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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SCT171+3 : TPTP v9.2.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n021.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 : Tue May  5 05:06:18 PM UTC 2026

% Result   : Theorem 3.47s 2.88s
% Output   : CNFRefutation 3.65s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 3299)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ! [X14] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X14)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => ( ( hAPP_A1637648121di_nat(h,X14) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X14)),c),e))) )
            & ( hAPP_A1637648121di_nat(h,X14) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X14)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_,axiom,
    ~ ! [X78] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X78),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)))
       => ( ! [X30] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X78))
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X30))),lab)),lba)))) )
         => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X78),one_one_nat)))),lab)),lba)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) ).

fof(fact_1114_card__less__Suc2,axiom,
    ! [X26,X220] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X220))
     => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),X220))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X26)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X220))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X26))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_card__less__Suc2) ).

fof(fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ! [X14] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X14)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => ( ( hAPP_A1637648121di_nat(h,X14) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X14)),c),e))) )
            & ( hAPP_A1637648121di_nat(h,X14) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X14)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).

fof(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
    ! [X14] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X14)))
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X14)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => ( ( hAPP_A1637648121di_nat(h,X14) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X14)),c),e))) )
            & ( hAPP_A1637648121di_nat(h,X14) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X14)),e))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).

fof(fact_86_notin__Lin__iff,axiom,
    ! [X4,X5,X6] :
      ( ( is_Arr1861959080le_alt(X4)
        & is_Arr1861959080le_alt(X5) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
       => ( X4 != X5
         => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),X6))
          <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X5),X4)),X6)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_notin__Lin__iff) ).

fof(fact_87_Lin__irrefl,axiom,
    ! [X12,X13,X6] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),X6))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X13),X12)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Lin__irrefl) ).

fof(fact_904_add__leE,axiom,
    ! [X195,X196,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X196)),X197))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X196),X197)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_add__leE) ).

fof(fact_999_not__add__less1,axiom,
    ! [X207,X208] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X208)),X207)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_not__add__less1) ).

fof(fact_1000_not__add__less2,axiom,
    ! [X208,X207] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X208),X207)),X207)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_not__add__less2) ).

fof(fact_193_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X75),pi_Pro1928973619le_alt(X72,X76)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X75,X4)),hAPP_P1341894483t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_PiE) ).

fof(fact_192_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X75),pi_boo115158845le_alt(X72,X76)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X75,X4)),hAPP_b1703662281t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_PiE) ).

fof(fact_191_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X75),pi_Arr1199386158le_alt(X72,X76)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X75,X4)),hAPP_A1677245848t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_PiE) ).

fof(fact_219_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X75),pi_fun150026276t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X75,X4)),hAPP_f1277514478l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_PiE) ).

fof(fact_201_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X75),pi_Pro718203741t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X75,X4)),hAPP_P1294997365l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_PiE) ).

fof(fact_200_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X75),pi_boo538701011t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X75,X4)),hAPP_b1812770943l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_PiE) ).

fof(fact_220_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X75),pi_Arr990697634t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X75,X4)),hAPP_A60074736l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_PiE) ).

fof(fact_199_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X75),pi_Pro1880661658t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X75,X4)),hAPP_P1171466554l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_PiE) ).

fof(fact_198_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X75),pi_boo1117000868t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X75,X4)),hAPP_b517355696l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_PiE) ).

fof(fact_197_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X75),pi_Arr1936979349t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X75,X4)),hAPP_A1112981887l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_PiE) ).

fof(fact_196_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X75),pi_Pro610293528t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X75,X4)),hAPP_P254387896l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_PiE) ).

fof(fact_195_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X75),pi_boo175444770t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X75,X4)),hAPP_b1048178734l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_PiE) ).

fof(fact_194_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X75),pi_Arr2020412179t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X75,X4)),hAPP_A1952883197l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_PiE) ).

fof(fact_218_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X75),pi_nat_Product_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X75,X4)),hAPP_n454528608t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_PiE) ).

fof(fact_215_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X75),pi_fun308431217t_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X75,X4)),hAPP_f1710744577t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_PiE) ).

fof(fact_212_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X75),pi_fun321364250t_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X75,X4)),hAPP_f1866147972t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_PiE) ).

fof(fact_209_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X75),pi_fun1877263000t_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X75,X4)),hAPP_f1891021702t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_PiE) ).

fof(fact_206_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X75),pi_Pro1122146355t_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X75,X4)),hAPP_P332578347t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_PiE) ).

fof(fact_204_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X75),pi_Product_unit_nat(X72,X76)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X75,X4)),hAPP_P32877782t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_PiE) ).

fof(fact_203_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X75),pi_bool_nat(X72,X76)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X75,X4)),hAPP_b1013836512t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_PiE) ).

fof(fact_202_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X75),pi_Arr346900227di_nat(X72,X76)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X75,X4)),hAPP_A2046586321t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_PiE) ).

fof(fact_190_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X75),pi_Pro666468413t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X75,X4)),hAPP_P324742453l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_PiE) ).

fof(fact_214_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X75),pi_fun1575168891l_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X75,X4)),hAPP_f210572555l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_PiE) ).

fof(fact_211_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X75),pi_fun52649508l_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X75,X4)),hAPP_f1624277646l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_PiE) ).

fof(fact_208_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X75),pi_fun823343522l_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X75,X4)),hAPP_f839832464l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_PiE) ).

fof(fact_217_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X75),pi_nat_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X75,X4)),hAPP_n1006566506l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_PiE) ).

fof(fact_205_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X75),pi_Pro1270767662e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X75,X4)),hAPP_P1875867302i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_PiE) ).

fof(fact_213_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X75),pi_fun896360044e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X75,X4)),hAPP_f244157820i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_PiE) ).

fof(fact_210_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X75),pi_fun1002945429e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X75,X4)),hAPP_f1552576127i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_PiE) ).

fof(fact_207_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X75),pi_fun753830419e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X75,X4)),hAPP_f1948454017i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_PiE) ).

fof(fact_216_PiE,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X75),pi_nat660525389e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X75,X4)),hAPP_n821919323i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_PiE) ).

fof(fact_1056_ex__least__nat__less,axiom,
    ! [X27,X9] :
      ( ~ hBOOL(hAPP_nat_bool(X9,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X9,X27))
       => ? [X211] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X211),X27))
            & ! [X14] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X211))
               => ~ hBOOL(hAPP_nat_bool(X9,X14)) )
            & hBOOL(hAPP_nat_bool(X9,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X211),one_one_nat))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_ex__least__nat__less) ).

fof(fact_1091_not__less__eq__eq,axiom,
    ! [X200,X27] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X27)),X200)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_not__less__eq__eq) ).

fof(fact_1057_ex__least__nat__le,axiom,
    ! [X27,X9] :
      ( ~ hBOOL(hAPP_nat_bool(X9,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X9,X27))
       => ? [X211] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X211),X27))
            & ! [X14] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X211))
               => ~ hBOOL(hAPP_nat_bool(X9,X14)) )
            & hBOOL(hAPP_nat_bool(X9,X211)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_ex__least__nat__le) ).

fof(fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [X29] :
        ( is_fun961089132t_bool(X29)
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),X29))
         => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X29),arrow_1681063817le_Lin)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

fof(fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [X28] :
        ( is_fun961089132t_bool(X28)
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),X28))
         => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X28),arrow_1681063817le_Lin)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

fof(fact_1082_not__less__eq,axiom,
    ! [X200,X27] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),hAPP_nat_nat(suc,X200))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082_not__less__eq) ).

fof(fact_1087_le__SucE,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),hAPP_nat_nat(suc,X197)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
       => X195 = hAPP_nat_nat(suc,X197) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_le__SucE) ).

fof(fact_712_less__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X75),X81))
    <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X75),X81))
        & ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X81),X75)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_less__fun__def) ).

fof(fact_392_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
        & ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_less__le__not__le) ).

fof(fact_709_less__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X75),X81))
    <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X75),X81))
        & ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X81),X75)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_less__fun__def) ).

fof(fact_389_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X5))
    <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
        & ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_less__le__not__le) ).

fof(fact_710_less__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X75),X81))
    <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X75),X81))
        & ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X81),X75)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_less__fun__def) ).

fof(fact_390_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X5))
    <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
        & ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_less__le__not__le) ).

fof(fact_711_less__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X75),X81))
    <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X75),X81))
        & ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X81),X75)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_less__fun__def) ).

fof(fact_391_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X5))
    <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
        & ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_less__le__not__le) ).

fof(fact_707_less__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X75),X81))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X75),X81))
        & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X81),X75)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_707_less__fun__def) ).

fof(fact_387_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
        & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_less__le__not__le) ).

fof(fact_714_less__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X75),X81))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X75),X81))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X81),X75)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_less__fun__def) ).

fof(fact_395_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_less__le__not__le) ).

fof(fact_708_less__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X75),X81))
    <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X75),X81))
        & ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X81),X75)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_less__fun__def) ).

fof(fact_388_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
    <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
        & ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_less__le__not__le) ).

fof(fact_713_less__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X75),X81))
    <=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X75),X81))
        & ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X81),X75)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_less__fun__def) ).

fof(fact_394_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
        & ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_less__le__not__le) ).

fof(fact_396_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_less__le__not__le) ).

fof(fact_393_less__le__not__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X5))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
        & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_less__le__not__le) ).

fof(fact_1079_not__less__less__Suc__eq,axiom,
    ! [X27,X200] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),X200))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),hAPP_nat_nat(suc,X200)))
      <=> X27 = X200 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_not__less__less__Suc__eq) ).

fof(fact_1078_less__antisym,axiom,
    ! [X197,X195] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),X195))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),hAPP_nat_nat(suc,X195)))
       => X195 = X197 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_less__antisym) ).

fof(fact_1074_less__SucE,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),hAPP_nat_nat(suc,X197)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
       => X195 = X197 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_less__SucE) ).

fof(fact_1092_Suc__n__not__le__n,axiom,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X197)),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1092_Suc__n__not__le__n) ).

fof(fact_441_linorder__antisym__conv2,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
      <=> X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_linorder__antisym__conv2) ).

fof(fact_146_order__less__not__sym,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_order__less__not__sym) ).

fof(fact_142_order__less__imp__not__less,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_order__less__imp__not__less) ).

fof(fact_126_order__less__asym_H,axiom,
    ! [X12,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),X13))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_order__less__asym_H) ).

fof(fact_122_xt1_I9_J,axiom,
    ! [X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X12))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_xt1_I9_J) ).

fof(fact_94_order__less__asym,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_order__less__asym) ).

fof(fact_145_order__less__not__sym,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_order__less__not__sym) ).

fof(fact_141_order__less__imp__not__less,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_order__less__imp__not__less) ).

fof(fact_125_order__less__asym_H,axiom,
    ! [X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),X13))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_order__less__asym_H) ).

fof(fact_121_xt1_I9_J,axiom,
    ! [X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X12))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_xt1_I9_J) ).

fof(fact_93_order__less__asym,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_order__less__asym) ).

fof(fact_147_order__less__not__sym,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_order__less__not__sym) ).

fof(fact_143_order__less__imp__not__less,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_order__less__imp__not__less) ).

fof(fact_127_order__less__asym_H,axiom,
    ! [X12,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),X13))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_order__less__asym_H) ).

fof(fact_123_xt1_I9_J,axiom,
    ! [X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X12))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_xt1_I9_J) ).

fof(fact_95_order__less__asym,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_order__less__asym) ).

fof(fact_375_linorder__not__le,axiom,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_linorder__not__le) ).

fof(fact_430_leD,axiom,
    ! [X118,X119] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X118),X119))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X119),X118)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_leD) ).

fof(fact_374_linorder__not__less,axiom,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_linorder__not__less) ).

fof(fact_156_not__less__iff__gr__or__eq,axiom,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X4))
        | X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_not__less__iff__gr__or__eq) ).

fof(fact_148_order__less__not__sym,axiom,
    ! [X63,X64] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X63),X64))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X64),X63)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_order__less__not__sym) ).

fof(fact_144_order__less__imp__not__less,axiom,
    ! [X61,X62] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X61),X62))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X62),X61)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_order__less__imp__not__less) ).

fof(fact_128_order__less__asym_H,axiom,
    ! [X55,X56] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X55),X56))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X55)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_order__less__asym_H) ).

fof(fact_124_xt1_I9_J,axiom,
    ! [X53,X54] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X53),X54))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X54),X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_xt1_I9_J) ).

fof(fact_96_order__less__asym,axiom,
    ! [X33,X34] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X33),X34))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X34),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_order__less__asym) ).

fof(fact_409_linorder__antisym__conv1,axiom,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
      <=> X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_linorder__antisym__conv1) ).

fof(fact_983_linorder__neqE__nat,axiom,
    ! [X201,X202] :
      ( X201 != X202
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X201),X202))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X202),X201)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_linorder__neqE__nat) ).

fof(fact_154_linorder__antisym__conv3,axiom,
    ! [X5,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X4))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
      <=> X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_linorder__antisym__conv3) ).

fof(fact_153_linorder__neqE,axiom,
    ! [X67,X68] :
      ( X67 != X68
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X67),X68))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X68),X67)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_linorder__neqE) ).

fof(fact_92_linorder__cases,axiom,
    ! [X31,X32] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X31),X32))
     => ( X31 != X32
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_linorder__cases) ).

fof(fact_238_linorder__le__cases,axiom,
    ! [X79,X80] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X79),X80))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X80),X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_linorder__le__cases) ).

fof(fact_407_leI,axiom,
    ! [X110,X111] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X110),X111))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X111),X110)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_leI) ).

fof(fact_408_not__leE,axiom,
    ! [X112,X113] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X112),X113))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X113),X112)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_not__leE) ).

fof(help_fconj_2_1_U,axiom,
    ! [X227,X228] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X227),X228))
      | hBOOL(X227) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

fof(help_fconj_3_1_U,axiom,
    ! [X227,X228] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X227),X228))
      | hBOOL(X228) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X201,X202] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X201),X202))
      | X201 = X202 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

fof(fact_159_order__less__irrefl,axiom,
    ! [X4] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_order__less__irrefl) ).

fof(fact_158_order__less__irrefl,axiom,
    ! [X4] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_order__less__irrefl) ).

fof(fact_160_order__less__irrefl,axiom,
    ! [X4] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_order__less__irrefl) ).

fof(fact_984_less__irrefl__nat,axiom,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_less__irrefl__nat) ).

fof(fact_981_less__not__refl,axiom,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_less__not__refl) ).

fof(fact_161_order__less__irrefl,axiom,
    ! [X71] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X71),X71)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_order__less__irrefl) ).

fof(fact_1046_less__nat__zero__code,axiom,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),zero_zero_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_less__nat__zero__code) ).

fof(fact_1044_not__less0,axiom,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),zero_zero_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_not__less0) ).

fof(fact_1042_less__zeroE,axiom,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),zero_zero_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_less__zeroE) ).

fof(fact_59_not__top__less,axiom,
    ! [X12] : ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__top__less) ).

fof(fact_55_not__top__less,axiom,
    ! [X12] : ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_not__top__less) ).

fof(fact_57_not__top__less,axiom,
    ! [X12] : ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_not__top__less) ).

fof(fact_56_not__top__less,axiom,
    ! [X12] : ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_not__top__less) ).

fof(fact_62_not__top__less,axiom,
    ! [X12] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_not__top__less) ).

fof(fact_61_not__top__less,axiom,
    ! [X12] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_not__top__less) ).

fof(fact_60_not__top__less,axiom,
    ! [X12] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_not__top__less) ).

fof(fact_58_not__top__less,axiom,
    ! [X12] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_not__top__less) ).

fof(help_fconj_1_1_U,axiom,
    ! [X228,X227] :
      ( ~ hBOOL(X227)
      | ~ hBOOL(X228)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X227),X228)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

fof(fact_953_equalityE,axiom,
    ! [X72,X76] :
      ( X72 = X76
     => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
         => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X76),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_equalityE) ).

fof(fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).

fof(fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_14_PW,axiom,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).

fof(fact_6__C2_C,axiom,
    ! [X8,X9,X10,X11,X12,X13] :
      ( ( is_Arr1861959080le_alt(X10)
        & is_Arr1861959080le_alt(X11)
        & is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13) )
     => ( X12 != X13
       => ( X10 != X11
         => ( X12 != X11
           => ( X13 != X10
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X9),arrow_1721807329e_Prof))
               => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X8),arrow_1721807329e_Prof))
                 => ( ! [X14] :
                        ( is_Arr43961803e_indi(X14)
                       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_A1677245848t_bool(X9,X14)))
                        <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X10),X11)),hAPP_A1677245848t_bool(X8,X14))) ) )
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_f412050202t_bool(f,X9)))
                    <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X10),X11)),hAPP_f412050202t_bool(f,X8))) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C2_C) ).

fof(fact_7__C1_C,axiom,
    ! [X8,X9,X10,X11,X12,X13] :
      ( ( is_Arr1861959080le_alt(X10)
        & is_Arr1861959080le_alt(X11)
        & is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13) )
     => ( X12 != X13
       => ( X10 != X11
         => ( X12 != X11
           => ( X13 != X10
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X9),arrow_1721807329e_Prof))
               => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X8),arrow_1721807329e_Prof))
                 => ( ! [X14] :
                        ( is_Arr43961803e_indi(X14)
                       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_A1677245848t_bool(X9,X14)))
                        <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X10),X11)),hAPP_A1677245848t_bool(X8,X14))) ) )
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_f412050202t_bool(f,X9)))
                     => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X10),X11)),hAPP_f412050202t_bool(f,X8))) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__C1_C) ).

fof(fact_9_pairwise__neutrality,axiom,
    ! [X8,X9,X10,X11,X12,X13] :
      ( ( is_Arr1861959080le_alt(X10)
        & is_Arr1861959080le_alt(X11)
        & is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13) )
     => ( X12 != X13
       => ( X10 != X11
         => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X9),arrow_1721807329e_Prof))
           => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X8),arrow_1721807329e_Prof))
             => ( ! [X14] :
                    ( is_Arr43961803e_indi(X14)
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_A1677245848t_bool(X9,X14)))
                    <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X10),X11)),hAPP_A1677245848t_bool(X8,X14))) ) )
               => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_f412050202t_bool(f,X9)))
                <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X10),X11)),hAPP_f412050202t_bool(f,X8))) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).

fof(fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I,axiom,
    ? [X78] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X78),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)))
      & ! [X30] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X78))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X30))),lab)),lba)))) )
      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X78),one_one_nat)))),lab)),lba)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) ).

