TSTP Solution File: SCT123+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n032.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 14:22:10 EDT 2023
% Result : Theorem 254.26s 33.69s
% Output : Proof 254.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Thu Aug 24 16:27:27 EDT 2023
% 0.11/0.30 % CPUTime :
% 254.26/33.69 Command-line arguments: --flatten
% 254.26/33.69
% 254.26/33.69 % SZS status Theorem
% 254.26/33.69
% 254.26/33.71 % SZS output start Proof
% 254.26/33.71 Take the following subset of the input axioms:
% 254.26/33.71 fof(conj_0, hypothesis, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))).
% 254.26/33.71 fof(conj_1, conjecture, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))).
% 254.26/33.71 fof(fact_Pi__I, axiom, ![V_f_2, T_a, V_B_2, V_A_2, T_b]: (![B_x]: (hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)) => hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), hAPP(V_B_2, B_x)))) => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, V_B_2))))).
% 254.26/33.71 fof(fact_Prof__def, axiom, c_Arrow__Order__Mirabelle_OProf=c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))).
% 254.26/33.71 fof(help_c__COMBK__1, axiom, ![V_P, V_Q, T_a2, T_b2]: hAPP(c_COMBK(T_a2, T_b2, V_P), V_Q)=V_P).
% 254.26/33.71
% 254.26/33.71 Now clausify the problem and encode Horn clauses using encoding 3 of
% 254.26/33.71 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 254.26/33.71 We repeatedly replace C & s=t => u=v by the two clauses:
% 254.26/33.71 fresh(y, y, x1...xn) = u
% 254.26/33.71 C => fresh(s, t, x1...xn) = v
% 254.26/33.71 where fresh is a fresh function symbol and x1..xn are the free
% 254.26/33.71 variables of u and v.
% 254.26/33.71 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 254.26/33.71 input problem has no model of domain size 1).
% 254.26/33.71
% 254.26/33.71 The encoding turns the above axioms into the following unit equations and goals:
% 254.26/33.71
% 254.26/33.71 Axiom 1 (help_c__COMBK__1): hAPP(c_COMBK(X, Y, Z), W) = Z.
% 254.26/33.71 Axiom 2 (fact_in__mono): fresh215(X, X, Y, Z, W, V) = hBOOL(hAPP(hAPP(c_member(V), Y), Z)).
% 254.26/33.71 Axiom 3 (fact_Pi__I_1): fresh396(X, X, Y, Z, W, V, U) = true2.
% 254.26/33.71 Axiom 4 (fact_extensional__funcset__mem): fresh236(X, X, Y, Z, W, V, U, T) = hBOOL(hAPP(hAPP(c_member(U), hAPP(V, Y)), Z)).
% 254.26/33.71 Axiom 5 (fact_PiE): fresh398(X, X, Y, Z, W, V, U, T) = hBOOL(hAPP(hAPP(c_member(U), hAPP(V, Y)), hAPP(Z, Y))).
% 254.26/33.71 Axiom 6 (conj_0): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)) = true2.
% 254.26/33.71 Axiom 7 (fact_Prof__def): c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)).
% 254.26/33.71 Axiom 8 (fact_Pi__I_1): fresh396(hBOOL(hAPP(hAPP(c_member(X), hAPP(Y, b_x33(Z, Y, X, W, V))), hAPP(Z, b_x33(Z, Y, X, W, V)))), true2, Z, Y, X, W, V) = hBOOL(hAPP(hAPP(c_member(tc_fun(V, X)), Y), c_FuncSet_OPi(V, X, W, Z))).
% 254.26/33.71
% 254.26/33.71 Lemma 9: fresh215(X, X, hAPP(Y, Z), W, V, U) = fresh236(T, T, Z, W, S, Y, U, X2).
% 254.26/33.71 Proof:
% 254.26/33.71 fresh215(X, X, hAPP(Y, Z), W, V, U)
% 254.26/33.71 = { by axiom 2 (fact_in__mono) }
% 254.26/33.71 hBOOL(hAPP(hAPP(c_member(U), hAPP(Y, Z)), W))
% 254.26/33.71 = { by axiom 4 (fact_extensional__funcset__mem) R->L }
% 254.26/33.71 fresh236(T, T, Z, W, S, Y, U, X2)
% 254.26/33.71
% 254.26/33.71 Lemma 10: fresh236(X, X, Y, hAPP(Z, Y), W, V, U, T) = fresh398(S, S, Y, Z, X2, V, U, Y2).
% 254.26/33.71 Proof:
% 254.26/33.71 fresh236(X, X, Y, hAPP(Z, Y), W, V, U, T)
% 254.26/33.71 = { by lemma 9 R->L }
% 254.26/33.71 fresh215(Z2, Z2, hAPP(V, Y), hAPP(Z, Y), W2, U)
% 254.26/33.71 = { by axiom 2 (fact_in__mono) }
% 254.26/33.71 hBOOL(hAPP(hAPP(c_member(U), hAPP(V, Y)), hAPP(Z, Y)))
% 254.26/33.71 = { by axiom 5 (fact_PiE) R->L }
% 254.26/33.71 fresh398(S, S, Y, Z, X2, V, U, Y2)
% 254.26/33.71
% 254.26/33.71 Goal 1 (conj_1): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf)) = true2.
% 254.26/33.71 Proof:
% 254.26/33.71 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))
% 254.26/33.71 = { by axiom 7 (fact_Prof__def) }
% 254.26/33.71 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))))
% 254.26/33.71 = { by axiom 8 (fact_Pi__I_1) R->L }
% 254.26/33.71 fresh396(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi))), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)))), true2, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.71 = { by axiom 2 (fact_in__mono) R->L }
% 254.26/33.71 fresh396(fresh215(X, X, hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), Y, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), true2, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.71 = { by lemma 9 }
% 254.26/33.71 fresh396(fresh236(Z, Z, b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), W, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), V), true2, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.71 = { by lemma 10 }
% 254.26/33.71 fresh396(fresh398(U, U, b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), T, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), S), true2, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.71 = { by axiom 6 (conj_0) R->L }
% 254.26/33.71 fresh396(fresh398(U, U, b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), T, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), S), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.71 = { by lemma 10 R->L }
% 254.26/33.72 fresh396(fresh236(X2, X2, b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), Y2, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), Z2), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.72 = { by axiom 1 (help_c__COMBK__1) }
% 254.26/33.72 fresh396(fresh236(X2, X2, b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_Arrow__Order__Mirabelle_OLin, Y2, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), Z2), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.72 = { by lemma 9 R->L }
% 254.26/33.72 fresh396(fresh215(W2, W2, hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), b_x33(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), c_Arrow__Order__Mirabelle_OLin, V2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.72 = { by axiom 1 (help_c__COMBK__1) }
% 254.26/33.72 fresh396(fresh215(W2, W2, v_L, c_Arrow__Order__Mirabelle_OLin, V2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.72 = { by axiom 2 (fact_in__mono) }
% 254.26/33.72 fresh396(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
% 254.26/33.72 = { by axiom 3 (fact_Pi__I_1) }
% 254.26/33.72 true2
% 254.26/33.72 % SZS output end Proof
% 254.26/33.72
% 254.26/33.72 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------