/6.80 The encoding turns the above axioms into the following unit equations and goals:
% 51.09/6.80
% 51.09/6.80 Axiom 1 (clsarity_bool__Lattices_Olattice): class_Lattices_Olattice(tc_bool) = true2.
% 51.09/6.80 Axiom 2 (clsarity_fun__Lattices_Olower__semilattice): fresh71(X, X, Y, Z) = true2.
% 51.09/6.80 Axiom 3 (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).
% 51.09/6.80 Axiom 4 (cls_asm_0): fresh302(X, X, Y, Z, W) = true2.
% 51.09/6.80 Axiom 5 (cls_cut_0): fresh281(X, X, Y, Z, W) = true2.
% 51.09/6.80 Axiom 6 (cls_le__iff__inf_0): fresh184(X, X, Y, Z, W) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(Y), Z), W).
% 51.09/6.80 Axiom 7 (clsarity_fun__Lattices_Olower__semilattice): fresh71(class_Lattices_Olattice(X), true2, Y, X) = class_Lattices_Olower__semilattice(tc_fun(Y, X)).
% 51.09/6.80 Axiom 8 (cls_le__iff__inf_0): fresh57(X, X, Y, Z, W) = Z.
% 51.09/6.80 Axiom 9 (cls_empty__subsetI_0): c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)), Y, tc_fun(X, tc_bool)) = true2.
% 51.09/6.80 Axiom 10 (cls_cut_0): fresh282(X, X, Y, Z, W, V) = c_Hoare__Mirabelle_Ohoare__derivs(Y, Z, W).
% 51.09/6.80 Axiom 11 (cls_insert__mono_0): fresh196(X, X, Y, Z, W, V) = true2.
% 51.09/6.80 Axiom 12 (cls_subset__insertI_0): c_lessequals(X, hAPP(hAPP(c_Set_Oinsert(Y), Z), X), tc_fun(Y, tc_bool)) = true2.
% 51.09/6.80 Axiom 13 (cls_conjecture_0): c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), t_a) = true2.
% 51.09/6.80 Axiom 14 (cls_le__iff__inf_0): fresh184(c_lessequals(X, Y, Z), true2, Z, X, Y) = fresh57(class_Lattices_Olower__semilattice(Z), true2, Z, X, Y).
% 51.09/6.80 Axiom 15 (cls_Int__lower1_0): c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X, tc_bool)), Y), Z), Y, tc_fun(X, tc_bool)) = true2.
% 51.09/6.80 Axiom 16 (cls_cut_0): fresh282(c_Hoare__Mirabelle_Ohoare__derivs(X, Y, Z), true2, W, Y, Z, X) = fresh281(c_Hoare__Mirabelle_Ohoare__derivs(W, X, Z), true2, W, Y, Z).
% 51.09/6.80 Axiom 17 (cls_asm_0): fresh302(c_lessequals(X, Y, tc_fun(tc_Hoare__Mirabelle_Otriple(Z), tc_bool)), true2, Y, X, Z) = c_Hoare__Mirabelle_Ohoare__derivs(Y, X, Z).
% 51.09/6.80 Axiom 18 (cls_insert__mono_0): fresh196(c_lessequals(X, Y, tc_fun(Z, tc_bool)), true2, Z, W, X, Y) = c_lessequals(hAPP(hAPP(c_Set_Oinsert(Z), W), X), hAPP(hAPP(c_Set_Oinsert(Z), W), Y), tc_fun(Z, tc_bool)).
% 51.09/6.80
% 51.09/6.80 Goal 1 (cls_conjecture_1): tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), c_Hoare__Mirabelle_Ohoare__derivs(v_G, v_ts, t_a)) = tuple2(true2, true2).
% 51.09/6.80 Proof:
% 51.09/6.80 tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), c_Hoare__Mirabelle_Ohoare__derivs(v_G, v_ts, t_a))
% 51.09/6.80 = { by axiom 10 (cls_cut_0) R->L }
% 51.09/6.80 tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), fresh282(true2, true2, v_G, v_ts, t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)))
% 51.09/6.80 = { by axiom 4 (cls_asm_0) R->L }
% 51.09/6.80 tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), fresh282(fresh302(true2, true2, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), v_ts, t_a), true2, v_G, v_ts, t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)))
% 51.09/6.80 = { by axiom 12 (cls_subset__insertI_0) R->L }
% 51.09/6.80 tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), fresh282(fresh302(c_lessequals(v_ts, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), true2, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), v_ts, t_a), true2, v_G, v_ts, t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)))
% 51.09/6.80 = { by axiom 17 (cls_asm_0) }
% 51.09/6.80 tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), v_ts, t_a), true2, v_G, v_ts, t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)))
% 51.09/6.80 = { by axiom 16 (cls_cut_0) }
% 51.09/6.80 tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), fresh281(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), t_a), true2, v_G, v_ts, t_a))
% 51.09/6.80 = { by axiom 13 (cls_conjecture_0) }
% 51.09/6.80 tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), fresh281(true2, true2, v_G, v_ts, t_a))
% 51.09/6.80 = { by axiom 5 (cls_cut_0) }
% 51.09/6.80 tuple2(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), true2)
% 51.09/6.80 = { by axiom 10 (cls_cut_0) R->L }
% 51.09/6.80 tuple2(fresh282(true2, true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 4 (cls_asm_0) R->L }
% 51.09/6.80 tuple2(fresh282(fresh302(true2, true2, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)))), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 15 (cls_Int__lower1_0) R->L }
% 51.09/6.80 tuple2(fresh282(fresh302(c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), true2, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)))), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 17 (cls_asm_0) }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)))), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 3 (cls_Int__commute_0) }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 6 (cls_le__iff__inf_0) R->L }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), fresh184(true2, true2, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 11 (cls_insert__mono_0) R->L }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), fresh184(fresh196(true2, true2, tc_Hoare__Mirabelle_Otriple(t_a), v_t, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), v_ts), true2, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 9 (cls_empty__subsetI_0) R->L }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), fresh184(fresh196(c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), v_ts, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_t, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), v_ts), true2, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 18 (cls_insert__mono_0) }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), fresh184(c_lessequals(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), true2, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 14 (cls_le__iff__inf_0) }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), fresh57(class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), true2, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 7 (clsarity_fun__Lattices_Olower__semilattice) R->L }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), fresh57(fresh71(class_Lattices_Olattice(tc_bool), true2, tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), true2, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 1 (clsarity_bool__Lattices_Olattice) }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), fresh57(fresh71(true2, true2, tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), true2, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 2 (clsarity_fun__Lattices_Olower__semilattice) }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), fresh57(true2, true2, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 8 (cls_le__iff__inf_0) }
% 51.09/6.80 tuple2(fresh282(c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts)), true2)
% 51.09/6.80 = { by axiom 16 (cls_cut_0) }
% 51.09/6.80 tuple2(fresh281(c_Hoare__Mirabelle_Ohoare__derivs(v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts), t_a), true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), true2)
% 51.09/6.80 = { by axiom 13 (cls_conjecture_0) }
% 51.09/6.80 tuple2(fresh281(true2, true2, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))), t_a), true2)
% 51.09/6.80 = { by axiom 5 (cls_cut_0) }
% 51.09/6.80 tuple2(true2, true2)
% 51.09/6.80 % SZS output end Proof
% 51.09/6.80
% 51.09/6.80 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------