fof(fact_23_IIA__def,axiom,
    ! [X23] :
      ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X23))
    <=> ! [X24] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X24),arrow_1721807329e_Prof))
         => ! [X25] :
              ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X25),arrow_1721807329e_Prof))
             => ! [X17,X18] :
                  ( ( is_Arr1861959080le_alt(X17)
                    & is_Arr1861959080le_alt(X18) )
                 => ( ! [X14] :
                        ( is_Arr43961803e_indi(X14)
                       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18)),hAPP_A1677245848t_bool(X24,X14)))
                        <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18)),hAPP_A1677245848t_bool(X25,X14))) ) )
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18)),hAPP_f412050202t_bool(X23,X24)))
                    <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18)),hAPP_f412050202t_bool(X23,X25))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_IIA__def) ).

fof(fact_8__C4_C,axiom,
    ! [X8,X9,X15,X12,X13] :
      ( ( is_Arr1861959080le_alt(X15)
        & is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13) )
     => ( X12 != X13
       => ( X13 != X15
         => ( X12 != X15
           => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X9),arrow_1721807329e_Prof))
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X8),arrow_1721807329e_Prof))
               => ( ! [X14] :
                      ( is_Arr43961803e_indi(X14)
                     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_A1677245848t_bool(X9,X14)))
                      <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X13),X15)),hAPP_A1677245848t_bool(X8,X14))) ) )
                 => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_f412050202t_bool(f,X9)))
                  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X13),X15)),hAPP_f412050202t_bool(f,X8))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C4_C) ).

fof(fact_85_n_I2_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),n))
     => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X30))),lab)),lba)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_n_I2_J) ).

fof(fact_81_PiProf,axiom,
    ! [X27] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X27))),lab)),lba)),arrow_1721807329e_Prof)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_PiProf) ).

fof(fact_787_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X75,X149)),hAPP_f899613158t_bool(X75,X24))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_xt4) ).

fof(fact_870_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X75,X24)),hAPP_f899613158t_bool(X75,X149))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_order__le__less__subst2) ).

fof(fact_778_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X75,X149)),hAPP_n588788980t_bool(X75,X24))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_xt4) ).

fof(fact_766_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X149)),hAPP_n588788980t_bool(X75,X24))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_766_xt6) ).

fof(fact_861_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X75,X24)),hAPP_n588788980t_bool(X75,X149))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_order__le__less__subst2) ).

fof(fact_898_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X24)),hAPP_n588788980t_bool(X75,X149))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_order__less__le__subst2) ).

fof(fact_784_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X75,X149)),hAPP_f769545506l_bool(X75,X24))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_xt4) ).

fof(fact_867_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X75,X24)),hAPP_f769545506l_bool(X75,X149))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_order__le__less__subst2) ).

fof(fact_775_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X75,X149)),hAPP_n1674354836l_bool(X75,X24))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_xt4) ).

fof(fact_763_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X149)),hAPP_n1674354836l_bool(X75,X24))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_xt6) ).

fof(fact_858_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X75,X24)),hAPP_n1674354836l_bool(X75,X149))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_order__le__less__subst2) ).

fof(fact_895_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X24)),hAPP_n1674354836l_bool(X75,X149))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_order__less__le__subst2) ).

fof(fact_785_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X75,X149)),hAPP_f1449238989l_bool(X75,X24))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_xt4) ).

fof(fact_868_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X75,X24)),hAPP_f1449238989l_bool(X75,X149))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_868_order__le__less__subst2) ).

fof(fact_776_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X75,X149)),hAPP_n295497947l_bool(X75,X24))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_776_xt4) ).

fof(fact_764_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X149)),hAPP_n295497947l_bool(X75,X24))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_xt6) ).

fof(fact_859_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X75,X24)),hAPP_n295497947l_bool(X75,X149))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_859_order__le__less__subst2) ).

fof(fact_896_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X24)),hAPP_n295497947l_bool(X75,X149))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_order__less__le__subst2) ).

fof(fact_786_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X75,X149)),hAPP_f226010187l_bool(X75,X24))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_xt4) ).

fof(fact_869_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X75,X24)),hAPP_f226010187l_bool(X75,X149))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_order__le__less__subst2) ).

fof(fact_777_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X75,X149)),hAPP_n2095207769l_bool(X75,X24))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_xt4) ).

fof(fact_765_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X149)),hAPP_n2095207769l_bool(X75,X24))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_xt6) ).

fof(fact_860_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X75,X24)),hAPP_n2095207769l_bool(X75,X149))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_order__le__less__subst2) ).

fof(fact_897_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X24)),hAPP_n2095207769l_bool(X75,X149))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_897_order__less__le__subst2) ).

fof(fact_782_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X75,X149)),hAPP_f1061584978t_bool(X75,X24))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_782_xt4) ).

fof(fact_865_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X75,X24)),hAPP_f1061584978t_bool(X75,X149))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_order__le__less__subst2) ).

fof(fact_773_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X75,X149)),hAPP_n454528608t_bool(X75,X24))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_xt4) ).

fof(fact_761_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X149)),hAPP_n454528608t_bool(X75,X24))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_xt6) ).

fof(fact_856_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X75,X24)),hAPP_n454528608t_bool(X75,X149))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_order__le__less__subst2) ).

fof(fact_893_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X24)),hAPP_n454528608t_bool(X75,X149))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_order__less__le__subst2) ).

fof(fact_797_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun2093718614t_bool(X24)
                & is_fun2093718614t_bool(X149) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X75,X149)),hAPP_f1363542492t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_xt4) ).

fof(fact_880_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun2093718614t_bool(X24)
                & is_fun2093718614t_bool(X149) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X75,X24)),hAPP_f1363542492t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_order__le__less__subst2) ).

fof(fact_793_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun961089132t_bool(X24)
                & is_fun961089132t_bool(X149) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X75,X149)),hAPP_f856106132t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_xt4) ).

fof(fact_876_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun961089132t_bool(X24)
                & is_fun961089132t_bool(X149) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X75,X24)),hAPP_f856106132t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_order__le__less__subst2) ).

fof(fact_792_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun288122577l_bool(X24)
                & is_fun288122577l_bool(X149) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X75,X149)),hAPP_f985923321t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_792_xt4) ).

fof(fact_875_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun288122577l_bool(X24)
                & is_fun288122577l_bool(X149) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X75,X24)),hAPP_f985923321t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_order__le__less__subst2) ).

fof(fact_791_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun158382675l_bool(X24)
                & is_fun158382675l_bool(X149) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X75,X149)),hAPP_f839525755t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_xt4) ).

fof(fact_874_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun158382675l_bool(X24)
                & is_fun158382675l_bool(X149) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X75,X24)),hAPP_f839525755t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_order__le__less__subst2) ).

fof(fact_790_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun279392540l_bool(X24)
                & is_fun279392540l_bool(X149) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X75,X149)),hAPP_f464145314t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_790_xt4) ).

fof(fact_873_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun279392540l_bool(X24)
                & is_fun279392540l_bool(X149) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X75,X24)),hAPP_f464145314t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_order__le__less__subst2) ).

fof(fact_795_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X75,X149)),hAPP_f2026336507t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_xt4) ).

fof(fact_759_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X149)),hAPP_f2026336507t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_xt6) ).

fof(fact_878_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X75,X24)),hAPP_f2026336507t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_878_order__le__less__subst2) ).

fof(fact_891_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X24)),hAPP_f2026336507t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_order__less__le__subst2) ).

fof(fact_796_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X75,X149)),hAPP_f543204480t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_xt4) ).

fof(fact_758_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X149)),hAPP_f543204480t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_xt6) ).

fof(fact_879_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X75,X24)),hAPP_f543204480t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_order__le__less__subst2) ).

fof(fact_890_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X24)),hAPP_f543204480t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_order__less__le__subst2) ).

fof(fact_794_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_bool(X24)
                & is_bool(X149) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X75,X149)),hAPP_b1013836512t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_794_xt4) ).

fof(fact_877_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_bool(X24)
                & is_bool(X149) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X75,X24)),hAPP_b1013836512t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_order__le__less__subst2) ).

fof(fact_781_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X75,X149)),hAPP_f800510211t_bool(X75,X24))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_781_xt4) ).

fof(fact_757_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X149),X24))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X149)),hAPP_f800510211t_bool(X75,X24))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_757_xt6) ).

fof(fact_864_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X75,X24)),hAPP_f800510211t_bool(X75,X149))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_order__le__less__subst2) ).

fof(fact_889_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X24),X149))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X24)),hAPP_f800510211t_bool(X75,X149))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_order__less__le__subst2) ).

fof(fact_772_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X75,X149)),hAPP_n1699378549t_bool(X75,X24))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_xt4) ).

fof(fact_760_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X149)),hAPP_n1699378549t_bool(X75,X24))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_xt6) ).

fof(fact_855_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X75,X24)),hAPP_n1699378549t_bool(X75,X149))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_order__le__less__subst2) ).

fof(fact_892_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X24)),hAPP_n1699378549t_bool(X75,X149))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_order__less__le__subst2) ).

fof(fact_783_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X75,X149)),hAPP_f632777549i_bool(X75,X24))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_xt4) ).

fof(fact_866_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X75,X24)),hAPP_f632777549i_bool(X75,X149))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_order__le__less__subst2) ).

fof(fact_774_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X75,X149)),hAPP_n821919323i_bool(X75,X24))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_xt4) ).

fof(fact_762_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X149)),hAPP_n821919323i_bool(X75,X24))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_762_xt6) ).

fof(fact_857_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X75,X24)),hAPP_n821919323i_bool(X75,X149))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_order__le__less__subst2) ).

fof(fact_894_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X24)),hAPP_n821919323i_bool(X75,X149))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_894_order__less__le__subst2) ).

fof(fact_789_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X75,X149)),hAPP_f861874780t_bool(X75,X24))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_xt4) ).

fof(fact_872_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X75,X24)),hAPP_f861874780t_bool(X75,X149))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_order__le__less__subst2) ).

fof(fact_780_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X75,X149)),hAPP_n539120590t_bool(X75,X24))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_xt4) ).

fof(fact_768_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X149)),hAPP_n539120590t_bool(X75,X24))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_xt6) ).

fof(fact_863_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X75,X24)),hAPP_n539120590t_bool(X75,X149))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_order__le__less__subst2) ).

fof(fact_900_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X24)),hAPP_n539120590t_bool(X75,X149))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_order__less__le__subst2) ).

fof(fact_805_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun2093718614t_bool(X24)
                & is_fun2093718614t_bool(X149) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X75,X149)),hAPP_f1358350510ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_805_xt4) ).

fof(fact_888_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun2093718614t_bool(X24)
                & is_fun2093718614t_bool(X149) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X75,X24)),hAPP_f1358350510ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_order__le__less__subst2) ).

fof(fact_801_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun961089132t_bool(X24)
                & is_fun961089132t_bool(X149) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X75,X149)),hAPP_f816335862ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_xt4) ).

fof(fact_884_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun961089132t_bool(X24)
                & is_fun961089132t_bool(X149) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X75,X24)),hAPP_f816335862ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_order__le__less__subst2) ).

fof(fact_800_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun288122577l_bool(X24)
                & is_fun288122577l_bool(X149) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X75,X149)),hAPP_f897066961ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_800_xt4) ).

fof(fact_883_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun288122577l_bool(X24)
                & is_fun288122577l_bool(X149) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X75,X24)),hAPP_f897066961ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_order__le__less__subst2) ).

fof(fact_799_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun158382675l_bool(X24)
                & is_fun158382675l_bool(X149) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X75,X149)),hAPP_f1695077327ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_xt4) ).

fof(fact_882_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun158382675l_bool(X24)
                & is_fun158382675l_bool(X149) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X75,X24)),hAPP_f1695077327ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_order__le__less__subst2) ).

fof(fact_798_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun279392540l_bool(X24)
                & is_fun279392540l_bool(X149) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X75,X149)),hAPP_f1313392232ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_xt4) ).

fof(fact_881_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun279392540l_bool(X24)
                & is_fun279392540l_bool(X149) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X75,X24)),hAPP_f1313392232ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_881_order__le__less__subst2) ).

fof(fact_804_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X75,X149)),hAPP_f2030293770ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_804_xt4) ).

fof(fact_770_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X149)),hAPP_f2030293770ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_770_xt6) ).

fof(fact_887_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X75,X24)),hAPP_f2030293770ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_order__le__less__subst2) ).

fof(fact_902_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X24)),hAPP_f2030293770ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_902_order__less__le__subst2) ).

fof(fact_769_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X149),X24))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X75,X149)),hAPP_f22106695ol_nat(X75,X24))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_xt6) ).

fof(fact_901_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X24),X149))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X75,X24)),hAPP_f22106695ol_nat(X75,X149))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_order__less__le__subst2) ).

fof(fact_802_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_bool(X24)
                & is_bool(X149) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X75,X149)),hAPP_bool_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_xt4) ).

fof(fact_885_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_bool(X24)
                & is_bool(X149) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X75,X24)),hAPP_bool_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_order__le__less__subst2) ).

fof(fact_803_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X75,X149)),hAPP_f2120083535ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_803_xt4) ).

fof(fact_771_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X75,X13)),X12))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X15),X13))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X149)),hAPP_f2120083535ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_771_xt6) ).

fof(fact_886_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X75,X24)),hAPP_f2120083535ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_order__le__less__subst2) ).

fof(fact_903_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),X13))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X24)),hAPP_f2120083535ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_order__less__le__subst2) ).

fof(fact_788_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X75,X149)),hAPP_f54304608l_bool(X75,X24))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_788_xt4) ).

fof(fact_871_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X75,X24)),hAPP_f54304608l_bool(X75,X149))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_order__le__less__subst2) ).

fof(fact_779_xt4,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X149)),hAPP_nat_bool(X75,X24))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_xt4) ).

fof(fact_767_xt6,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X13)),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X13))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X149)),hAPP_nat_bool(X75,X24))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X15)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_xt6) ).

fof(fact_862_order__le__less__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X24)),hAPP_nat_bool(X75,X149))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_862_order__le__less__subst2) ).

fof(fact_899_order__less__le__subst2,axiom,
    ! [X75,X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X13)),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X24)),hAPP_nat_bool(X75,X149))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X12)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_899_order__less__le__subst2) ).

fof(fact_688_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X15),hAPP_f899613158t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X75,X149)),hAPP_f899613158t_bool(X75,X24))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X15),hAPP_f899613158t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_xt7) ).

fof(fact_679_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X15),hAPP_n588788980t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X75,X149)),hAPP_n588788980t_bool(X75,X24))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X15),hAPP_n588788980t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_xt7) ).

fof(fact_667_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X15),hAPP_n588788980t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X149)),hAPP_n588788980t_bool(X75,X24))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X15),hAPP_n588788980t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_xt5) ).

fof(fact_836_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X12),hAPP_f899613158t_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X75,X24)),hAPP_f899613158t_bool(X75,X149))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X12),hAPP_f899613158t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_order__less__le__subst1) ).

fof(fact_827_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X12),hAPP_n588788980t_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X75,X24)),hAPP_n588788980t_bool(X75,X149))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X12),hAPP_n588788980t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_order__less__le__subst1) ).

fof(fact_815_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X12),hAPP_n588788980t_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X75,X24)),hAPP_n588788980t_bool(X75,X149))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X12),hAPP_n588788980t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_order__le__less__subst1) ).

fof(fact_685_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X15),hAPP_f769545506l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X75,X149)),hAPP_f769545506l_bool(X75,X24))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X15),hAPP_f769545506l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_xt7) ).

fof(fact_676_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X15),hAPP_n1674354836l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X75,X149)),hAPP_n1674354836l_bool(X75,X24))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X15),hAPP_n1674354836l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_xt7) ).

fof(fact_664_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X15),hAPP_n1674354836l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X149)),hAPP_n1674354836l_bool(X75,X24))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X15),hAPP_n1674354836l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_xt5) ).

fof(fact_833_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X12),hAPP_f769545506l_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X75,X24)),hAPP_f769545506l_bool(X75,X149))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X12),hAPP_f769545506l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_order__less__le__subst1) ).

fof(fact_824_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X12),hAPP_n1674354836l_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X75,X24)),hAPP_n1674354836l_bool(X75,X149))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X12),hAPP_n1674354836l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_order__less__le__subst1) ).

fof(fact_812_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X12),hAPP_n1674354836l_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X75,X24)),hAPP_n1674354836l_bool(X75,X149))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X12),hAPP_n1674354836l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_order__le__less__subst1) ).

fof(fact_686_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X15),hAPP_f1449238989l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X75,X149)),hAPP_f1449238989l_bool(X75,X24))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X15),hAPP_f1449238989l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_xt7) ).

fof(fact_677_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X15),hAPP_n295497947l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X75,X149)),hAPP_n295497947l_bool(X75,X24))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X15),hAPP_n295497947l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_xt7) ).

fof(fact_665_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X15),hAPP_n295497947l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X149)),hAPP_n295497947l_bool(X75,X24))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X15),hAPP_n295497947l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_xt5) ).

fof(fact_834_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X12),hAPP_f1449238989l_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X75,X24)),hAPP_f1449238989l_bool(X75,X149))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X12),hAPP_f1449238989l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_order__less__le__subst1) ).

fof(fact_825_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X12),hAPP_n295497947l_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X75,X24)),hAPP_n295497947l_bool(X75,X149))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X12),hAPP_n295497947l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_order__less__le__subst1) ).

fof(fact_813_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X12),hAPP_n295497947l_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X75,X24)),hAPP_n295497947l_bool(X75,X149))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X12),hAPP_n295497947l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_order__le__less__subst1) ).

fof(fact_687_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X15),hAPP_f226010187l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X75,X149)),hAPP_f226010187l_bool(X75,X24))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X15),hAPP_f226010187l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_xt7) ).

fof(fact_678_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X15),hAPP_n2095207769l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X75,X149)),hAPP_n2095207769l_bool(X75,X24))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X15),hAPP_n2095207769l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_xt7) ).

fof(fact_666_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X15),hAPP_n2095207769l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X149)),hAPP_n2095207769l_bool(X75,X24))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X15),hAPP_n2095207769l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_xt5) ).

fof(fact_835_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X12),hAPP_f226010187l_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X75,X24)),hAPP_f226010187l_bool(X75,X149))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X12),hAPP_f226010187l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_order__less__le__subst1) ).

fof(fact_826_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X12),hAPP_n2095207769l_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X75,X24)),hAPP_n2095207769l_bool(X75,X149))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X12),hAPP_n2095207769l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_826_order__less__le__subst1) ).

fof(fact_814_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X12),hAPP_n2095207769l_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X75,X24)),hAPP_n2095207769l_bool(X75,X149))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X12),hAPP_n2095207769l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_order__le__less__subst1) ).

fof(fact_683_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X15),hAPP_f1061584978t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X75,X149)),hAPP_f1061584978t_bool(X75,X24))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X15),hAPP_f1061584978t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_xt7) ).

fof(fact_674_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X15),hAPP_n454528608t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X75,X149)),hAPP_n454528608t_bool(X75,X24))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X15),hAPP_n454528608t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_xt7) ).

