TSTP Solution File: SCT097-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT097-1 : 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 : n011.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 14:22:06 EDT 2023
% Result : Unsatisfiable 129.90s 16.97s
% Output : Proof 129.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SCT097-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.32 % Computer : n011.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Thu Aug 24 15:09:22 EDT 2023
% 0.14/0.32 % CPUTime :
% 129.90/16.97 Command-line arguments: --no-flatten-goal
% 129.90/16.97
% 129.90/16.97 % SZS status Unsatisfiable
% 129.90/16.97
% 129.90/16.97 % SZS output start Proof
% 129.90/16.97 Take the following subset of the input axioms:
% 129.90/16.98 fof(cls_CHAINED_0, axiom, ![V_m]: (hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), V_m), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_Lab____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_Lba____)))) | ~c_lessequals(V_m, v_n____, tc_nat))).
% 129.90/16.98 fof(cls_CHAINED_1, axiom, hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_e____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_c____), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))))) | ~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_Lab____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_Lba____))))).
% 129.90/16.98 fof(cls_conjecture_0, negated_conjecture, ~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_e____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_c____), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)))))).
% 129.90/16.98 fof(cls_le__refl_0, axiom, ![V_n]: c_lessequals(V_n, V_n, tc_nat)).
% 129.90/16.98
% 129.90/16.98 Now clausify the problem and encode Horn clauses using encoding 3 of
% 129.90/16.98 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 129.90/16.98 We repeatedly replace C & s=t => u=v by the two clauses:
% 129.90/16.98 fresh(y, y, x1...xn) = u
% 129.90/16.98 C => fresh(s, t, x1...xn) = v
% 129.90/16.98 where fresh is a fresh function symbol and x1..xn are the free
% 129.90/16.98 variables of u and v.
% 129.90/16.98 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 129.90/16.98 input problem has no model of domain size 1).
% 129.90/16.98
% 129.90/16.98 The encoding turns the above axioms into the following unit equations and goals:
% 129.90/16.98
% 129.90/16.98 Axiom 1 (cls_CHAINED_1): fresh968(X, X) = true2.
% 129.90/16.98 Axiom 2 (cls_CHAINED_0): fresh969(X, X, Y) = true2.
% 129.90/16.98 Axiom 3 (cls_le__refl_0): c_lessequals(X, X, tc_nat) = true2.
% 129.90/16.98 Axiom 4 (cls_CHAINED_0): fresh969(c_lessequals(X, v_n____, tc_nat), true2, X) = hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), X), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_Lab____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_Lba____)))).
% 129.90/16.98 Axiom 5 (cls_CHAINED_1): fresh968(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_Lab____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_Lba____)))), true2) = hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_e____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_c____), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))))).
% 129.90/16.98
% 129.90/16.98 Goal 1 (cls_conjecture_0): hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_e____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_c____), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))))) = true2.
% 129.90/16.98 Proof:
% 129.90/16.98 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_e____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_c____), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_e____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)))))
% 129.90/16.99 = { by axiom 5 (cls_CHAINED_1) R->L }
% 129.90/16.99 fresh968(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), v_n____), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_Lab____), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), v_Lba____)))), true2)
% 129.90/16.99 = { by axiom 4 (cls_CHAINED_0) R->L }
% 129.90/16.99 fresh968(fresh969(c_lessequals(v_n____, v_n____, tc_nat), true2, v_n____), true2)
% 129.90/16.99 = { by axiom 3 (cls_le__refl_0) }
% 129.90/16.99 fresh968(fresh969(true2, true2, v_n____), true2)
% 129.90/16.99 = { by axiom 2 (cls_CHAINED_0) }
% 129.90/16.99 fresh968(true2, true2)
% 129.90/16.99 = { by axiom 1 (cls_CHAINED_1) }
% 129.90/16.99 true2
% 129.90/16.99 % SZS output end Proof
% 129.90/16.99
% 129.90/16.99 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------