TSTP Solution File: SCT171+6 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT171+6 : TPTP v8.1.2. Released v5.3.0.
% 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 : n031.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 14:22:23 EDT 2023
% Result : Theorem 45.42s 6.18s
% Output : Proof 45.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT171+6 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 15:24:51 EDT 2023
% 0.14/0.34 % CPUTime :
% 45.42/6.18 Command-line arguments: --no-flatten-goal
% 45.42/6.18
% 45.42/6.18 % SZS status Theorem
% 45.42/6.18
% 45.67/6.20 % SZS output start Proof
% 45.67/6.20 Take the following subset of the input axioms:
% 45.67/6.20 fof(conj_0, conjecture, hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, p)))).
% 45.67/6.21 fof(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, axiom, hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), ord_less(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1427655034_mktop), p)), e))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), fequal(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), arrow_14103264_above), p)), c)), e))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1278947948_mkbot), p)), e))))))).
% 45.67/6.22 fof(fact_14_PW, axiom, hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, p))) <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), ord_less(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1427655034_mktop), p)), e))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), fequal(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), arrow_14103264_above), p)), c)), e))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1278947948_mkbot), p)), e))))))).
% 45.67/6.22
% 45.67/6.22 Now clausify the problem and encode Horn clauses using encoding 3 of
% 45.67/6.22 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 45.67/6.22 We repeatedly replace C & s=t => u=v by the two clauses:
% 45.67/6.22 fresh(y, y, x1...xn) = u
% 45.67/6.22 C => fresh(s, t, x1...xn) = v
% 45.67/6.22 where fresh is a fresh function symbol and x1..xn are the free
% 45.67/6.22 variables of u and v.
% 45.67/6.22 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 45.67/6.22 input problem has no model of domain size 1).
% 45.67/6.22
% 45.67/6.22 The encoding turns the above axioms into the following unit equations and goals:
% 45.67/6.22
% 45.67/6.22 Axiom 1 (fact_14_PW): fresh380(X, X) = true2.
% 45.67/6.23 Axiom 2 (fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto): hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), ord_less(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1427655034_mktop), p)), e))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), fequal(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), arrow_14103264_above), p)), c)), e))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1278947948_mkbot), p)), e)))))) = true2.
% 45.96/6.23 Axiom 3 (fact_14_PW): fresh380(hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), ord_less(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1427655034_mktop), p)), e))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), fequal(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), arrow_14103264_above), p)), c)), e))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1278947948_mkbot), p)), e)))))), true2) = hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, p))).
% 45.96/6.23
% 45.96/6.23 Goal 1 (conj_0): hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, p))) = true2.
% 45.96/6.23 Proof:
% 45.96/6.23 hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, p)))
% 45.96/6.23 = { by axiom 3 (fact_14_PW) R->L }
% 45.96/6.24 fresh380(hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool, hAPP(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), bool), member(product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), hAPP(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt), hAPP(arrow_490897120le_alt, fun(arrow_490897120le_alt, product_prod(arrow_490897120le_alt, arrow_490897120le_alt)), product_Pair(arrow_490897120le_alt, arrow_490897120le_alt), c), d)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), f, hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), ord_less(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1427655034_mktop), p)), e))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combs(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, bool), fun(arrow_660593299e_indi, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(bool, fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), if(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(nat, fun(arrow_660593299e_indi, bool), hAPP(fun(arrow_660593299e_indi, fun(nat, bool)), fun(nat, fun(arrow_660593299e_indi, bool)), combc(arrow_660593299e_indi, nat, bool), hAPP(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool)), hAPP(fun(nat, fun(nat, bool)), fun(fun(arrow_660593299e_indi, nat), fun(arrow_660593299e_indi, fun(nat, bool))), combb(nat, fun(nat, bool), arrow_660593299e_indi), fequal(nat)), h)), n))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), arrow_660593299e_indi), arrow_14103264_above), p)), c)), e))), hAPP(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(arrow_490897120le_alt, fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), combc(arrow_660593299e_indi, arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), hAPP(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), hAPP(fun(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool))), fun(fun(arrow_660593299e_indi, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), fun(arrow_660593299e_indi, fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)))), combb(fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool), fun(arrow_490897120le_alt, fun(product_prod(arrow_490897120le_alt, arrow_490897120le_alt), bool)), arrow_660593299e_indi), arrow_1278947948_mkbot), p)), e)))))), true2)
% 45.96/6.24 = { by axiom 2 (fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) }
% 45.96/6.24 fresh380(true2, true2)
% 45.96/6.24 = { by axiom 1 (fact_14_PW) }
% 45.96/6.24 true2
% 45.96/6.24 % SZS output end Proof
% 45.96/6.24
% 45.96/6.24 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------