fof(fact_662_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X15),hAPP_n454528608t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X149)),hAPP_n454528608t_bool(X75,X24))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X15),hAPP_n454528608t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_xt5) ).

fof(fact_831_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),hAPP_f1061584978t_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X75,X24)),hAPP_f1061584978t_bool(X75,X149))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),hAPP_f1061584978t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_order__less__le__subst1) ).

fof(fact_822_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),hAPP_n454528608t_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X75,X24)),hAPP_n454528608t_bool(X75,X149))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),hAPP_n454528608t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_order__less__le__subst1) ).

fof(fact_810_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X12),hAPP_n454528608t_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X75,X24)),hAPP_n454528608t_bool(X75,X149))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),hAPP_n454528608t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_order__le__less__subst1) ).

fof(fact_698_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f1363542492t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun2093718614t_bool(X24)
                & is_fun2093718614t_bool(X149) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X75,X149)),hAPP_f1363542492t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f1363542492t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_xt7) ).

fof(fact_694_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f856106132t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun961089132t_bool(X24)
                & is_fun961089132t_bool(X149) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X75,X149)),hAPP_f856106132t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f856106132t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_xt7) ).

fof(fact_693_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f985923321t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun288122577l_bool(X24)
                & is_fun288122577l_bool(X149) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X75,X149)),hAPP_f985923321t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f985923321t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_xt7) ).

fof(fact_692_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f839525755t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun158382675l_bool(X24)
                & is_fun158382675l_bool(X149) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X75,X149)),hAPP_f839525755t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f839525755t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_xt7) ).

fof(fact_691_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f464145314t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun279392540l_bool(X24)
                & is_fun279392540l_bool(X149) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X75,X149)),hAPP_f464145314t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f464145314t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_xt7) ).

fof(fact_696_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f2026336507t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X75,X149)),hAPP_f2026336507t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f2026336507t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_xt7) ).

fof(fact_660_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),hAPP_f2026336507t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X149)),hAPP_f2026336507t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f2026336507t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_xt5) ).

fof(fact_697_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f543204480t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X75,X149)),hAPP_f543204480t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f543204480t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_xt7) ).

fof(fact_659_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),hAPP_f543204480t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X149)),hAPP_f543204480t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f543204480t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_xt5) ).

fof(fact_695_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_b1013836512t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_bool(X24)
                & is_bool(X149) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X149),X24))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X75,X149)),hAPP_b1013836512t_bool(X75,X24))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_b1013836512t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_xt7) ).

fof(fact_682_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f800510211t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X75,X149)),hAPP_f800510211t_bool(X75,X24))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f800510211t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_xt7) ).

fof(fact_658_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),hAPP_f800510211t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X149),X24))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X149)),hAPP_f800510211t_bool(X75,X24))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_f800510211t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_xt5) ).

fof(fact_673_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_n1699378549t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X75,X149)),hAPP_n1699378549t_bool(X75,X24))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_n1699378549t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_xt7) ).

fof(fact_661_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X15),hAPP_n1699378549t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X149)),hAPP_n1699378549t_bool(X75,X24))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X15),hAPP_n1699378549t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_xt5) ).

fof(fact_846_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f1363542492t_bool(X75,X13)))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun2093718614t_bool(X24)
                & is_fun2093718614t_bool(X149) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X75,X24)),hAPP_f1363542492t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f1363542492t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_order__less__le__subst1) ).

fof(fact_842_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f856106132t_bool(X75,X13)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun961089132t_bool(X24)
                & is_fun961089132t_bool(X149) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X75,X24)),hAPP_f856106132t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f856106132t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_order__less__le__subst1) ).

fof(fact_841_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f985923321t_bool(X75,X13)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun288122577l_bool(X24)
                & is_fun288122577l_bool(X149) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X75,X24)),hAPP_f985923321t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f985923321t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_841_order__less__le__subst1) ).

fof(fact_840_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f839525755t_bool(X75,X13)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun158382675l_bool(X24)
                & is_fun158382675l_bool(X149) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X75,X24)),hAPP_f839525755t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f839525755t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_order__less__le__subst1) ).

fof(fact_839_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f464145314t_bool(X75,X13)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun279392540l_bool(X24)
                & is_fun279392540l_bool(X149) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X75,X24)),hAPP_f464145314t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f464145314t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_order__less__le__subst1) ).

fof(fact_844_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f2026336507t_bool(X75,X13)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X75,X24)),hAPP_f2026336507t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f2026336507t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_order__less__le__subst1) ).

fof(fact_808_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),hAPP_f2026336507t_bool(X75,X13)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X75,X24)),hAPP_f2026336507t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f2026336507t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_order__le__less__subst1) ).

fof(fact_845_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f543204480t_bool(X75,X13)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X75,X24)),hAPP_f543204480t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f543204480t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_order__less__le__subst1) ).

fof(fact_807_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),hAPP_f543204480t_bool(X75,X13)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X75,X24)),hAPP_f543204480t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f543204480t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_order__le__less__subst1) ).

fof(fact_843_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_b1013836512t_bool(X75,X13)))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_bool(X24)
                & is_bool(X149) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X24),X149))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X75,X24)),hAPP_b1013836512t_bool(X75,X149))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_b1013836512t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_order__less__le__subst1) ).

fof(fact_830_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f800510211t_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X75,X24)),hAPP_f800510211t_bool(X75,X149))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f800510211t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_order__less__le__subst1) ).

fof(fact_806_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),hAPP_f800510211t_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X24),X149))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X75,X24)),hAPP_f800510211t_bool(X75,X149))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_f800510211t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_806_order__le__less__subst1) ).

fof(fact_821_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_n1699378549t_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X75,X24)),hAPP_n1699378549t_bool(X75,X149))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_n1699378549t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_821_order__less__le__subst1) ).

fof(fact_809_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),hAPP_n1699378549t_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X75,X24)),hAPP_n1699378549t_bool(X75,X149))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),hAPP_n1699378549t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_order__le__less__subst1) ).

fof(fact_684_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X15),hAPP_f632777549i_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X75,X149)),hAPP_f632777549i_bool(X75,X24))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X15),hAPP_f632777549i_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_xt7) ).

fof(fact_675_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X15),hAPP_n821919323i_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X75,X149)),hAPP_n821919323i_bool(X75,X24))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X15),hAPP_n821919323i_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_xt7) ).

fof(fact_663_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X15),hAPP_n821919323i_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X149)),hAPP_n821919323i_bool(X75,X24))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X15),hAPP_n821919323i_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_xt5) ).

fof(fact_832_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),hAPP_f632777549i_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X75,X24)),hAPP_f632777549i_bool(X75,X149))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),hAPP_f632777549i_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_order__less__le__subst1) ).

fof(fact_823_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),hAPP_n821919323i_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X75,X24)),hAPP_n821919323i_bool(X75,X149))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),hAPP_n821919323i_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_order__less__le__subst1) ).

fof(fact_811_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X12),hAPP_n821919323i_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X75,X24)),hAPP_n821919323i_bool(X75,X149))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),hAPP_n821919323i_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_811_order__le__less__subst1) ).

fof(fact_690_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X15),hAPP_f861874780t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X75,X149)),hAPP_f861874780t_bool(X75,X24))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X15),hAPP_f861874780t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_xt7) ).

fof(fact_681_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X15),hAPP_n539120590t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X75,X149)),hAPP_n539120590t_bool(X75,X24))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X15),hAPP_n539120590t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_xt7) ).

fof(fact_669_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X15),hAPP_n539120590t_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X149)),hAPP_n539120590t_bool(X75,X24))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X15),hAPP_n539120590t_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_xt5) ).

fof(fact_838_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X12),hAPP_f861874780t_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X75,X24)),hAPP_f861874780t_bool(X75,X149))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X12),hAPP_f861874780t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_order__less__le__subst1) ).

fof(fact_829_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X12),hAPP_n539120590t_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X75,X24)),hAPP_n539120590t_bool(X75,X149))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X12),hAPP_n539120590t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_order__less__le__subst1) ).

fof(fact_817_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X12),hAPP_n539120590t_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X75,X24)),hAPP_n539120590t_bool(X75,X149))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X12),hAPP_n539120590t_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_order__le__less__subst1) ).

fof(fact_706_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f1358350510ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun2093718614t_bool(X24)
                & is_fun2093718614t_bool(X149) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X75,X149)),hAPP_f1358350510ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f1358350510ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_xt7) ).

fof(fact_702_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f816335862ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun961089132t_bool(X24)
                & is_fun961089132t_bool(X149) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X75,X149)),hAPP_f816335862ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f816335862ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_xt7) ).

fof(fact_701_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f897066961ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun288122577l_bool(X24)
                & is_fun288122577l_bool(X149) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X75,X149)),hAPP_f897066961ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f897066961ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_xt7) ).

fof(fact_700_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f1695077327ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun158382675l_bool(X24)
                & is_fun158382675l_bool(X149) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X75,X149)),hAPP_f1695077327ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f1695077327ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_xt7) ).

fof(fact_699_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f1313392232ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun279392540l_bool(X24)
                & is_fun279392540l_bool(X149) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X75,X149)),hAPP_f1313392232ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f1313392232ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_xt7) ).

fof(fact_705_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f2030293770ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X75,X149)),hAPP_f2030293770ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f2030293770ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_705_xt7) ).

fof(fact_671_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_f2030293770ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X149)),hAPP_f2030293770ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f2030293770ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_xt5) ).

fof(fact_670_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_f22106695ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X149),X24))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X75,X149)),hAPP_f22106695ol_nat(X75,X24))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f22106695ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_xt5) ).

fof(fact_703_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_bool_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_bool(X24)
                & is_bool(X149) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X75,X149)),hAPP_bool_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_bool_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_xt7) ).

fof(fact_704_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f2120083535ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X75,X149)),hAPP_f2120083535ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f2120083535ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_704_xt7) ).

fof(fact_672_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_f2120083535ol_nat(X75,X13)))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X149),X24))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X149)),hAPP_f2120083535ol_nat(X75,X24))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_f2120083535ol_nat(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_xt5) ).

fof(fact_854_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f1358350510ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun2093718614t_bool(X24)
                & is_fun2093718614t_bool(X149) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X75,X24)),hAPP_f1358350510ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f1358350510ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_order__less__le__subst1) ).

fof(fact_850_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f816335862ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun961089132t_bool(X24)
                & is_fun961089132t_bool(X149) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X75,X24)),hAPP_f816335862ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f816335862ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_order__less__le__subst1) ).

fof(fact_849_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f897066961ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun288122577l_bool(X24)
                & is_fun288122577l_bool(X149) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X75,X24)),hAPP_f897066961ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f897066961ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_order__less__le__subst1) ).

fof(fact_848_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f1695077327ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun158382675l_bool(X24)
                & is_fun158382675l_bool(X149) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X75,X24)),hAPP_f1695077327ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f1695077327ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_order__less__le__subst1) ).

fof(fact_847_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f1313392232ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun279392540l_bool(X24)
                & is_fun279392540l_bool(X149) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X75,X24)),hAPP_f1313392232ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f1313392232ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_order__less__le__subst1) ).

fof(fact_853_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f2030293770ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X75,X24)),hAPP_f2030293770ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f2030293770ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_order__less__le__subst1) ).

fof(fact_819_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_f2030293770ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1568535512t_bool(X24)
                & is_fun1568535512t_bool(X149) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X75,X24)),hAPP_f2030293770ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f2030293770ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_order__le__less__subst1) ).

fof(fact_818_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_f22106695ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X24),X149))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X75,X24)),hAPP_f22106695ol_nat(X75,X149))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f22106695ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_818_order__le__less__subst1) ).

fof(fact_851_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_bool_nat(X75,X13)))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_bool(X24)
                & is_bool(X149) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X75,X24)),hAPP_bool_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_bool_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_order__less__le__subst1) ).

fof(fact_852_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f2120083535ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X75,X24)),hAPP_f2120083535ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f2120083535ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_order__less__le__subst1) ).

fof(fact_820_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_f2120083535ol_nat(X75,X13)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X15))
       => ( ! [X24,X149] :
              ( ( is_fun1236654035i_bool(X24)
                & is_fun1236654035i_bool(X149) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X24),X149))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X75,X24)),hAPP_f2120083535ol_nat(X75,X149))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_f2120083535ol_nat(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_order__le__less__subst1) ).

fof(fact_689_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X15),hAPP_f54304608l_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X149),X24))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X75,X149)),hAPP_f54304608l_bool(X75,X24))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X15),hAPP_f54304608l_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_xt7) ).

fof(fact_680_xt7,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X12))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X15),hAPP_nat_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X149),X24))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X149)),hAPP_nat_bool(X75,X24))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X15),hAPP_nat_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_xt7) ).

fof(fact_668_xt5,axiom,
    ! [X15,X75,X13,X12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X12))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X15),hAPP_nat_bool(X75,X13)))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),X24))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X149)),hAPP_nat_bool(X75,X24))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X15),hAPP_nat_bool(X75,X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_xt5) ).

fof(fact_837_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X12),hAPP_f54304608l_bool(X75,X13)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X149))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X75,X24)),hAPP_f54304608l_bool(X75,X149))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X12),hAPP_f54304608l_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_order__less__le__subst1) ).

fof(fact_828_order__less__le__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X12),hAPP_nat_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X149))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X24)),hAPP_nat_bool(X75,X149))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X12),hAPP_nat_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_order__less__le__subst1) ).

fof(fact_816_order__le__less__subst1,axiom,
    ! [X15,X12,X75,X13] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),hAPP_nat_bool(X75,X13)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X15))
       => ( ! [X24,X149] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X149))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X75,X24)),hAPP_nat_bool(X75,X149))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X12),hAPP_nat_bool(X75,X15))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_order__le__less__subst1) ).

fof(fact_1112_card__less__Suc,axiom,
    ! [X26,X220] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X220))
     => hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),X220))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X26))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X220))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X26))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_card__less__Suc) ).

fof(fact_10__C3_C,axiom,
    ! [X8,X9,X12,X13] :
      ( ( is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X9),arrow_1721807329e_Prof))
         => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X8),arrow_1721807329e_Prof))
           => ( ! [X14] :
                  ( is_Arr43961803e_indi(X14)
                 => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_A1677245848t_bool(X9,X14)))
                  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X13),X12)),hAPP_A1677245848t_bool(X8,X14))) ) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),hAPP_f412050202t_bool(f,X9)))
              <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X13),X12)),hAPP_f412050202t_bool(f,X8))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__C3_C) ).

fof(fact_718_pred__subset__eq2,axiom,
    ! [X74,X73] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X74)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X73)))
    <=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X74),X73)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_pred__subset__eq2) ).

fof(fact_24_unanimity__def,axiom,
    ! [X23] :
      ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X23))
    <=> ! [X24] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X24),arrow_1721807329e_Prof))
         => ! [X17,X18] :
              ( ( is_Arr1861959080le_alt(X17)
                & is_Arr1861959080le_alt(X18) )
             => ( ! [X14] :
                    ( is_Arr43961803e_indi(X14)
                   => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18)),hAPP_A1677245848t_bool(X24,X14))) )
               => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18)),hAPP_f412050202t_bool(X23,X24))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_unanimity__def) ).

fof(fact_1023_mono__nat__linear__lb,axiom,
    ! [X200,X206,X75] :
      ( ! [X30,X78] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X78))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X75,X30)),hAPP_nat_nat(X75,X78))) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X75,X200)),X206)),hAPP_nat_nat(X75,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X200),X206)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_mono__nat__linear__lb) ).

fof(fact_181_pred__equals__eq2,axiom,
    ! [X73,X74] :
      ( ( is_fun961089132t_bool(X73)
        & is_fun961089132t_bool(X74) )
     => ( ! [X24,X25] :
            ( ( is_Arr1861959080le_alt(X24)
              & is_Arr1861959080le_alt(X25) )
           => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X24),X25)),X74))
            <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X24),X25)),X73)) ) )
      <=> X74 = X73 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_pred__equals__eq2) ).

fof(fact_1113_card__less,axiom,
    ! [X26,X220] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X220))
     => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X220))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X26))))) != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_card__less) ).

fof(fact_1024_less__mono__imp__le__mono,axiom,
    ! [X26,X212,X75] :
      ( ! [X14,X213] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X213))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X75,X14)),hAPP_nat_nat(X75,X213))) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X212))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X75,X26)),hAPP_nat_nat(X75,X212))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_less__mono__imp__le__mono) ).

fof(fact_180_in__above,axiom,
    ! [X4,X5,X6,X12,X13] :
      ( ( is_Arr1861959080le_alt(X4)
        & is_Arr1861959080le_alt(X5)
        & is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
         => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X6),X12),X13)))
          <=> ( X4 != X5
              & ( X4 = X13
               => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X5)),X6)) )
              & ( X4 != X13
               => ( ( X5 = X13
                   => ( X4 = X12
                      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X12)),X6)) ) )
                  & ( X5 != X13
                   => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),X6)) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_in__above) ).

fof(fact_621_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X24),X72))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X75,X24)),hAPP_P332578347t_bool(X76,X24))) )
     => hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X75),pi_Pro1122146355t_unit(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_Pi__I) ).

fof(fact_648_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X24),X72))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X75,X24)),hAPP_P324742453l_bool(X76,X24))) )
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X75),pi_Pro666468413t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_Pi__I) ).

fof(fact_620_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X24),X72))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X75,X24)),hAPP_P1875867302i_bool(X76,X24))) )
     => hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X75),pi_Pro1270767662e_indi(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_Pi__I) ).

fof(fact_630_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_fun961089132t_bool(X24)
         => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X24),X72))
           => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X75,X24)),hAPP_f1710744577t_bool(X76,X24))) ) )
     => hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X75),pi_fun308431217t_unit(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_Pi__I) ).

fof(fact_629_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_fun961089132t_bool(X24)
         => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X24),X72))
           => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X75,X24)),hAPP_f210572555l_bool(X76,X24))) ) )
     => hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X75),pi_fun1575168891l_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_Pi__I) ).

fof(fact_628_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_fun961089132t_bool(X24)
         => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X24),X72))
           => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X75,X24)),hAPP_f244157820i_bool(X76,X24))) ) )
     => hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X75),pi_fun896360044e_indi(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_Pi__I) ).

fof(fact_627_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X24),X72))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X75,X24)),hAPP_f1866147972t_bool(X76,X24))) )
     => hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X75),pi_fun321364250t_unit(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_Pi__I) ).

fof(fact_626_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X24),X72))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X75,X24)),hAPP_f1624277646l_bool(X76,X24))) )
     => hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X75),pi_fun52649508l_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_Pi__I) ).

fof(fact_625_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X24),X72))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X75,X24)),hAPP_f1552576127i_bool(X76,X24))) )
     => hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X75),pi_fun1002945429e_indi(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_Pi__I) ).

fof(fact_649_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X24),X72))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X75,X24)),hAPP_f1277514478l_bool(X76,X24))) )
     => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X75),pi_fun150026276t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_Pi__I) ).

