TSTP Solution File: SWV829-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV829-1 : 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 : n026.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 23:06:26 EDT 2023
% Result : Unsatisfiable 72.70s 9.79s
% Output : Proof 72.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV829-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 05:25:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 72.70/9.79 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 72.70/9.79
% 72.70/9.79 % SZS status Unsatisfiable
% 72.70/9.79
% 72.70/9.80 % SZS output start Proof
% 72.70/9.80 Take the following subset of the input axioms:
% 72.70/9.80 fof(cls_COMBB__def_0, axiom, ![T_a, T_b, V_P, V_Q, T_c, V_R]: hAPP(c_COMBB(V_P, V_Q, T_b, T_a, T_c), V_R)=hAPP(V_P, hAPP(V_Q, V_R))).
% 72.70/9.80 fof(cls_COMBS__def_0, axiom, ![T_a2, T_b2, V_P2, V_Q2, T_c2, V_R2]: hAPP(c_COMBS(V_P2, V_Q2, T_b2, T_c2, T_a2), V_R2)=hAPP(hAPP(V_P2, V_R2), hAPP(V_Q2, V_R2))).
% 72.70/9.80 fof(cls_Collect__def_0, axiom, ![T_a2, V_P2]: c_Collect(V_P2, T_a2)=V_P2).
% 72.70/9.80 fof(cls_conjecture_0, negated_conjecture, hBOOL(c_in(v_pn, v_Procs, tc_Com_Opname))).
% 72.70/9.80 fof(cls_conjecture_1, negated_conjecture, ~c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))).
% 72.70/9.80 fof(cls_empty__subsetI_0, axiom, ![V_A, T_a2]: c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), V_A, tc_fun(T_a2, tc_bool))).
% 72.70/9.81 fof(cls_image__insert_0, axiom, ![V_a, V_B, V_f, T_a2, T_b2]: c_Set_Oimage(V_f, c_Set_Oinsert(V_a, V_B, T_b2), T_b2, T_a2)=c_Set_Oinsert(hAPP(V_f, V_a), c_Set_Oimage(V_f, V_B, T_b2, T_a2), T_a2)).
% 72.70/9.81 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)))).
% 72.70/9.81 fof(cls_insert__mono_0, axiom, ![V_C, V_D, T_a2, V_a2]: (c_lessequals(c_Set_Oinsert(V_a2, V_C, T_a2), c_Set_Oinsert(V_a2, V_D, T_a2), tc_fun(T_a2, tc_bool)) | ~c_lessequals(V_C, V_D, tc_fun(T_a2, tc_bool)))).
% 72.70/9.81 fof(cls_singleton__conv2_0, axiom, ![T_a2, V_a2]: c_Collect(c_fequal(V_a2, T_a2), T_a2)=c_Set_Oinsert(V_a2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2)).
% 72.70/9.81
% 72.70/9.81 Now clausify the problem and encode Horn clauses using encoding 3 of
% 72.70/9.81 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 72.70/9.81 We repeatedly replace C & s=t => u=v by the two clauses:
% 72.70/9.81 fresh(y, y, x1...xn) = u
% 72.70/9.81 C => fresh(s, t, x1...xn) = v
% 72.70/9.81 where fresh is a fresh function symbol and x1..xn are the free
% 72.70/9.81 variables of u and v.
% 72.70/9.81 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 72.70/9.81 input problem has no model of domain size 1).
% 72.70/9.81
% 72.70/9.81 The encoding turns the above axioms into the following unit equations and goals:
% 72.70/9.81
% 72.70/9.81 Axiom 1 (cls_Collect__def_0): c_Collect(X, Y) = X.
% 72.70/9.81 Axiom 2 (cls_conjecture_0): hBOOL(c_in(v_pn, v_Procs, tc_Com_Opname)) = true2.
% 72.70/9.81 Axiom 3 (cls_singleton__conv2_0): c_Collect(c_fequal(X, Y), Y) = c_Set_Oinsert(X, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_bool)), Y).
% 72.70/9.81 Axiom 4 (cls_insert__absorb_0): fresh11(X, X, Y, Z, W) = Z.
