TSTP Solution File: SCT149+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SCT149+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n007.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 : 600s
% DateTime : Mon Jul 18 22:16:20 EDT 2022
% Result : Theorem 2.54s 2.70s
% Output : Proof 2.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SCT149+1 : TPTP v8.1.0. Released v5.2.0.
% 0.09/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 21:20:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.54/2.70 % SZS status Theorem
% 2.54/2.70 (* PROOF-FOUND *)
% 2.54/2.70 (* BEGIN-PROOF *)
% 2.54/2.70 % SZS output start Proof
% 2.54/2.70 1. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ### Axiom
% 2.54/2.70 2. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) ### Axiom
% 2.54/2.70 3. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ### Equiv 1 2
% 2.54/2.70 4. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) ### Axiom
% 2.54/2.70 5. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ### Equiv 3 4
% 2.54/2.70 6. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) ### Axiom
% 2.54/2.70 7. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) ### Equiv 5 6
% 2.54/2.70 8. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) ### Axiom
% 2.54/2.70 9. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod 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(v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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) 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(hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) ### Equiv 7 8
% 2.54/2.71 10. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____))))) ### Axiom
% 2.54/2.71 11. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) ### Axiom
% 2.54/2.71 12. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) ### Axiom
% 2.54/2.71 13. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) ### Axiom
% 2.54/2.71 14. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ### Axiom
% 2.54/2.71 15. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) ### Equiv 13 14
% 2.54/2.71 16. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) ### Equiv 12 15
% 2.54/2.71 17. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) 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(v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) 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(hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod 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% 2.54/2.71 18. 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% 2.54/2.71 19. (-. 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(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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (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_HOL_Obool))) (hAPP (hAPP (c_COMBC (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_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (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_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) ### NotEquiv 9 18
% 2.54/2.71 % SZS output end Proof
% 2.54/2.71 (* END-PROOF *)
%------------------------------------------------------------------------------