fof(fact_624_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X24),X72))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X75,X24)),hAPP_f1891021702t_bool(X76,X24))) )
     => hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X75),pi_fun1877263000t_unit(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_Pi__I) ).

fof(fact_623_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X24),X72))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X75,X24)),hAPP_f839832464l_bool(X76,X24))) )
     => hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X75),pi_fun823343522l_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_Pi__I) ).

fof(fact_622_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X24),X72))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X75,X24)),hAPP_f1948454017i_bool(X76,X24))) )
     => hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X75),pi_fun753830419e_indi(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_Pi__I) ).

fof(fact_636_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X24),X72))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X75,X24)),hAPP_P1341894483t_bool(X76,X24))) )
     => hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X75),pi_Pro1928973619le_alt(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_Pi__I) ).

fof(fact_644_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X24),X72))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X75,X24)),hAPP_P1294997365l_bool(X76,X24))) )
     => hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X75),pi_Pro718203741t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_Pi__I) ).

fof(fact_642_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X24),X72))
         => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X75,X24)),hAPP_P1171466554l_bool(X76,X24))) )
     => hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X75),pi_Pro1880661658t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_Pi__I) ).

fof(fact_639_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X24),X72))
         => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X75,X24)),hAPP_P254387896l_bool(X76,X24))) )
     => hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X75),pi_Pro610293528t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_Pi__I) ).

fof(fact_647_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X24),X72))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X75,X24)),hAPP_P32877782t_bool(X76,X24))) )
     => hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X75),pi_Product_unit_nat(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_Pi__I) ).

fof(fact_633_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),X72))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X75,X24)),hAPP_n454528608t_bool(X76,X24))) )
     => hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X75),pi_nat_Product_unit(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_Pi__I) ).

fof(fact_632_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),X72))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X75,X24)),hAPP_n1006566506l_bool(X76,X24))) )
     => hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X75),pi_nat_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_Pi__I) ).

fof(fact_631_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),X72))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X75,X24)),hAPP_n821919323i_bool(X76,X24))) )
     => hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X75),pi_nat660525389e_indi(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_Pi__I) ).

fof(fact_635_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_bool(X24)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X24),X72))
           => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X75,X24)),hAPP_b1703662281t_bool(X76,X24))) ) )
     => hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X75),pi_boo115158845le_alt(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_Pi__I) ).

fof(fact_643_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_bool(X24)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X24),X72))
           => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X75,X24)),hAPP_b1812770943l_bool(X76,X24))) ) )
     => hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X75),pi_boo538701011t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_Pi__I) ).

fof(fact_641_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_bool(X24)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X24),X72))
           => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X75,X24)),hAPP_b517355696l_bool(X76,X24))) ) )
     => hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X75),pi_boo1117000868t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_Pi__I) ).

fof(fact_638_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_bool(X24)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X24),X72))
           => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X75,X24)),hAPP_b1048178734l_bool(X76,X24))) ) )
     => hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X75),pi_boo175444770t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_Pi__I) ).

fof(fact_646_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_bool(X24)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X24),X72))
           => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X75,X24)),hAPP_b1013836512t_bool(X76,X24))) ) )
     => hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X75),pi_bool_nat(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_Pi__I) ).

fof(fact_634_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_Arr43961803e_indi(X24)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X24),X72))
           => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X75,X24)),hAPP_A1677245848t_bool(X76,X24))) ) )
     => hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X75),pi_Arr1199386158le_alt(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Pi__I) ).

fof(fact_650_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_Arr43961803e_indi(X24)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X24),X72))
           => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X75,X24)),hAPP_A60074736l_bool(X76,X24))) ) )
     => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X75),pi_Arr990697634t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_Pi__I) ).

fof(fact_640_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_Arr43961803e_indi(X24)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X24),X72))
           => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X75,X24)),hAPP_A1112981887l_bool(X76,X24))) ) )
     => hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X75),pi_Arr1936979349t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_Pi__I) ).

fof(fact_637_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_Arr43961803e_indi(X24)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X24),X72))
           => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X75,X24)),hAPP_A1952883197l_bool(X76,X24))) ) )
     => hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X75),pi_Arr2020412179t_bool(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_Pi__I) ).

fof(fact_645_Pi__I,axiom,
    ! [X75,X76,X72] :
      ( ! [X24] :
          ( is_Arr43961803e_indi(X24)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X24),X72))
           => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X75,X24)),hAPP_A2046586321t_bool(X76,X24))) ) )
     => hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X75),pi_Arr346900227di_nat(X72,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_Pi__I) ).

fof(fact_225_in__below,axiom,
    ! [X4,X5,X6,X12,X13] :
      ( ( is_Arr1861959080le_alt(X4)
        & is_Arr1861959080le_alt(X5)
        & is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
         => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),arrow_1539419881_below(X6,X12,X13)))
          <=> ( X4 != X5
              & ( X5 = X12
               => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X13)),X6)) )
              & ( X5 != X12
               => ( ( X4 = X12
                   => ( X5 = X13
                      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X13),X5)),X6)) ) )
                  & ( X4 != X12
                   => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),X6)) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_in__below) ).

fof(fact_182_dictatorI,axiom,
    ! [X26,X23] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X23),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin))))
     => ( ! [X24] :
            ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X24),arrow_1721807329e_Prof))
           => ! [X17,X18] :
                ( ( is_Arr1861959080le_alt(X17)
                  & is_Arr1861959080le_alt(X18) )
               => ( X17 != X18
                 => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18)),hAPP_A1677245848t_bool(X24,X26)))
                   => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18)),hAPP_f412050202t_bool(X23,X24))) ) ) ) )
       => hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X23),X26)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_dictatorI) ).

fof(fact_1166_Suc__mult__le__cancel1,axiom,
    ! [X206,X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X206)),X200)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X206)),X27)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1166_Suc__mult__le__cancel1) ).

fof(fact_1163_Suc__mult__less__cancel1,axiom,
    ! [X206,X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X206)),X200)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X206)),X27)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_Suc__mult__less__cancel1) ).

fof(fact_1040_finite__less__ub,axiom,
    ! [X215,X75] :
      ( ! [X78] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X78),hAPP_nat_nat(X75,X78)))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),X75)),X215)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_finite__less__ub) ).

fof(fact_1037_finite__M__bounded__by__nat,axiom,
    ! [X9,X26] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),X9)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X26))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_finite__M__bounded__by__nat) ).

fof(fact_4_in__mkbot,axiom,
    ! [X4,X5,X6,X7] :
      ( ( is_Arr1861959080le_alt(X4)
        & is_Arr1861959080le_alt(X5)
        & is_Arr1861959080le_alt(X7) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X6),X7)))
      <=> ( X5 != X7
          & ( X4 = X7
           => X4 != X5 )
          & ( X4 != X7
           => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),X6)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_in__mkbot) ).

fof(fact_5_in__mktop,axiom,
    ! [X4,X5,X6,X7] :
      ( ( is_Arr1861959080le_alt(X4)
        & is_Arr1861959080le_alt(X5)
        & is_Arr1861959080le_alt(X7) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X6),X7)))
      <=> ( X4 != X7
          & ( X5 = X7
           => X4 != X5 )
          & ( X5 != X7
           => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),X6)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_in__mktop) ).

fof(fact_1130_subset__card__intvl__is__intvl,axiom,
    ! [X72,X206] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),hAPP_n1699378549t_bool(ord_at4362885an_nat(X206),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X206),hAPP_f22106695ol_nat(finite_card_nat,X72)))))
     => X72 = hAPP_n1699378549t_bool(ord_at4362885an_nat(X206),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X206),hAPP_f22106695ol_nat(finite_card_nat,X72))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_subset__card__intvl__is__intvl) ).

fof(fact_1180_left__add__mult__distrib,axiom,
    ! [X207,X225,X208,X196] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X207),X225)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X208),X225)),X196)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X208)),X225)),X196),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_left__add__mult__distrib) ).

fof(fact_1186_weak__decr__stable,axiom,
    ! [X75] :
      ( ! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X75,hAPP_nat_nat(suc,X14))),hAPP_nat_nat(X75,X14)))
     => ? [X14] :
        ! [X211] : hAPP_nat_nat(X75,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X211)) = hAPP_nat_nat(X75,X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_weak__decr__stable) ).

fof(fact_752_le__funI,axiom,
    ! [X75,X81] :
      ( ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X75,X24)),hAPP_P606313927t_bool(X81,X24)))
     => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X75),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_le__funI) ).

fof(fact_369_le__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X75),X81))
    <=> ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X75,X24)),hAPP_P606313927t_bool(X81,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_le__fun__def) ).

fof(fact_749_le__funI,axiom,
    ! [X75,X81] :
      ( ! [X24] :
          ( is_fun961089132t_bool(X24)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X75,X24)),hAPP_f592646513l_bool(X81,X24))) )
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X75),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_749_le__funI) ).

fof(fact_366_le__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X75),X81))
    <=> ! [X24] :
          ( is_fun961089132t_bool(X24)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X75,X24)),hAPP_f592646513l_bool(X81,X24))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_le__fun__def) ).

fof(fact_750_le__funI,axiom,
    ! [X75,X81] :
      ( ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X75,X24)),hAPP_f312250286l_bool(X81,X24)))
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X75),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_750_le__funI) ).

fof(fact_367_le__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X75),X81))
    <=> ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X75,X24)),hAPP_f312250286l_bool(X81,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_le__fun__def) ).

fof(fact_751_le__funI,axiom,
    ! [X75,X81] :
      ( ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X75,X24)),hAPP_f965095724l_bool(X81,X24)))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X75),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_751_le__funI) ).

fof(fact_368_le__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X75),X81))
    <=> ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X75,X24)),hAPP_f965095724l_bool(X81,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_le__fun__def) ).

fof(fact_754_le__funI,axiom,
    ! [X75,X81] :
      ( ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X75,X24)),hAPP_P1676879539t_bool(X81,X24)))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X75),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_le__funI) ).

fof(fact_371_le__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X75),X81))
    <=> ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X75,X24)),hAPP_P1676879539t_bool(X81,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_le__fun__def) ).

fof(fact_756_le__funI,axiom,
    ! [X75,X81] :
      ( ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X24)),hAPP_nat_bool(X81,X24)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X75),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_le__funI) ).

fof(fact_373_le__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X75),X81))
    <=> ! [X24] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X24)),hAPP_nat_bool(X81,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_le__fun__def) ).

fof(fact_753_le__funI,axiom,
    ! [X75,X81] :
      ( ! [X24] :
          ( is_Arr43961803e_indi(X24)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X75,X24)),hAPP_A1785763630i_bool(X81,X24))) )
     => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X75),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_le__funI) ).

fof(fact_370_le__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X75),X81))
    <=> ! [X24] :
          ( is_Arr43961803e_indi(X24)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X75,X24)),hAPP_A1785763630i_bool(X81,X24))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_le__fun__def) ).

fof(fact_755_le__funI,axiom,
    ! [X75,X81] :
      ( ! [X24] :
          ( is_Arr1861959080le_alt(X24)
         => hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X75,X24)),hAPP_A1664620203t_bool(X81,X24))) )
     => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X75),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_le__funI) ).

fof(fact_372_le__fun__def,axiom,
    ! [X75,X81] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X75),X81))
    <=> ! [X24] :
          ( is_Arr1861959080le_alt(X24)
         => hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X75,X24)),hAPP_A1664620203t_bool(X81,X24))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_le__fun__def) ).

fof(fact_90_above__Lin,axiom,
    ! [X6,X4,X5] :
      ( ( is_Arr1861959080le_alt(X4)
        & is_Arr1861959080le_alt(X5) )
     => ( X4 != X5
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X6),X4),X5)),arrow_1681063817le_Lin)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_above__Lin) ).

fof(fact_741_add__le__cancel__right,axiom,
    ! [X12,X15,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X15)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_add__le__cancel__right) ).

fof(fact_736_add__le__imp__le__right,axiom,
    ! [X166,X167,X168] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X166),X167)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X168),X167)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X166),X168)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_add__le__imp__le__right) ).

fof(fact_1016_nat__add__left__cancel__le,axiom,
    ! [X206,X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X206),X200)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X206),X27)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_nat__add__left__cancel__le) ).

fof(fact_740_add__le__cancel__left,axiom,
    ! [X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X12)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X13)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_add__le__cancel__left) ).

fof(fact_735_add__le__imp__le__left,axiom,
    ! [X163,X164,X165] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X163),X164)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X163),X165)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X164),X165)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_add__le__imp__le__left) ).

fof(fact_748_add__less__cancel__right,axiom,
    ! [X12,X15,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X15)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_add__less__cancel__right) ).

fof(fact_743_add__less__imp__less__right,axiom,
    ! [X182,X183,X184] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X182),X183)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X184),X183)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X182),X184)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_add__less__imp__less__right) ).

fof(fact_1001_nat__add__left__cancel__less,axiom,
    ! [X206,X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X206),X200)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X206),X27)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_nat__add__left__cancel__less) ).

fof(fact_747_add__less__cancel__left,axiom,
    ! [X15,X12,X13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X12)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X13)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_add__less__cancel__left) ).

fof(fact_742_add__less__imp__less__left,axiom,
    ! [X179,X180,X181] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X179),X180)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X179),X181)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X180),X181)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_add__less__imp__less__left) ).

fof(fact_980_pred__subset__eq,axiom,
    ! [X74,X73] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X74)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X73)))
    <=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X74),X73)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_pred__subset__eq) ).

fof(fact_977_pred__subset__eq,axiom,
    ! [X74,X73] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X74)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X73)))
    <=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X74),X73)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_pred__subset__eq) ).

fof(fact_978_pred__subset__eq,axiom,
    ! [X74,X73] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X74)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X73)))
    <=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X74),X73)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_pred__subset__eq) ).

fof(fact_979_pred__subset__eq,axiom,
    ! [X74,X73] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X74)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X73)))
    <=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X74),X73)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_pred__subset__eq) ).

fof(fact_976_pred__subset__eq,axiom,
    ! [X74,X73] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X74)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X73)))
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X74),X73)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_pred__subset__eq) ).

fof(fact_1020_add__le__mono,axiom,
    ! [X196,X210,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X208))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X196),X210))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X196)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X208),X210))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_add__le__mono) ).

fof(fact_737_add__mono,axiom,
    ! [X169,X170,X171,X172] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X171),X172))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X169),X170))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X171),X169)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X172),X170))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_737_add__mono) ).

fof(fact_654_add__less__le__mono,axiom,
    ! [X141,X142,X143,X144] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X143),X144))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X141),X142))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X143),X141)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X144),X142))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_add__less__le__mono) ).

fof(fact_655_add__le__less__mono,axiom,
    ! [X145,X146,X147,X148] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X147),X148))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X145),X146))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X147),X145)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X148),X146))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_add__le__less__mono) ).

fof(fact_1005_add__less__mono,axiom,
    ! [X196,X210,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X208))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X196),X210))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X196)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X208),X210))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_add__less__mono) ).

fof(fact_744_add__strict__mono,axiom,
    ! [X185,X186,X187,X188] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X187),X188))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X185),X186))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X187),X185)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X188),X186))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_add__strict__mono) ).

fof(fact_1171_one__le__mult__iff,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X200),X27)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X200))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_one__le__mult__iff) ).

fof(fact_1170_one__less__mult,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X197))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X195))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X195),X197))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_one__less__mult) ).

fof(fact_1115_inc__induct,axiom,
    ! [X9,X26,X212] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X212))
     => ( hBOOL(hAPP_nat_bool(X9,X212))
       => ( ! [X14] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X212))
             => ( hBOOL(hAPP_nat_bool(X9,hAPP_nat_nat(suc,X14)))
               => hBOOL(hAPP_nat_bool(X9,X14)) ) )
         => hBOOL(hAPP_nat_bool(X9,X26)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_inc__induct) ).

fof(fact_1172_mult__le__cancel2,axiom,
    ! [X200,X206,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X200),X206)),hAPP_nat_nat(times_times_nat(X27),X206)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X206))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_mult__le__cancel2) ).

fof(fact_1176_nat__mult__le__cancel1,axiom,
    ! [X200,X27,X206] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X206))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X206),X200)),hAPP_nat_nat(times_times_nat(X206),X27)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_nat__mult__le__cancel1) ).

fof(fact_1173_mult__le__cancel1,axiom,
    ! [X206,X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X206),X200)),hAPP_nat_nat(times_times_nat(X206),X27)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X206))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_mult__le__cancel1) ).

fof(fact_1177_nat__mult__less__cancel1,axiom,
    ! [X200,X27,X206] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X206))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X206),X200)),hAPP_nat_nat(times_times_nat(X206),X27)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_nat__mult__less__cancel1) ).

fof(fact_1022_add__leD1,axiom,
    ! [X195,X196,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X196)),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_add__leD1) ).

fof(fact_1021_add__leD2,axiom,
    ! [X195,X196,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X196)),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X196),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_add__leD2) ).

fof(fact_1007_add__lessD1,axiom,
    ! [X207,X208,X196] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X208)),X196))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X196)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_add__lessD1) ).

fof(fact_598_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X75),pi_Pro1928973619le_alt(X72,hAPP_f1066247963t_bool(cOMBK_812212462t_unit,X76))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_funcset__mem) ).

fof(fact_597_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X75),pi_boo115158845le_alt(X72,hAPP_f340261009t_bool(cOMBK_545135096l_bool,X76))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_funcset__mem) ).

fof(fact_596_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X75),pi_Arr1199386158le_alt(X72,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X76))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_funcset__mem) ).

fof(fact_610_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X75),pi_fun150026276t_bool(X72,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,X76))))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_funcset__mem) ).

fof(fact_606_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X75),pi_Pro718203741t_bool(X72,hAPP_f2028504885l_bool(cOMBK_384545070t_unit,X76))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_funcset__mem) ).

fof(fact_605_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X75),pi_boo538701011t_bool(X72,hAPP_f256804927l_bool(cOMBK_69806648l_bool,X76))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_funcset__mem) ).

fof(fact_611_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X75),pi_Arr990697634t_bool(X72,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,X76))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_funcset__mem) ).

fof(fact_604_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X75),pi_Pro1880661658t_bool(X72,hAPP_f1028353513l_bool(cOMBK_731023445t_unit,X76))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_funcset__mem) ).

fof(fact_603_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X75),pi_boo1117000868t_bool(X72,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,X76))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_funcset__mem) ).

fof(fact_602_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X75),pi_Arr1936979349t_bool(X72,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,X76))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_funcset__mem) ).

fof(fact_601_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X75),pi_Pro610293528t_bool(X72,hAPP_f512628453l_bool(cOMBK_295807955t_unit,X76))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_funcset__mem) ).

fof(fact_600_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X75),pi_boo175444770t_bool(X72,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,X76))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_funcset__mem) ).

fof(fact_599_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X75),pi_Arr2020412179t_bool(X72,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,X76))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_funcset__mem) ).