% 72.70/9.81 Axiom 5 (cls_COMBB__def_0): hAPP(c_COMBB(X, Y, Z, W, V), U) = hAPP(X, hAPP(Y, U)).
% 72.70/9.81 Axiom 6 (cls_COMBS__def_0): hAPP(c_COMBS(X, Y, Z, W, V), U) = hAPP(hAPP(X, U), hAPP(Y, U)).
% 72.70/9.81 Axiom 7 (cls_empty__subsetI_0): c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)), Y, tc_fun(X, tc_bool)) = true2.
% 72.70/9.81 Axiom 8 (cls_insert__mono_0): fresh339(X, X, Y, Z, W, V) = true2.
% 72.70/9.81 Axiom 9 (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).
% 72.70/9.81 Axiom 10 (cls_insert__absorb_0): fresh11(hBOOL(c_in(X, Y, Z)), true2, X, Y, Z) = c_Set_Oinsert(X, Y, Z).
% 72.70/9.81 Axiom 11 (cls_insert__mono_0): fresh339(c_lessequals(X, Y, tc_fun(Z, tc_bool)), true2, W, X, Z, Y) = c_lessequals(c_Set_Oinsert(W, X, Z), c_Set_Oinsert(W, Y, Z), tc_fun(Z, tc_bool)).
% 72.70/9.81
% 72.70/9.81 Lemma 12: c_Set_Oinsert(X, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_bool)), Y) = c_fequal(X, Y).
% 72.70/9.81 Proof:
% 72.70/9.81 c_Set_Oinsert(X, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_bool)), Y)
% 72.70/9.81 = { by axiom 3 (cls_singleton__conv2_0) R->L }
% 72.70/9.81 c_Collect(c_fequal(X, Y), Y)
% 72.70/9.81 = { by axiom 1 (cls_Collect__def_0) }
% 72.70/9.81 c_fequal(X, Y)
% 72.70/9.81
% 72.70/9.81 Goal 1 (cls_conjecture_1): c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)) = true2.
% 72.70/9.81 Proof:
% 72.70/9.81 c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by lemma 12 }
% 72.70/9.81 c_lessequals(c_fequal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by axiom 4 (cls_insert__absorb_0) R->L }
% 72.70/9.81 c_lessequals(c_fequal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), fresh11(true2, true2, v_pn, v_Procs, tc_Com_Opname), tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by axiom 2 (cls_conjecture_0) R->L }
% 72.70/9.81 c_lessequals(c_fequal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), fresh11(hBOOL(c_in(v_pn, v_Procs, tc_Com_Opname)), true2, v_pn, v_Procs, tc_Com_Opname), tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by axiom 10 (cls_insert__absorb_0) }
% 72.70/9.81 c_lessequals(c_fequal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oinsert(v_pn, v_Procs, tc_Com_Opname), tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by axiom 9 (cls_image__insert_0) }
% 72.70/9.81 c_lessequals(c_fequal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oinsert(hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_pn), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by axiom 6 (cls_COMBS__def_0) }
% 72.70/9.81 c_lessequals(c_fequal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oinsert(hAPP(hAPP(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_pn), hAPP(v_Q, v_pn)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by axiom 6 (cls_COMBS__def_0) }
% 72.70/9.81 c_lessequals(c_fequal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oinsert(hAPP(hAPP(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), v_pn), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by axiom 5 (cls_COMBB__def_0) }
% 72.70/9.81 c_lessequals(c_fequal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by lemma 12 R->L }
% 72.70/9.81 c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))
% 72.70/9.81 = { by axiom 11 (cls_insert__mono_0) R->L }
% 72.70/9.81 fresh339(c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)), tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), true2, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)))
% 72.70/9.81 = { by axiom 7 (cls_empty__subsetI_0) }
% 72.70/9.81 fresh339(true2, true2, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(v_P, v_pn)), hAPP(c_Com_Ocom_OBODY, v_pn)), hAPP(v_Q, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a), c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Com_Ocom_OBODY, tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a))), v_Q, tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_a)), v_Procs, tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a)))
% 72.70/9.81 = { by axiom 8 (cls_insert__mono_0) }
% 72.70/9.81 true2
% 72.70/9.81 % SZS output end Proof
% 72.70/9.81
% 72.70/9.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------