fof(fact_595_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X75),pi_nat_Product_unit(X72,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,X76))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_funcset__mem) ).

fof(fact_592_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X75),pi_fun308431217t_unit(X72,hAPP_f478658281t_bool(cOMBK_1589894370t_bool,X76))))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_funcset__mem) ).

fof(fact_589_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X75),pi_fun321364250t_unit(X72,hAPP_f894574520t_bool(cOMBK_1733280085t_bool,X76))))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_funcset__mem) ).

fof(fact_586_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X75),pi_fun1877263000t_unit(X72,hAPP_f587035834t_bool(cOMBK_1048254163t_bool,X76))))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_funcset__mem) ).

fof(fact_583_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X75),pi_Pro1122146355t_unit(X72,hAPP_f1165814111t_bool(cOMBK_859929070le_alt,X76))))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_funcset__mem) ).

fof(fact_609_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X75),pi_Product_unit_nat(X72,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,X76))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_funcset__mem) ).

fof(fact_608_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X75),pi_bool_nat(X72,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,X76))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_funcset__mem) ).

fof(fact_607_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X75),pi_Arr346900227di_nat(X72,hAPP_f1491725936t_bool(cOMBK_847149194e_indi,X76))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_funcset__mem) ).

fof(fact_581_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X75),pi_Pro666468413t_bool(X72,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,X76))))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_funcset__mem) ).

fof(fact_591_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X75),pi_fun1575168891l_bool(X72,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,X76))))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_funcset__mem) ).

fof(fact_588_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X75),pi_fun52649508l_bool(X72,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,X76))))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_funcset__mem) ).

fof(fact_585_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X75),pi_fun823343522l_bool(X72,hAPP_f746617550l_bool(cOMBK_370033373t_bool,X76))))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_funcset__mem) ).

fof(fact_594_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X75),pi_nat_bool(X72,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,X76))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_funcset__mem) ).

fof(fact_582_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X75),pi_Pro1270767662e_indi(X72,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,X76))))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_funcset__mem) ).

fof(fact_590_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X75),pi_fun896360044e_indi(X72,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,X76))))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_funcset__mem) ).

fof(fact_587_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X75),pi_fun1002945429e_indi(X72,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,X76))))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_funcset__mem) ).

fof(fact_584_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X75),pi_fun753830419e_indi(X72,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,X76))))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_funcset__mem) ).

fof(fact_593_funcset__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X75),pi_nat660525389e_indi(X72,hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,X76))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X75,X4)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_funcset__mem) ).

fof(fact_1169_n__less__n__mult__m,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X197))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X195))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),hAPP_nat_nat(times_times_nat(X197),X195))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_n__less__n__mult__m) ).

fof(fact_1168_n__less__m__mult__n,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X197))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X195))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),hAPP_nat_nat(times_times_nat(X195),X197))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_n__less__m__mult__n) ).

fof(fact_578_below__Lin,axiom,
    ! [X6,X4,X5] :
      ( ( is_Arr1861959080le_alt(X4)
        & is_Arr1861959080le_alt(X5) )
     => ( X4 != X5
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,arrow_1539419881_below(X6,X4,X5)),arrow_1681063817le_Lin)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_below__Lin) ).

fof(fact_1019_add__le__mono1,axiom,
    ! [X196,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X208))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X196)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X208),X196))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_add__le__mono1) ).

fof(fact_739_add__right__mono,axiom,
    ! [X176,X177,X178] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X177),X178))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X177),X176)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X178),X176))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_add__right__mono) ).

fof(fact_738_add__left__mono,axiom,
    ! [X173,X174,X175] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X174),X175))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X173),X174)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X173),X175))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_add__left__mono) ).

fof(fact_1004_add__less__mono1,axiom,
    ! [X196,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X208))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X196)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X208),X196))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_add__less__mono1) ).

fof(fact_746_add__strict__right__mono,axiom,
    ! [X192,X193,X194] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X193),X194))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X193),X192)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X194),X192))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_add__strict__right__mono) ).

fof(fact_745_add__strict__left__mono,axiom,
    ! [X189,X190,X191] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X190),X191))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X189),X190)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X189),X191))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_add__strict__left__mono) ).

fof(conj_0,conjecture,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(fact_1160_mult__less__cancel2,axiom,
    ! [X200,X206,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X200),X206)),hAPP_nat_nat(times_times_nat(X27),X206)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X206))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_mult__less__cancel2) ).

fof(fact_1161_mult__less__cancel1,axiom,
    ! [X206,X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X206),X200)),hAPP_nat_nat(times_times_nat(X206),X27)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X206))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_mult__less__cancel1) ).

fof(fact_564_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X75),pi_Pro1928973619le_alt(X72,X76)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X75,X4)),hAPP_P1341894483t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_Pi__mem) ).

fof(fact_563_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X75),pi_boo115158845le_alt(X72,X76)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X75,X4)),hAPP_b1703662281t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_Pi__mem) ).

fof(fact_562_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X75),pi_Arr1199386158le_alt(X72,X76)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X75,X4)),hAPP_A1677245848t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_Pi__mem) ).

fof(fact_576_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X75),pi_fun150026276t_bool(X72,X76)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X75,X4)),hAPP_f1277514478l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_Pi__mem) ).

fof(fact_572_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X75),pi_Pro718203741t_bool(X72,X76)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X75,X4)),hAPP_P1294997365l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_Pi__mem) ).

fof(fact_571_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X75),pi_boo538701011t_bool(X72,X76)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X75,X4)),hAPP_b1812770943l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_Pi__mem) ).

fof(fact_577_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X75),pi_Arr990697634t_bool(X72,X76)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X75,X4)),hAPP_A60074736l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_Pi__mem) ).

fof(fact_570_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X75),pi_Pro1880661658t_bool(X72,X76)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X75,X4)),hAPP_P1171466554l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_Pi__mem) ).

fof(fact_569_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X75),pi_boo1117000868t_bool(X72,X76)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X75,X4)),hAPP_b517355696l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_Pi__mem) ).

fof(fact_568_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X75),pi_Arr1936979349t_bool(X72,X76)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X75,X4)),hAPP_A1112981887l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_Pi__mem) ).

fof(fact_567_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X75),pi_Pro610293528t_bool(X72,X76)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X75,X4)),hAPP_P254387896l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_Pi__mem) ).

fof(fact_566_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X75),pi_boo175444770t_bool(X72,X76)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X75,X4)),hAPP_b1048178734l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_Pi__mem) ).

fof(fact_565_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X75),pi_Arr2020412179t_bool(X72,X76)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X75,X4)),hAPP_A1952883197l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_Pi__mem) ).

fof(fact_561_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X75),pi_nat_Product_unit(X72,X76)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X75,X4)),hAPP_n454528608t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_Pi__mem) ).

fof(fact_558_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X75),pi_fun308431217t_unit(X72,X76)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X75,X4)),hAPP_f1710744577t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_Pi__mem) ).

fof(fact_555_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X75),pi_fun321364250t_unit(X72,X76)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X75,X4)),hAPP_f1866147972t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_Pi__mem) ).

fof(fact_552_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X75),pi_fun1877263000t_unit(X72,X76)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X75,X4)),hAPP_f1891021702t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_Pi__mem) ).

fof(fact_549_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X75),pi_Pro1122146355t_unit(X72,X76)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X75,X4)),hAPP_P332578347t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_Pi__mem) ).

fof(fact_575_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X75),pi_Product_unit_nat(X72,X76)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X75,X4)),hAPP_P32877782t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_Pi__mem) ).

fof(fact_574_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X75),pi_bool_nat(X72,X76)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X75,X4)),hAPP_b1013836512t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_Pi__mem) ).

fof(fact_573_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X75),pi_Arr346900227di_nat(X72,X76)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X75,X4)),hAPP_A2046586321t_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_Pi__mem) ).

fof(fact_547_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X75),pi_Pro666468413t_bool(X72,X76)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X75,X4)),hAPP_P324742453l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_Pi__mem) ).

fof(fact_557_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X75),pi_fun1575168891l_bool(X72,X76)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X75,X4)),hAPP_f210572555l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_Pi__mem) ).

fof(fact_554_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X75),pi_fun52649508l_bool(X72,X76)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X75,X4)),hAPP_f1624277646l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_Pi__mem) ).

fof(fact_551_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X75),pi_fun823343522l_bool(X72,X76)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X75,X4)),hAPP_f839832464l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_Pi__mem) ).

fof(fact_560_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X75),pi_nat_bool(X72,X76)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X75,X4)),hAPP_n1006566506l_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_Pi__mem) ).

fof(fact_548_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X75),pi_Pro1270767662e_indi(X72,X76)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X75,X4)),hAPP_P1875867302i_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_Pi__mem) ).

fof(fact_556_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X75),pi_fun896360044e_indi(X72,X76)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X75,X4)),hAPP_f244157820i_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_Pi__mem) ).

fof(fact_553_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X75),pi_fun1002945429e_indi(X72,X76)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X75,X4)),hAPP_f1552576127i_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_Pi__mem) ).

fof(fact_550_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X75),pi_fun753830419e_indi(X72,X76)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X75,X4)),hAPP_f1948454017i_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_Pi__mem) ).

fof(fact_559_Pi__mem,axiom,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X75),pi_nat660525389e_indi(X72,X76)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X75,X4)),hAPP_n821919323i_bool(X76,X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_Pi__mem) ).

fof(fact_1144_mult__le__mono,axiom,
    ! [X196,X210,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X208))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X196),X210))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X207),X196)),hAPP_nat_nat(times_times_nat(X208),X210))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_mult__le__mono) ).

fof(fact_1159_mult__less__mono1,axiom,
    ! [X196,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X208))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X196))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X207),X196)),hAPP_nat_nat(times_times_nat(X208),X196))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_mult__less__mono1) ).

fof(fact_1158_mult__less__mono2,axiom,
    ! [X196,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X208))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X196))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X196),X207)),hAPP_nat_nat(times_times_nat(X196),X208))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1158_mult__less__mono2) ).

fof(fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

fof(fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(fact_1196_atLeastLessThan__add__Un,axiom,
    ! [X206,X26,X212] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X212))
     => hAPP_n1699378549t_bool(ord_at4362885an_nat(X26),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X212),X206)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(X26),X212)),hAPP_n1699378549t_bool(ord_at4362885an_nat(X212),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X212),X206))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_atLeastLessThan__add__Un) ).

fof(fact_1055_add__gr__0,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X200),X27)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X200))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_add__gr__0) ).

fof(fact_88_mktop__Lin,axiom,
    ! [X4,X6] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X6),X4)),arrow_1681063817le_Lin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mktop__Lin) ).

fof(fact_89_mkbot__Lin,axiom,
    ! [X4,X6] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X6),X4)),arrow_1681063817le_Lin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mkbot__Lin) ).

fof(fact_1136_less__eq__nat_Osimps_I2_J,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X200)),X27))
    <=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,X200)),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_less__eq__nat_Osimps_I2_J) ).

fof(fact_1191_ex__nat__less,axiom,
    ! [X9,X27] :
      ( ? [X30] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X27))
          & hBOOL(hAPP_nat_bool(X9,X30)) )
    <=> ? [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X27)))
          & hBOOL(hAPP_nat_bool(X9,X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1191_ex__nat__less) ).

fof(fact_1134_ex__nat__less__eq,axiom,
    ! [X9,X27] :
      ( ? [X30] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X27))
          & hBOOL(hAPP_nat_bool(X9,X30)) )
    <=> ? [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X27)))
          & hBOOL(hAPP_nat_bool(X9,X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1134_ex__nat__less__eq) ).

fof(fact_221_complete__Lin,axiom,
    ! [X12,X13] :
      ( ( is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13) )
     => ( X12 != X13
       => ? [X24] :
            ( is_fun961089132t_bool(X24)
            & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X24),arrow_1681063817le_Lin))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_complete__Lin) ).

fof(fact_1192_all__nat__less,axiom,
    ! [X9,X27] :
      ( ! [X30] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X27))
         => hBOOL(hAPP_nat_bool(X9,X30)) )
    <=> ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X27)))
         => hBOOL(hAPP_nat_bool(X9,X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1192_all__nat__less) ).

fof(fact_1133_all__nat__less__eq,axiom,
    ! [X9,X27] :
      ( ! [X30] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X27))
         => hBOOL(hAPP_nat_bool(X9,X30)) )
    <=> ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X27)))
         => hBOOL(hAPP_nat_bool(X9,X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1133_all__nat__less__eq) ).

fof(fact_1142_mult__le__mono1,axiom,
    ! [X196,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X208))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X207),X196)),hAPP_nat_nat(times_times_nat(X208),X196))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_mult__le__mono1) ).

fof(fact_1143_mult__le__mono2,axiom,
    ! [X196,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X208))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X196),X207)),hAPP_nat_nat(times_times_nat(X196),X208))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_mult__le__mono2) ).

fof(fact_1195_image__add__atLeastAtMost,axiom,
    ! [X206,X26,X212] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X206)),hAPP_n1699378549t_bool(ord_at238088361st_nat(X26),X212)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X26),X206)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X212),X206)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1195_image__add__atLeastAtMost) ).

fof(fact_1132_image__add__atLeastLessThan,axiom,
    ! [X206,X26,X212] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X206)),hAPP_n1699378549t_bool(ord_at4362885an_nat(X26),X212)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X26),X206)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X212),X206)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_image__add__atLeastLessThan) ).

fof(fact_15_split__paired__All,axiom,
    ! [X9] :
      ( ! [X16] : hBOOL(hAPP_P606313927t_bool(X9,X16))
    <=> ! [X17,X18] :
          ( ( is_Arr1861959080le_alt(X17)
            & is_Arr1861959080le_alt(X18) )
         => hBOOL(hAPP_P606313927t_bool(X9,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X17),X18))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_split__paired__All) ).

fof(fact_1089_Suc__le__mono,axiom,
    ! [X27,X200] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X27)),hAPP_nat_nat(suc,X200)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X200)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1089_Suc__le__mono) ).

fof(fact_1080_Suc__less__eq,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X200)),hAPP_nat_nat(suc,X27)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_Suc__less__eq) ).

fof(fact_1072_Suc__less__SucD,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X195)),hAPP_nat_nat(suc,X197)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1072_Suc__less__SucD) ).

fof(fact_1099_less__add__Suc1,axiom,
    ! [X207,X195] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X195)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_less__add__Suc1) ).

fof(fact_1100_less__add__Suc2,axiom,
    ! [X207,X195] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X207)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_less__add__Suc2) ).

fof(fact_1075_less__trans__Suc,axiom,
    ! [X196,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X208))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X208),X196))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X207)),X196)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_less__trans__Suc) ).

fof(fact_1122_Suc__lessE,axiom,
    ! [X207,X196] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X207)),X196))
     => ~ ! [X213] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X213))
           => X196 != hAPP_nat_nat(suc,X213) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1122_Suc__lessE) ).

fof(fact_1096_less__Suc__eq__0__disj,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),hAPP_nat_nat(suc,X27)))
    <=> ( X200 = zero_zero_nat
        | ? [X213] :
            ( X200 = hAPP_nat_nat(suc,X213)
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X213),X27)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1096_less__Suc__eq__0__disj) ).

fof(fact_545_inj__onD,axiom,
    ! [X4,X5,X75,X72] :
      ( ( is_Arr43961803e_indi(X4)
        & is_Arr43961803e_indi(X5) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),X72))
       => ( hAPP_A1637648121di_nat(X75,X4) = hAPP_A1637648121di_nat(X75,X5)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
           => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5),X72))
             => X4 = X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_inj__onD) ).

fof(fact_541_inj__on__contraD,axiom,
    ! [X4,X5,X75,X72] :
      ( ( is_Arr43961803e_indi(X4)
        & is_Arr43961803e_indi(X5) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),X72))
       => ( X4 != X5
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
           => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5),X72))
             => hAPP_A1637648121di_nat(X75,X4) != hAPP_A1637648121di_nat(X75,X5) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_inj__on__contraD) ).

fof(fact_543_inj__on__iff,axiom,
    ! [X5,X4,X75,X72] :
      ( ( is_Arr43961803e_indi(X5)
        & is_Arr43961803e_indi(X4) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),X72))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5),X72))
           => ( hAPP_A1637648121di_nat(X75,X4) = hAPP_A1637648121di_nat(X75,X5)
            <=> X4 = X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_inj__on__iff) ).

fof(fact_539_inj__on__def,axiom,
    ! [X75,X72] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),X72))
    <=> ! [X24] :
          ( is_Arr43961803e_indi(X24)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X24),X72))
           => ! [X25] :
                ( is_Arr43961803e_indi(X25)
               => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X25),X72))
                 => ( hAPP_A1637648121di_nat(X75,X24) = hAPP_A1637648121di_nat(X75,X25)
                   => X24 = X25 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_inj__on__def) ).

fof(fact_1162_nat__0__less__mult__iff,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X200),X27)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X200))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_nat__0__less__mult__iff) ).

fof(fact_1126_nat__induct,axiom,
    ! [X27,X9] :
      ( hBOOL(hAPP_nat_bool(X9,zero_zero_nat))
     => ( ! [X78] :
            ( hBOOL(hAPP_nat_bool(X9,X78))
           => hBOOL(hAPP_nat_bool(X9,hAPP_nat_nat(suc,X78))) )
       => hBOOL(hAPP_nat_bool(X9,X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_nat__induct) ).

fof(fact_544_inj__on__iff,axiom,
    ! [X5,X4,X75,X72] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),X72))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X72))
         => ( hAPP_nat_nat(X75,X4) = hAPP_nat_nat(X75,X5)
          <=> X4 = X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_inj__on__iff) ).

fof(fact_546_inj__onD,axiom,
    ! [X4,X5,X75,X72] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),X72))
     => ( hAPP_nat_nat(X75,X4) = hAPP_nat_nat(X75,X5)
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X72))
           => X4 = X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_inj__onD) ).

fof(fact_542_inj__on__contraD,axiom,
    ! [X4,X5,X75,X72] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),X72))
     => ( X4 != X5
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X72))
           => hAPP_nat_nat(X75,X4) != hAPP_nat_nat(X75,X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_inj__on__contraD) ).

fof(fact_540_inj__on__def,axiom,
    ! [X75,X72] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),X72))
    <=> ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),X72))
         => ! [X25] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X25),X72))
             => ( hAPP_nat_nat(X75,X24) = hAPP_nat_nat(X75,X25)
               => X24 = X25 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_inj__on__def) ).

fof(fact_715_Pi__anti__mono,axiom,
    ! [X76,X150,X72] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X150),X72))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(X72,X76)),pi_Pro666468413t_bool(X150,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_Pi__anti__mono) ).

fof(fact_716_Pi__anti__mono,axiom,
    ! [X76,X150,X72] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X150),X72))
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(X72,X76)),pi_fun150026276t_bool(X150,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_Pi__anti__mono) ).

fof(fact_717_Pi__anti__mono,axiom,
    ! [X76,X150,X72] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X150),X72))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(X72,X76)),pi_Arr990697634t_bool(X150,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_Pi__anti__mono) ).

fof(fact_343_le__funD,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X75),X81))
     => hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X75,X4)),hAPP_A1664620203t_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_le__funD) ).

fof(fact_245_le__funE,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X75),X81))
     => hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X75,X4)),hAPP_A1664620203t_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_le__funE) ).

fof(fact_340_le__funD,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X75,X4)),hAPP_P606313927t_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_le__funD) ).

fof(fact_242_le__funE,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X75,X4)),hAPP_P606313927t_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_le__funE) ).

fof(fact_337_le__funD,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X75,X4)),hAPP_f592646513l_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_le__funD) ).

fof(fact_239_le__funE,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X75,X4)),hAPP_f592646513l_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_le__funE) ).

fof(fact_338_le__funD,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X75,X4)),hAPP_f312250286l_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_le__funD) ).

fof(fact_240_le__funE,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X75,X4)),hAPP_f312250286l_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_le__funE) ).

fof(fact_339_le__funD,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X75,X4)),hAPP_f965095724l_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_le__funD) ).

fof(fact_241_le__funE,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X75,X4)),hAPP_f965095724l_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_le__funE) ).

fof(fact_342_le__funD,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X75,X4)),hAPP_P1676879539t_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_le__funD) ).

fof(fact_244_le__funE,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X75,X4)),hAPP_P1676879539t_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_le__funE) ).

fof(fact_344_le__funD,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X4)),hAPP_nat_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_le__funD) ).

fof(fact_246_le__funE,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X75,X4)),hAPP_nat_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_le__funE) ).

fof(fact_341_le__funD,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X75,X4)),hAPP_A1785763630i_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_le__funD) ).

fof(fact_243_le__funE,axiom,
    ! [X4,X75,X81] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X75),X81))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X75,X4)),hAPP_A1785763630i_bool(X81,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_le__funE) ).

fof(fact_1086_Suc__leD,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X195)),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_Suc__leD) ).

fof(fact_1108_Suc__le__lessD,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X195)),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_Suc__le__lessD) ).

fof(fact_1104_Suc__le__eq,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X200)),X27))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1104_Suc__le__eq) ).

fof(fact_1102_less__eq__Suc__le,axiom,
    ! [X27,X200] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),X200))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X27)),X200)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_less__eq__Suc__le) ).

fof(fact_1073_Suc__lessD,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X195)),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_Suc__lessD) ).

fof(fact_1025_termination__basic__simps_I3_J,axiom,
    ! [X205,X201,X202] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X201),X202))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X201),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X202),X205))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_termination__basic__simps_I3_J) ).

fof(fact_1017_trans__le__add1,axiom,
    ! [X195,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X208))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X208),X195))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_trans__le__add1) ).

fof(fact_1026_termination__basic__simps_I4_J,axiom,
    ! [X202,X201,X205] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X201),X205))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X201),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X202),X205))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_termination__basic__simps_I4_J) ).

fof(fact_1018_trans__le__add2,axiom,
    ! [X195,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X208))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X208))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_trans__le__add2) ).

fof(fact_1029_termination__basic__simps_I1_J,axiom,
    ! [X205,X201,X202] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X201),X202))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X201),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X202),X205))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1029_termination__basic__simps_I1_J) ).

fof(fact_1002_trans__less__add1,axiom,
    ! [X195,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X208))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X208),X195))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_trans__less__add1) ).

fof(fact_1028_termination__basic__simps_I2_J,axiom,
    ! [X202,X201,X205] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X201),X205))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X201),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X202),X205))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_termination__basic__simps_I2_J) ).

fof(fact_1003_trans__less__add2,axiom,
    ! [X195,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X208))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X208))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_trans__less__add2) ).

fof(fact_1032_finite__Collect__le__nat,axiom,
    ! [X206] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),X206)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1032_finite__Collect__le__nat) ).

fof(fact_1033_finite__Collect__less__nat,axiom,
    ! [X206] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X206)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1033_finite__Collect__less__nat) ).

fof(fact_1060_Suc__mono,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X195)),hAPP_nat_nat(suc,X197))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_Suc__mono) ).

fof(fact_964_set__rev__mp,axiom,
    ! [X76,X4,X72] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_set__rev__mp) ).

fof(fact_970_in__mono,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_in__mono) ).

fof(fact_959_set__mp,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_set__mp) ).

fof(fact_915_subsetD,axiom,
    ! [X15,X72,X76] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X15),X72))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X15),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_subsetD) ).

fof(fact_270_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X7))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_order__trans) ).

fof(fact_250_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X4))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7),X5))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_xt1_I6_J) ).

fof(fact_946_psubset__subset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X72),X76))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X76),X198))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_psubset__subset__trans) ).

fof(fact_477_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X5))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X7))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_order__less__le__trans) ).

fof(fact_951_subset__psubset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X76),X198))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_subset__psubset__trans) ).

fof(fact_497_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5),X7))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_order__le__less__trans) ).

fof(fact_487_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5),X4))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7),X5))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_xt1_I7_J) ).

fof(fact_507_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X4))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7),X5))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_xt1_I8_J) ).

fof(fact_267_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X7))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_order__trans) ).

fof(fact_247_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X4))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7),X5))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_xt1_I6_J) ).

fof(fact_943_psubset__subset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X72),X76))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X76),X198))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_psubset__subset__trans) ).

fof(fact_474_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X5))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X7))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_order__less__le__trans) ).

fof(fact_948_subset__psubset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X76),X198))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_subset__psubset__trans) ).

fof(fact_494_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5),X7))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_order__le__less__trans) ).

fof(fact_484_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5),X4))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7),X5))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_xt1_I7_J) ).

fof(fact_504_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X4))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7),X5))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_xt1_I8_J) ).

fof(fact_961_set__rev__mp,axiom,
    ! [X76,X4,X72] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_set__rev__mp) ).

fof(fact_967_in__mono,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_in__mono) ).

fof(fact_956_set__mp,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_set__mp) ).

fof(fact_918_subsetD,axiom,
    ! [X15,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X15),X72))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X15),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_subsetD) ).

fof(fact_268_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X7))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_order__trans) ).

fof(fact_248_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X4))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7),X5))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_xt1_I6_J) ).

fof(fact_944_psubset__subset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X72),X76))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X76),X198))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_psubset__subset__trans) ).

fof(fact_475_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X5))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X7))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_order__less__le__trans) ).

fof(fact_949_subset__psubset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X76),X198))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_subset__psubset__trans) ).

fof(fact_495_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5),X7))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_order__le__less__trans) ).

fof(fact_485_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5),X4))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7),X5))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_xt1_I7_J) ).

fof(fact_505_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X4))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7),X5))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_xt1_I8_J) ).

fof(fact_962_set__rev__mp,axiom,
    ! [X76,X4,X72] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_set__rev__mp) ).

fof(fact_968_in__mono,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_in__mono) ).

fof(fact_957_set__mp,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_set__mp) ).

fof(fact_917_subsetD,axiom,
    ! [X15,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X15),X72))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X15),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_subsetD) ).

fof(fact_269_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X7))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_order__trans) ).

fof(fact_249_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X4))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7),X5))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_xt1_I6_J) ).

fof(fact_945_psubset__subset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X72),X76))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X76),X198))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_psubset__subset__trans) ).

fof(fact_476_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X5))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X7))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_order__less__le__trans) ).

fof(fact_950_subset__psubset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X76),X198))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_subset__psubset__trans) ).

fof(fact_496_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5),X7))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_order__le__less__trans) ).

fof(fact_486_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5),X4))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7),X5))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_xt1_I7_J) ).

fof(fact_506_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X4))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7),X5))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_xt1_I8_J) ).

fof(fact_963_set__rev__mp,axiom,
    ! [X76,X4,X72] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_set__rev__mp) ).

fof(fact_969_in__mono,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_in__mono) ).

fof(fact_958_set__mp,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_set__mp) ).

fof(fact_916_subsetD,axiom,
    ! [X15,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X15),X72))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X15),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_subsetD) ).

fof(fact_273_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X7))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_order__trans) ).

fof(fact_253_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X4))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7),X5))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_xt1_I6_J) ).

fof(fact_941_psubset__subset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X72),X76))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X76),X198))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_941_psubset__subset__trans) ).

fof(fact_472_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X7))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_order__less__le__trans) ).

fof(fact_492_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X7))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_order__le__less__trans) ).

fof(fact_102_order__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X7))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_order__less__trans) ).

fof(fact_482_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7),X5))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_xt1_I7_J) ).

fof(fact_502_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X4))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7),X5))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_xt1_I8_J) ).

fof(fact_98_xt1_I10_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7),X5))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_xt1_I10_J) ).

fof(fact_914_subsetD,axiom,
    ! [X15,X72,X76] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X72),X76))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X15),X72))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X15),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_914_subsetD) ).

fof(fact_954_subset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X76),X198))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_subset__trans) ).

fof(fact_276_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X7))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_order__trans) ).

fof(fact_256_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X4))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),X5))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_xt1_I6_J) ).

fof(fact_947_psubset__subset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X72),X76))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X76),X198))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_psubset__subset__trans) ).

fof(fact_480_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X7))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_order__less__le__trans) ).

fof(fact_952_subset__psubset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X76),X198))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_subset__psubset__trans) ).

fof(fact_500_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X7))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_order__le__less__trans) ).

fof(fact_101_order__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X7))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_order__less__trans) ).

fof(fact_490_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),X5))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_xt1_I7_J) ).

fof(fact_510_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X4))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7),X5))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_xt1_I8_J) ).

fof(fact_97_xt1_I10_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7),X5))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_xt1_I10_J) ).

fof(fact_960_set__rev__mp,axiom,
    ! [X76,X4,X72] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_set__rev__mp) ).

fof(fact_966_in__mono,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_in__mono) ).

fof(fact_955_set__mp,axiom,
    ! [X4,X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_set__mp) ).

fof(fact_919_subsetD,axiom,
    ! [X15,X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X15),X72))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X15),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_subsetD) ).

fof(fact_913_subsetD,axiom,
    ! [X15,X72,X76] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,X72),X76))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X15),X72))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X15),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_subsetD) ).

fof(fact_272_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X7))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_order__trans) ).

fof(fact_252_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X4))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7),X5))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_xt1_I6_J) ).

fof(fact_942_psubset__subset__trans,axiom,
    ! [X198,X72,X76] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X72),X76))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X76),X198))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X72),X198)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_psubset__subset__trans) ).

fof(fact_473_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X7))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_order__less__le__trans) ).

fof(fact_493_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X7))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_order__le__less__trans) ).

fof(fact_103_order__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X7))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order__less__trans) ).

fof(fact_483_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7),X5))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_xt1_I7_J) ).

fof(fact_503_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X4))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7),X5))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_xt1_I8_J) ).

fof(fact_99_xt1_I10_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7),X5))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_xt1_I10_J) ).

fof(fact_912_subsetD,axiom,
    ! [X15,X72,X76] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X72),X76))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X15),X72))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X15),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_912_subsetD) ).

fof(fact_499_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5),X7))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_order__le__less__trans) ).

fof(fact_479_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X5))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X7))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_order__less__le__trans) ).

fof(fact_509_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X4))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X7),X5))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_xt1_I8_J) ).

fof(fact_489_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5),X4))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7),X5))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_xt1_I7_J) ).

fof(fact_274_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X7))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_order__trans) ).

fof(fact_254_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X4))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7),X5))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_xt1_I6_J) ).

fof(fact_996_le__trans,axiom,
    ! [X196,X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X208))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X208),X196))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X207),X196)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_le__trans) ).

fof(fact_275_order__trans,axiom,
    ! [X87,X88,X89] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X88),X89))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X89),X87))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X88),X87)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_order__trans) ).

fof(fact_255_xt1_I6_J,axiom,
    ! [X82,X83,X84] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X83),X84))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),X83))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),X84)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_xt1_I6_J) ).

fof(fact_481_order__less__le__trans,axiom,
    ! [X128,X129,X130] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X129),X130))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X130),X128))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X129),X128)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_order__less__le__trans) ).

fof(fact_501_order__le__less__trans,axiom,
    ! [X134,X135,X136] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X135),X136))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X136),X134))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X135),X134)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_order__le__less__trans) ).

fof(fact_104_order__less__trans,axiom,
    ! [X38,X39,X40] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X39),X40))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X40),X38))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X39),X38)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_order__less__trans) ).

fof(fact_491_xt1_I7_J,axiom,
    ! [X131,X132,X133] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X132),X133))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X131),X132))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X131),X133)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_xt1_I7_J) ).

fof(fact_511_xt1_I8_J,axiom,
    ! [X137,X138,X139] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X138),X139))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X137),X138))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X137),X139)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_xt1_I8_J) ).

fof(fact_100_xt1_I10_J,axiom,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X36),X37))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X35),X36))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X35),X37)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_xt1_I10_J) ).

fof(fact_271_order__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X7))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_order__trans) ).

fof(fact_251_xt1_I6_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X4))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7),X5))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_xt1_I6_J) ).

fof(fact_478_order__less__le__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X5))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X7))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_order__less__le__trans) ).

fof(fact_498_order__le__less__trans,axiom,
    ! [X7,X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5),X7))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_order__le__less__trans) ).

fof(fact_488_xt1_I7_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5),X4))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7),X5))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_xt1_I7_J) ).

fof(fact_508_xt1_I8_J,axiom,
    ! [X7,X5,X4] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X4))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X7),X5))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X7),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_xt1_I8_J) ).

fof(fact_1149_add__mult__distrib,axiom,
    ! [X195,X197,X196] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X197)),X196) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X195),X196)),hAPP_nat_nat(times_times_nat(X197),X196)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_add__mult__distrib) ).

fof(fact_1107_le__less__Suc__eq,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),hAPP_nat_nat(suc,X200)))
      <=> X27 = X200 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1107_le__less__Suc__eq) ).

fof(fact_1006_less__add__eq__less,axiom,
    ! [X195,X197,X196,X210] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X196),X210))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X210) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X196),X197)
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_less__add__eq__less) ).

fof(fact_1038_finite__nat__set__iff__bounded__le,axiom,
    ! [X209] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X209))
    <=> ? [X30] :
        ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),X209))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1038_finite__nat__set__iff__bounded__le) ).

fof(fact_1039_finite__nat__set__iff__bounded,axiom,
    ! [X209] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X209))
    <=> ? [X30] :
        ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),X209))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1039_finite__nat__set__iff__bounded) ).

fof(fact_1041_bounded__nat__set__is__finite,axiom,
    ! [X27,X209] :
      ( ! [X24] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X24),X209))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X27)) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X209)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1041_bounded__nat__set__is__finite) ).

fof(fact_1141_le__cube,axiom,
    ! [X195] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),hAPP_nat_nat(times_times_nat(X195),hAPP_nat_nat(times_times_nat(X195),X195)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_le__cube) ).

fof(fact_998_inj__on__add__nat,axiom,
    ! [X206,X209] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X206)),X209)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_998_inj__on__add__nat) ).

fof(fact_1120_Suc__le__D,axiom,
    ! [X197,X221] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X197)),X221))
     => ? [X30] : X221 = hAPP_nat_nat(suc,X30) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_Suc__le__D) ).

fof(fact_1076_Suc__lessI,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
     => ( hAPP_nat_nat(suc,X195) != X197
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X195)),X197)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1076_Suc__lessI) ).

fof(fact_990_nat__add__assoc,axiom,
    ! [X195,X197,X196] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X197)),X196) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X197),X196)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_nat__add__assoc) ).

fof(fact_733_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X160,X161,X162] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X160),X161)),X162) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X160),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X161),X162)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_1106_Suc__leI,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X195)),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1106_Suc__leI) ).

fof(fact_1090_le__Suc__eq,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),hAPP_nat_nat(suc,X27)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27))
        | X200 = hAPP_nat_nat(suc,X27) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1090_le__Suc__eq) ).

fof(fact_91_const__Lin__Prof,axiom,
    ! [X6] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X6)),arrow_1721807329e_Prof)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_const__Lin__Prof) ).

fof(fact_1081_less__Suc__eq,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),hAPP_nat_nat(suc,X27)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27))
        | X200 = X27 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1081_less__Suc__eq) ).

fof(fact_1103_less__Suc__eq__le,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),hAPP_nat_nat(suc,X27)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_less__Suc__eq__le) ).

fof(fact_73_dictator__def,axiom,
    ! [X23,X26] :
      ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X23),X26))
    <=> ! [X24] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X24),arrow_1721807329e_Prof))
         => hAPP_f412050202t_bool(X23,X24) = hAPP_A1677245848t_bool(X24,X26) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_dictator__def) ).

fof(fact_1121_lessE,axiom,
    ! [X207,X196] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X196))
     => ( X196 != hAPP_nat_nat(suc,X207)
       => ~ ! [X213] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X213))
             => X196 != hAPP_nat_nat(suc,X213) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_lessE) ).

fof(fact_616_inv__into__f__f,axiom,
    ! [X4,X75,X72] :
      ( is_Arr43961803e_indi(X4)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),X72))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
         => hAPP_n1951273283e_indi(hilber693666498di_nat(X72,X75),hAPP_A1637648121di_nat(X75,X4)) = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_inv__into__f__f) ).

fof(fact_618_inv__into__f__eq,axiom,
    ! [X5,X4,X75,X72] :
      ( is_Arr43961803e_indi(X4)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),X72))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
         => ( hAPP_A1637648121di_nat(X75,X4) = X5
           => hAPP_n1951273283e_indi(hilber693666498di_nat(X72,X75),X5) = X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_inv__into__f__eq) ).

fof(fact_1116_less__imp__Suc__add,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
     => ? [X211] : X197 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X211)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1116_less__imp__Suc__add) ).

fof(fact_1101_less__iff__Suc__add,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27))
    <=> ? [X211] : X27 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X200),X211)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_less__iff__Suc__add) ).

fof(fact_910_equalityI,axiom,
    ! [X72,X76] :
      ( ( is_fun1568535512t_bool(X72)
        & is_fun1568535512t_bool(X76) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X72),X76))
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X76),X72))
         => X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_equalityI) ).

fof(fact_361_order__eq__iff,axiom,
    ! [X4,X5] :
      ( ( is_fun1568535512t_bool(X4)
        & is_fun1568535512t_bool(X5) )
     => ( X4 = X5
      <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_order__eq__iff) ).

fof(fact_333_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( ( is_fun1568535512t_bool(X5)
        & is_fun1568535512t_bool(X4) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X4))
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
        <=> X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_order__antisym__conv) ).

fof(fact_283_order__antisym,axiom,
    ! [X4,X5] :
      ( ( is_fun1568535512t_bool(X4)
        & is_fun1568535512t_bool(X5) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X4))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_order__antisym) ).

fof(fact_263_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( ( is_fun1568535512t_bool(X5)
        & is_fun1568535512t_bool(X4) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X4))
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_xt1_I5_J) ).

fof(fact_362_order__eq__iff,axiom,
    ! [X4,X5] :
      ( ( is_fun2093718614t_bool(X4)
        & is_fun2093718614t_bool(X5) )
     => ( X4 = X5
      <=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_order__eq__iff) ).

fof(fact_334_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( ( is_fun2093718614t_bool(X5)
        & is_fun2093718614t_bool(X4) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X4))
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
        <=> X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_order__antisym__conv) ).

fof(fact_284_order__antisym,axiom,
    ! [X4,X5] :
      ( ( is_fun2093718614t_bool(X4)
        & is_fun2093718614t_bool(X5) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X4))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_order__antisym) ).

fof(fact_264_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( ( is_fun2093718614t_bool(X5)
        & is_fun2093718614t_bool(X4) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X4))
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_xt1_I5_J) ).

fof(fact_909_equalityI,axiom,
    ! [X72,X76] :
      ( ( is_fun1236654035i_bool(X72)
        & is_fun1236654035i_bool(X76) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X72),X76))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X76),X72))
         => X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_equalityI) ).

fof(fact_360_order__eq__iff,axiom,
    ! [X4,X5] :
      ( ( is_fun1236654035i_bool(X4)
        & is_fun1236654035i_bool(X5) )
     => ( X4 = X5
      <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_order__eq__iff) ).

fof(fact_332_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( ( is_fun1236654035i_bool(X5)
        & is_fun1236654035i_bool(X4) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X4))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
        <=> X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_order__antisym__conv) ).

fof(fact_282_order__antisym,axiom,
    ! [X4,X5] :
      ( ( is_fun1236654035i_bool(X4)
        & is_fun1236654035i_bool(X5) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X4))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_order__antisym) ).

fof(fact_262_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( ( is_fun1236654035i_bool(X5)
        & is_fun1236654035i_bool(X4) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X4))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_xt1_I5_J) ).

fof(fact_908_equalityI,axiom,
    ! [X72,X76] :
      ( ( is_fun961089132t_bool(X72)
        & is_fun961089132t_bool(X76) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X76),X72))
         => X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_equalityI) ).

fof(fact_358_order__eq__iff,axiom,
    ! [X4,X5] :
      ( ( is_fun961089132t_bool(X4)
        & is_fun961089132t_bool(X5) )
     => ( X4 = X5
      <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_order__eq__iff) ).

fof(fact_330_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( ( is_fun961089132t_bool(X5)
        & is_fun961089132t_bool(X4) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X4))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
        <=> X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_order__antisym__conv) ).

fof(fact_280_order__antisym,axiom,
    ! [X4,X5] :
      ( ( is_fun961089132t_bool(X4)
        & is_fun961089132t_bool(X5) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X4))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_order__antisym) ).

fof(fact_260_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( ( is_fun961089132t_bool(X5)
        & is_fun961089132t_bool(X4) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X4))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_xt1_I5_J) ).

fof(fact_907_equalityI,axiom,
    ! [X72,X76] :
      ( ( is_fun288122577l_bool(X72)
        & is_fun288122577l_bool(X76) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X76),X72))
         => X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_equalityI) ).

fof(fact_357_order__eq__iff,axiom,
    ! [X4,X5] :
      ( ( is_fun288122577l_bool(X4)
        & is_fun288122577l_bool(X5) )
     => ( X4 = X5
      <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_order__eq__iff) ).

fof(fact_329_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( ( is_fun288122577l_bool(X5)
        & is_fun288122577l_bool(X4) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X4))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
        <=> X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_order__antisym__conv) ).

fof(fact_279_order__antisym,axiom,
    ! [X4,X5] :
      ( ( is_fun288122577l_bool(X4)
        & is_fun288122577l_bool(X5) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X4))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_order__antisym) ).

fof(fact_259_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( ( is_fun288122577l_bool(X5)
        & is_fun288122577l_bool(X4) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X4))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_xt1_I5_J) ).

fof(fact_905_equalityI,axiom,
    ! [X72,X76] :
      ( ( is_fun279392540l_bool(X72)
        & is_fun279392540l_bool(X76) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X76),X72))
         => X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_equalityI) ).

fof(fact_355_order__eq__iff,axiom,
    ! [X4,X5] :
      ( ( is_fun279392540l_bool(X4)
        & is_fun279392540l_bool(X5) )
     => ( X4 = X5
      <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_order__eq__iff) ).

fof(fact_327_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( ( is_fun279392540l_bool(X5)
        & is_fun279392540l_bool(X4) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X4))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
        <=> X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_order__antisym__conv) ).

fof(fact_277_order__antisym,axiom,
    ! [X4,X5] :
      ( ( is_fun279392540l_bool(X4)
        & is_fun279392540l_bool(X5) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X4))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_order__antisym) ).

fof(fact_257_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( ( is_fun279392540l_bool(X5)
        & is_fun279392540l_bool(X4) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X4))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_xt1_I5_J) ).

fof(fact_906_equalityI,axiom,
    ! [X72,X76] :
      ( ( is_fun158382675l_bool(X72)
        & is_fun158382675l_bool(X76) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X76),X72))
         => X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_equalityI) ).

fof(fact_356_order__eq__iff,axiom,
    ! [X4,X5] :
      ( ( is_fun158382675l_bool(X4)
        & is_fun158382675l_bool(X5) )
     => ( X4 = X5
      <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_order__eq__iff) ).

fof(fact_328_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( ( is_fun158382675l_bool(X5)
        & is_fun158382675l_bool(X4) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X4))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
        <=> X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_order__antisym__conv) ).

fof(fact_278_order__antisym,axiom,
    ! [X4,X5] :
      ( ( is_fun158382675l_bool(X4)
        & is_fun158382675l_bool(X5) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X4))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_order__antisym) ).

fof(fact_258_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( ( is_fun158382675l_bool(X5)
        & is_fun158382675l_bool(X4) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X4))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_xt1_I5_J) ).

fof(fact_617_inv__into__f__f,axiom,
    ! [X4,X75,X72] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),X72))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => hAPP_nat_nat(hilber195283148at_nat(X72,X75),hAPP_nat_nat(X75,X4)) = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_inv__into__f__f) ).

fof(fact_619_inv__into__f__eq,axiom,
    ! [X5,X4,X75,X72] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),X72))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
       => ( hAPP_nat_nat(X75,X4) = X5
         => hAPP_nat_nat(hilber195283148at_nat(X72,X75),X5) = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_inv__into__f__eq) ).

fof(fact_359_order__eq__iff,axiom,
    ! [X5,X4] :
      ( ( hBOOL(X4)
      <=> hBOOL(X5) )
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_order__eq__iff) ).

fof(fact_331_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X4))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
      <=> ( hBOOL(X4)
        <=> hBOOL(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_order__antisym__conv) ).

fof(fact_281_order__antisym,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X4))
       => ( hBOOL(X4)
        <=> hBOOL(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_order__antisym) ).

fof(fact_261_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X4))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
       => ( hBOOL(X4)
        <=> hBOOL(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_xt1_I5_J) ).

fof(fact_651_inj__imp__inv__eq,axiom,
    ! [X81,X75] :
      ( is_fun1217980910e_indi(X81)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),top_to1576102282i_bool))
       => ( ! [X24] : hAPP_A1637648121di_nat(X75,hAPP_n1951273283e_indi(X81,X24)) = X24
         => hilber693666498di_nat(top_to1576102282i_bool,X75) = X81 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_inj__imp__inv__eq) ).

fof(fact_130_order__less__imp__triv,axiom,
    ! [X9,X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4))
       => hBOOL(X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_order__less__imp__triv) ).

fof(fact_129_order__less__imp__triv,axiom,
    ! [X9,X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4))
       => hBOOL(X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_order__less__imp__triv) ).

fof(fact_131_order__less__imp__triv,axiom,
    ! [X9,X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4))
       => hBOOL(X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_order__less__imp__triv) ).

fof(fact_132_order__less__imp__triv,axiom,
    ! [X9,X4,X5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X4))
       => hBOOL(X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_order__less__imp__triv) ).

fof(fact_1150_add__mult__distrib2,axiom,
    ! [X196,X195,X197] : hAPP_nat_nat(times_times_nat(X196),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X197)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X196),X195)),hAPP_nat_nat(times_times_nat(X196),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1150_add__mult__distrib2) ).

fof(fact_652_inj__imp__inv__eq,axiom,
    ! [X81,X75] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),top_top_fun_nat_bool))
     => ( ! [X24] : hAPP_nat_nat(X75,hAPP_nat_nat(X81,X24)) = X24
       => hilber195283148at_nat(top_top_fun_nat_bool,X75) = X81 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_inj__imp__inv__eq) ).

fof(fact_974_set__eq__subset,axiom,
    ! [X72,X76] :
      ( X72 = X76
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X76),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_set__eq__subset) ).

fof(fact_911_equalityI,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X76),X72))
       => X72 = X76 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_911_equalityI) ).

fof(fact_364_order__eq__iff,axiom,
    ! [X4,X5] :
      ( X4 = X5
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_order__eq__iff) ).

fof(fact_336_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X4))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
      <=> X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_order__antisym__conv) ).

fof(fact_286_order__antisym,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X4))
       => X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_order__antisym) ).

fof(fact_266_xt1_I5_J,axiom,
    ! [X5,X4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X4))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
       => X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_xt1_I5_J) ).

fof(fact_997_le__antisym,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X197),X195))
       => X195 = X197 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_le__antisym) ).

fof(fact_363_order__eq__iff,axiom,
    ! [X4,X5] :
      ( X4 = X5
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_order__eq__iff) ).

fof(fact_335_order__antisym__conv,axiom,
    ! [X5,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
      <=> X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_order__antisym__conv) ).

fof(fact_285_order__antisym,axiom,
    ! [X90,X91] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X90),X91))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X91),X90))
       => X90 = X91 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_order__antisym) ).

fof(fact_265_xt1_I5_J,axiom,
    ! [X85,X86] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X85),X86))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X86),X85))
       => X86 = X85 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_xt1_I5_J) ).

fof(fact_1058_less__imp__add__positive,axiom,
    ! [X207,X208] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X207),X208))
     => ? [X211] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X211))
          & hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X211) = X208 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_less__imp__add__positive) ).

fof(fact_1088_le__SucI,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),hAPP_nat_nat(suc,X197))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_le__SucI) ).

fof(fact_1105_le__imp__less__Suc,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),hAPP_nat_nat(suc,X197))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_le__imp__less__Suc) ).

fof(fact_1077_less__SucI,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),hAPP_nat_nat(suc,X197))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_less__SucI) ).

fof(fact_987_nat__less__cases,axiom,
    ! [X9,X200,X27] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X9,X27),X200)) )
     => ( ( X200 = X27
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X9,X27),X200)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),X200))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X9,X27),X200)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X9,X27),X200)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_nat__less__cases) ).

fof(fact_727_subset__inj__on,axiom,
    ! [X72,X75,X76] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),X76))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
       => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_subset__inj__on) ).

fof(fact_726_subset__inj__on,axiom,
    ! [X72,X75,X76] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),X76))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X72),X76))
       => hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_subset__inj__on) ).

fof(fact_1014_le__add1,axiom,
    ! [X197,X195] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X197),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X197),X195))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_le__add1) ).

fof(fact_1013_le__add2,axiom,
    ! [X197,X195] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X197),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X197))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_le__add2) ).

fof(fact_989_nat__add__left__commute,axiom,
    ! [X201,X202,X205] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X201),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X202),X205)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X202),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X201),X205)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_nat__add__left__commute) ).

fof(fact_653_less__add__one,axiom,
    ! [X140] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X140),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X140),one_one_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_less__add__one) ).

fof(fact_932_subset__iff__psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun961089132t_bool(X72)
        & is_fun961089132t_bool(X76) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76))
      <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X72),X76))
          | X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_subset__iff__psubset__eq) ).

fof(fact_925_psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun961089132t_bool(X72)
        & is_fun961089132t_bool(X76) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X72),X76))
      <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76))
          & X72 != X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_925_psubset__eq) ).

fof(fact_467_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( ( is_fun961089132t_bool(X13)
        & is_fun961089132t_bool(X12) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X13),X12))
       => ( X12 != X13
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_xt1_I11_J) ).

fof(fact_457_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun961089132t_bool(X12)
        & is_fun961089132t_bool(X13) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X12),X13))
       => ( X12 != X13
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_order__le__neq__trans) ).

fof(fact_447_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( ( is_fun961089132t_bool(X4)
        & is_fun961089132t_bool(X5) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_order__le__imp__less__or__eq) ).

fof(fact_415_order__neq__le__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun961089132t_bool(X12)
        & is_fun961089132t_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X12),X13))
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_order__neq__le__trans) ).

fof(fact_402_order__le__less,axiom,
    ! [X4,X5] :
      ( ( is_fun961089132t_bool(X4)
        & is_fun961089132t_bool(X5) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
      <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_order__le__less) ).

fof(fact_382_order__less__le,axiom,
    ! [X4,X5] :
      ( ( is_fun961089132t_bool(X4)
        & is_fun961089132t_bool(X5) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X5))
      <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
          & X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_order__less__le) ).

fof(fact_425_xt1_I12_J,axiom,
    ! [X12,X13] :
      ( ( is_fun961089132t_bool(X12)
        & is_fun961089132t_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X13),X12))
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_xt1_I12_J) ).

fof(fact_929_subset__iff__psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun279392540l_bool(X72)
        & is_fun279392540l_bool(X76) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76))
      <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X72),X76))
          | X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_subset__iff__psubset__eq) ).

fof(fact_922_psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun279392540l_bool(X72)
        & is_fun279392540l_bool(X76) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X72),X76))
      <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76))
          & X72 != X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_922_psubset__eq) ).

fof(fact_464_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( ( is_fun279392540l_bool(X13)
        & is_fun279392540l_bool(X12) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X13),X12))
       => ( X12 != X13
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_xt1_I11_J) ).

fof(fact_454_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun279392540l_bool(X12)
        & is_fun279392540l_bool(X13) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X12),X13))
       => ( X12 != X13
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_order__le__neq__trans) ).

fof(fact_444_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( ( is_fun279392540l_bool(X4)
        & is_fun279392540l_bool(X5) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_order__le__imp__less__or__eq) ).

fof(fact_412_order__neq__le__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun279392540l_bool(X12)
        & is_fun279392540l_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X12),X13))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_order__neq__le__trans) ).

fof(fact_399_order__le__less,axiom,
    ! [X4,X5] :
      ( ( is_fun279392540l_bool(X4)
        & is_fun279392540l_bool(X5) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
      <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_order__le__less) ).

fof(fact_379_order__less__le,axiom,
    ! [X4,X5] :
      ( ( is_fun279392540l_bool(X4)
        & is_fun279392540l_bool(X5) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X5))
      <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
          & X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_order__less__le) ).

fof(fact_422_xt1_I12_J,axiom,
    ! [X12,X13] :
      ( ( is_fun279392540l_bool(X12)
        & is_fun279392540l_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X13),X12))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_xt1_I12_J) ).

fof(fact_930_subset__iff__psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun158382675l_bool(X72)
        & is_fun158382675l_bool(X76) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76))
      <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X72),X76))
          | X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_subset__iff__psubset__eq) ).

fof(fact_923_psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun158382675l_bool(X72)
        & is_fun158382675l_bool(X76) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X72),X76))
      <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76))
          & X72 != X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_psubset__eq) ).

fof(fact_465_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( ( is_fun158382675l_bool(X13)
        & is_fun158382675l_bool(X12) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X13),X12))
       => ( X12 != X13
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_xt1_I11_J) ).

fof(fact_455_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun158382675l_bool(X12)
        & is_fun158382675l_bool(X13) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X12),X13))
       => ( X12 != X13
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_order__le__neq__trans) ).

fof(fact_445_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( ( is_fun158382675l_bool(X4)
        & is_fun158382675l_bool(X5) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_order__le__imp__less__or__eq) ).

fof(fact_413_order__neq__le__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun158382675l_bool(X12)
        & is_fun158382675l_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X12),X13))
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_order__neq__le__trans) ).

fof(fact_400_order__le__less,axiom,
    ! [X4,X5] :
      ( ( is_fun158382675l_bool(X4)
        & is_fun158382675l_bool(X5) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
      <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_order__le__less) ).

fof(fact_380_order__less__le,axiom,
    ! [X4,X5] :
      ( ( is_fun158382675l_bool(X4)
        & is_fun158382675l_bool(X5) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X5))
      <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
          & X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_order__less__le) ).

fof(fact_423_xt1_I12_J,axiom,
    ! [X12,X13] :
      ( ( is_fun158382675l_bool(X12)
        & is_fun158382675l_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X13),X12))
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_xt1_I12_J) ).

fof(fact_931_subset__iff__psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun288122577l_bool(X72)
        & is_fun288122577l_bool(X76) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76))
      <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X72),X76))
          | X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_subset__iff__psubset__eq) ).

fof(fact_924_psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun288122577l_bool(X72)
        & is_fun288122577l_bool(X76) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X72),X76))
      <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76))
          & X72 != X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_psubset__eq) ).

fof(fact_466_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( ( is_fun288122577l_bool(X13)
        & is_fun288122577l_bool(X12) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X13),X12))
       => ( X12 != X13
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_xt1_I11_J) ).

fof(fact_456_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun288122577l_bool(X12)
        & is_fun288122577l_bool(X13) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X12),X13))
       => ( X12 != X13
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_order__le__neq__trans) ).

fof(fact_446_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( ( is_fun288122577l_bool(X4)
        & is_fun288122577l_bool(X5) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_order__le__imp__less__or__eq) ).

fof(fact_414_order__neq__le__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun288122577l_bool(X12)
        & is_fun288122577l_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X12),X13))
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_order__neq__le__trans) ).

fof(fact_401_order__le__less,axiom,
    ! [X4,X5] :
      ( ( is_fun288122577l_bool(X4)
        & is_fun288122577l_bool(X5) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
      <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_order__le__less) ).

fof(fact_381_order__less__le,axiom,
    ! [X4,X5] :
      ( ( is_fun288122577l_bool(X4)
        & is_fun288122577l_bool(X5) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X5))
      <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
          & X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_order__less__le) ).

fof(fact_424_xt1_I12_J,axiom,
    ! [X12,X13] :
      ( ( is_fun288122577l_bool(X12)
        & is_fun288122577l_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X13),X12))
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_xt1_I12_J) ).

fof(fact_927_subset__iff__psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun1568535512t_bool(X72)
        & is_fun1568535512t_bool(X76) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X72),X76))
      <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X72),X76))
          | X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_subset__iff__psubset__eq) ).

fof(fact_920_psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun1568535512t_bool(X72)
        & is_fun1568535512t_bool(X76) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X72),X76))
      <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X72),X76))
          & X72 != X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_psubset__eq) ).

fof(fact_462_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( ( is_fun1568535512t_bool(X13)
        & is_fun1568535512t_bool(X12) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X13),X12))
       => ( X12 != X13
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_xt1_I11_J) ).

fof(fact_452_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun1568535512t_bool(X12)
        & is_fun1568535512t_bool(X13) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X12),X13))
       => ( X12 != X13
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_order__le__neq__trans) ).

fof(fact_442_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( ( is_fun1568535512t_bool(X4)
        & is_fun1568535512t_bool(X5) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_order__le__imp__less__or__eq) ).

fof(fact_410_order__neq__le__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun1568535512t_bool(X12)
        & is_fun1568535512t_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X12),X13))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_order__neq__le__trans) ).

fof(fact_397_order__le__less,axiom,
    ! [X4,X5] :
      ( ( is_fun1568535512t_bool(X4)
        & is_fun1568535512t_bool(X5) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
      <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_order__le__less) ).

fof(fact_377_order__less__le,axiom,
    ! [X4,X5] :
      ( ( is_fun1568535512t_bool(X4)
        & is_fun1568535512t_bool(X5) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
      <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
          & X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_order__less__le) ).

fof(fact_420_xt1_I12_J,axiom,
    ! [X12,X13] :
      ( ( is_fun1568535512t_bool(X12)
        & is_fun1568535512t_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X13),X12))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_xt1_I12_J) ).

fof(fact_928_subset__iff__psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun1236654035i_bool(X72)
        & is_fun1236654035i_bool(X76) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X72),X76))
      <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X72),X76))
          | X72 = X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_subset__iff__psubset__eq) ).

fof(fact_921_psubset__eq,axiom,
    ! [X72,X76] :
      ( ( is_fun1236654035i_bool(X72)
        & is_fun1236654035i_bool(X76) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X72),X76))
      <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X72),X76))
          & X72 != X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_psubset__eq) ).

fof(fact_463_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( ( is_fun1236654035i_bool(X13)
        & is_fun1236654035i_bool(X12) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X13),X12))
       => ( X12 != X13
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_xt1_I11_J) ).

fof(fact_453_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun1236654035i_bool(X12)
        & is_fun1236654035i_bool(X13) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X12),X13))
       => ( X12 != X13
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_order__le__neq__trans) ).

fof(fact_443_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( ( is_fun1236654035i_bool(X4)
        & is_fun1236654035i_bool(X5) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_order__le__imp__less__or__eq) ).

fof(fact_411_order__neq__le__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun1236654035i_bool(X12)
        & is_fun1236654035i_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X12),X13))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_order__neq__le__trans) ).

fof(fact_398_order__le__less,axiom,
    ! [X4,X5] :
      ( ( is_fun1236654035i_bool(X4)
        & is_fun1236654035i_bool(X5) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
      <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_order__le__less) ).

fof(fact_378_order__less__le,axiom,
    ! [X4,X5] :
      ( ( is_fun1236654035i_bool(X4)
        & is_fun1236654035i_bool(X5) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
      <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
          & X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_order__less__le) ).

fof(fact_421_xt1_I12_J,axiom,
    ! [X12,X13] :
      ( ( is_fun1236654035i_bool(X12)
        & is_fun1236654035i_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X13),X12))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_xt1_I12_J) ).

fof(fact_469_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( ( is_fun2093718614t_bool(X13)
        & is_fun2093718614t_bool(X12) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X13),X12))
       => ( X12 != X13
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_xt1_I11_J) ).

fof(fact_459_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun2093718614t_bool(X12)
        & is_fun2093718614t_bool(X13) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X12),X13))
       => ( X12 != X13
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_order__le__neq__trans) ).

fof(fact_449_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( ( is_fun2093718614t_bool(X4)
        & is_fun2093718614t_bool(X5) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_order__le__imp__less__or__eq) ).

fof(fact_417_order__neq__le__trans,axiom,
    ! [X12,X13] :
      ( ( is_fun2093718614t_bool(X12)
        & is_fun2093718614t_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X12),X13))
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X12),X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_order__neq__le__trans) ).

fof(fact_404_order__le__less,axiom,
    ! [X4,X5] :
      ( ( is_fun2093718614t_bool(X4)
        & is_fun2093718614t_bool(X5) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
      <=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X5))
          | X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_order__le__less) ).

fof(fact_384_order__less__le,axiom,
    ! [X4,X5] :
      ( ( is_fun2093718614t_bool(X4)
        & is_fun2093718614t_bool(X5) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X5))
      <=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
          & X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_order__less__le) ).

fof(fact_427_xt1_I12_J,axiom,
    ! [X12,X13] :
      ( ( is_fun2093718614t_bool(X12)
        & is_fun2093718614t_bool(X13) )
     => ( X12 != X13
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X13),X12))
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X13),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_xt1_I12_J) ).

fof(fact_321_ord__eq__le__trans,axiom,
    ! [X15,X13,X12] :
      ( ( hBOOL(X12)
      <=> hBOOL(X13) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X13),X15))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_ord__eq__le__trans) ).

fof(fact_291_xt1_I4_J,axiom,
    ! [X15,X13,X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X13),X12))
     => ( ( hBOOL(X13)
        <=> hBOOL(X15) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X15),X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_xt1_I4_J) ).

fof(fact_311_xt1_I3_J,axiom,
    ! [X15,X13,X12] :
      ( ( hBOOL(X12)
      <=> hBOOL(X13) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X15),X13))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X15),X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_xt1_I3_J) ).

fof(fact_301_ord__le__eq__trans,axiom,
    ! [X15,X12,X13] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),X13))
     => ( ( hBOOL(X13)
        <=> hBOOL(X15) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_ord__le__eq__trans) ).

fof(fact_1199_setsum__shift__lb__Suc0__0,axiom,
    ! [X206,X75] :
      ( hAPP_nat_nat(X75,zero_zero_nat) = zero_zero_nat
     => hAPP_f22106695ol_nat(big_co387207925at_nat(X75),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),X206)) = hAPP_f22106695ol_nat(big_co387207925at_nat(X75),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X206)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1199_setsum__shift__lb__Suc0__0) ).

fof(fact_1151_Suc__mult__cancel1,axiom,
    ! [X206,X200,X27] :
      ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X206)),X200) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X206)),X27)
    <=> X200 = X27 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_Suc__mult__cancel1) ).

fof(fact_468_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X13),X12))
     => ( ~ ( hBOOL(X12)
          <=> hBOOL(X13) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X13),X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_xt1_I11_J) ).

fof(fact_458_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),X13))
     => ( ~ ( hBOOL(X12)
          <=> hBOOL(X13) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X12),X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_order__le__neq__trans) ).

fof(fact_448_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X5))
        | ( hBOOL(X4)
        <=> hBOOL(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_order__le__imp__less__or__eq) ).

fof(fact_426_xt1_I12_J,axiom,
    ! [X13,X12] :
      ( ~ ( hBOOL(X12)
        <=> hBOOL(X13) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X13),X12))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X13),X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_xt1_I12_J) ).

fof(fact_416_order__neq__le__trans,axiom,
    ! [X13,X12] :
      ( ~ ( hBOOL(X12)
        <=> hBOOL(X13) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),X13))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X12),X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_order__neq__le__trans) ).

fof(fact_403_order__le__less,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X5))
        | ( hBOOL(X4)
        <=> hBOOL(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_order__le__less) ).

fof(fact_383_order__less__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X5))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
        & ~ ( hBOOL(X4)
          <=> hBOOL(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_order__less__le) ).

fof(fact_933_subset__iff__psubset__eq,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X72),X76))
        | X72 = X76 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_subset__iff__psubset__eq) ).

fof(fact_926_psubset__eq,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X72),X76))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
        & X72 != X76 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_psubset__eq) ).

fof(fact_470_xt1_I11_J,axiom,
    ! [X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
     => ( X12 != X13
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_xt1_I11_J) ).

fof(fact_460_order__le__neq__trans,axiom,
    ! [X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
     => ( X12 != X13
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_order__le__neq__trans) ).

fof(fact_450_order__le__imp__less__or__eq,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
        | X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_order__le__imp__less__or__eq) ).

fof(fact_418_order__neq__le__trans,axiom,
    ! [X12,X13] :
      ( X12 != X13
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X13))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_order__neq__le__trans) ).

fof(fact_405_order__le__less,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
        | X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_order__le__less) ).

fof(fact_385_order__less__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
        & X4 != X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_order__less__le) ).

fof(fact_428_xt1_I12_J,axiom,
    ! [X12,X13] :
      ( X12 != X13
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X12))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_xt1_I12_J) ).

fof(fact_1011_le__neq__implies__less,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
     => ( X195 != X197
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_le__neq__implies__less) ).

fof(fact_1009_le__eq__less__or__eq,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27))
        | X200 = X27 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_le__eq__less__or__eq) ).

fof(fact_1008_nat__less__le,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27))
        & X200 != X27 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_nat__less__le) ).

fof(fact_471_xt1_I11_J,axiom,
    ! [X126,X127] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X126),X127))
     => ( X127 != X126
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X127)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_xt1_I11_J) ).

fof(fact_461_order__le__neq__trans,axiom,
    ! [X124,X125] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X124),X125))
     => ( X124 != X125
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X124),X125)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_order__le__neq__trans) ).

fof(fact_451_order__le__imp__less__or__eq,axiom,
    ! [X122,X123] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X122),X123))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X122),X123))
        | X122 = X123 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_order__le__imp__less__or__eq) ).

fof(fact_419_order__neq__le__trans,axiom,
    ! [X114,X115] :
      ( X114 != X115
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X114),X115))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X114),X115)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_order__neq__le__trans) ).

fof(fact_406_order__le__less,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
        | X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_order__le__less) ).

fof(fact_386_order__less__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
        & X4 != X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_order__less__le) ).

fof(fact_429_xt1_I12_J,axiom,
    ! [X116,X117] :
      ( X116 != X117
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X117),X116))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X117),X116)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_xt1_I12_J) ).

fof(fact_965_predicate1D,axiom,
    ! [X4,X9,X199] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X199))
     => ( hBOOL(hAPP_nat_bool(X9,X4))
       => hBOOL(hAPP_nat_bool(X199,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_predicate1D) ).

fof(fact_973_rev__predicate1D,axiom,
    ! [X199,X9,X4] :
      ( hBOOL(hAPP_nat_bool(X9,X4))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X199))
       => hBOOL(hAPP_nat_bool(X199,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_rev__predicate1D) ).

fof(fact_939_psubset__imp__subset,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X72),X76))
     => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_939_psubset__imp__subset) ).

fof(fact_436_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X5))
     => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_order__less__imp__le) ).

fof(fact_936_psubset__imp__subset,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X72),X76))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_psubset__imp__subset) ).

fof(fact_433_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X5))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_order__less__imp__le) ).

fof(fact_937_psubset__imp__subset,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X72),X76))
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_psubset__imp__subset) ).

fof(fact_434_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X5))
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_order__less__imp__le) ).

fof(fact_938_psubset__imp__subset,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X72),X76))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_psubset__imp__subset) ).

fof(fact_435_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X5))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_order__less__imp__le) ).

fof(fact_934_psubset__imp__subset,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X72),X76))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X72),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_psubset__imp__subset) ).

fof(fact_431_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_order__less__imp__le) ).

fof(fact_940_psubset__imp__subset,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X72),X76))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_psubset__imp__subset) ).

fof(fact_439_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_order__less__imp__le) ).

fof(fact_935_psubset__imp__subset,axiom,
    ! [X72,X76] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X72),X76))
     => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X72),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_psubset__imp__subset) ).

fof(fact_432_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_order__less__imp__le) ).

fof(fact_438_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X5))
     => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_order__less__imp__le) ).

fof(fact_1027_termination__basic__simps_I5_J,axiom,
    ! [X201,X202] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X201),X202))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X201),X202)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_termination__basic__simps_I5_J) ).

fof(fact_1012_less__or__eq__imp__le,axiom,
    ! [X195,X197] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
        | X195 = X197 )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_less__or__eq__imp__le) ).

fof(fact_1010_less__imp__le__nat,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_less__imp__le__nat) ).

fof(fact_440_order__less__imp__le,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X120),X121))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X120),X121)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_order__less__imp__le) ).

fof(fact_437_order__less__imp__le,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X5))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_order__less__imp__le) ).

fof(fact_1015_le__iff__add,axiom,
    ! [X200,X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27))
    <=> ? [X211] : X27 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X200),X211) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_le__iff__add) ).

fof(fact_1095_less__Suc0,axiom,
    ! [X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),hAPP_nat_nat(suc,zero_zero_nat)))
    <=> X27 = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_less__Suc0) ).

fof(fact_1111_card__Collect__le__nat,axiom,
    ! [X27] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),X27))) = hAPP_nat_nat(suc,X27),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_card__Collect__le__nat) ).

fof(fact_1178_nat__mult__eq__cancel1,axiom,
    ! [X200,X27,X206] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X206))
     => ( hAPP_nat_nat(times_times_nat(X206),X200) = hAPP_nat_nat(times_times_nat(X206),X27)
      <=> X200 = X27 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1178_nat__mult__eq__cancel1) ).

fof(fact_1125_zero__induct,axiom,
    ! [X9,X206] :
      ( hBOOL(hAPP_nat_bool(X9,X206))
     => ( ! [X78] :
            ( hBOOL(hAPP_nat_bool(X9,hAPP_nat_nat(suc,X78)))
           => hBOOL(hAPP_nat_bool(X9,X78)) )
       => hBOOL(hAPP_nat_bool(X9,zero_zero_nat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_zero__induct) ).

fof(fact_1036_card__Collect__less__nat,axiom,
    ! [X27] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X27))) = X27,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1036_card__Collect__less__nat) ).

fof(fact_1084_add__Suc,axiom,
    ! [X195,X197] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X195)),X197) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_add__Suc) ).

fof(fact_982_nat__neq__iff,axiom,
    ! [X200,X27] :
      ( X200 != X27
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),X200)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_nat__neq__iff) ).

fof(fact_157_linorder__neq__iff,axiom,
    ! [X4,X5] :
      ( X4 != X5
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_linorder__neq__iff) ).

fof(fact_155_linorder__less__linear,axiom,
    ! [X69,X70] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70))
      | X69 = X70
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X70),X69)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_linorder__less__linear) ).

fof(fact_1175_nat__mult__assoc,axiom,
    ! [X195,X197,X196] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X195),X197)),X196) = hAPP_nat_nat(times_times_nat(X195),hAPP_nat_nat(times_times_nat(X197),X196)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_nat__mult__assoc) ).

fof(fact_994_nat__le__linear,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X197),X195)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_nat__le__linear) ).

fof(fact_365_linorder__linear,axiom,
    ! [X106,X107] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X106),X107))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X107),X106)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_linorder__linear) ).

fof(fact_376_linorder__le__less__linear,axiom,
    ! [X108,X109] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X108),X109))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X109),X108)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_linorder__le__less__linear) ).

fof(fact_1140_le__square,axiom,
    ! [X195] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),hAPP_nat_nat(times_times_nat(X195),X195))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_le__square) ).

fof(fact_165_mem__def,axiom,
    ! [X4,X72] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72))
    <=> hBOOL(hAPP_P606313927t_bool(X72,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_mem__def) ).

fof(fact_168_mem__def,axiom,
    ! [X4,X72] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72))
    <=> hBOOL(hAPP_f592646513l_bool(X72,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_mem__def) ).

fof(fact_167_mem__def,axiom,
    ! [X4,X72] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72))
    <=> hBOOL(hAPP_f312250286l_bool(X72,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_mem__def) ).

fof(fact_166_mem__def,axiom,
    ! [X4,X72] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72))
    <=> hBOOL(hAPP_f965095724l_bool(X72,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_mem__def) ).

fof(fact_164_mem__def,axiom,
    ! [X4,X72] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72))
    <=> hBOOL(hAPP_P1676879539t_bool(X72,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_mem__def) ).

fof(fact_169_mem__def,axiom,
    ! [X4,X72] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72))
    <=> hBOOL(hAPP_nat_bool(X72,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_mem__def) ).

fof(fact_163_mem__def,axiom,
    ! [X4,X72] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72))
    <=> hBOOL(hAPP_bool_bool(X72,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_mem__def) ).

fof(fact_162_mem__def,axiom,
    ! [X4,X72] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72))
    <=> hBOOL(hAPP_A1785763630i_bool(X72,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_mem__def) ).

fof(fact_22_Pair__eq,axiom,
    ! [X12,X13,X10,X11] :
      ( ( is_Arr1861959080le_alt(X12)
        & is_Arr1861959080le_alt(X13)
        & is_Arr1861959080le_alt(X10)
        & is_Arr1861959080le_alt(X11) )
     => ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X10),X11)
      <=> ( X12 = X10
          & X13 = X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Pair__eq) ).

fof(fact_21_Pair__inject,axiom,
    ! [X19,X20,X21,X22] :
      ( ( is_Arr1861959080le_alt(X19)
        & is_Arr1861959080le_alt(X20)
        & is_Arr1861959080le_alt(X21)
        & is_Arr1861959080le_alt(X22) )
     => ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X19),X20) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X21),X22)
       => ~ ( X19 = X21
           => X20 != X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Pair__inject) ).

fof(fact_1193_image__Suc__atLeastAtMost,axiom,
    ! [X26,X212] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(X26),X212)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,X26)),hAPP_nat_nat(suc,X212)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1193_image__Suc__atLeastAtMost) ).

fof(fact_1131_image__Suc__atLeastLessThan,axiom,
    ! [X26,X212] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(X26),X212)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,X26)),hAPP_nat_nat(suc,X212)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1131_image__Suc__atLeastLessThan) ).

fof(fact_1085_add__Suc__right,axiom,
    ! [X195,X197] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),hAPP_nat_nat(suc,X197)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_add__Suc__right) ).

fof(fact_1083_add__Suc__shift,axiom,
    ! [X195,X197] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X195)),X197) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),hAPP_nat_nat(suc,X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1083_add__Suc__shift) ).

fof(fact_1165_mult__Suc,axiom,
    ! [X195,X197] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X195)),X197) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X197),hAPP_nat_nat(times_times_nat(X195),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_mult__Suc) ).

fof(fact_1183_nat_Osize_I4_J,axiom,
    ! [X226] : hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,X226)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,X226)),hAPP_nat_nat(suc,zero_zero_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1183_nat_Osize_I4_J) ).

fof(fact_1181_nat_Osize_I2_J,axiom,
    ! [X226] : hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,X226)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,X226)),hAPP_nat_nat(suc,zero_zero_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1181_nat_Osize_I2_J) ).

fof(fact_188_inv__f__f,axiom,
    ! [X4,X75] :
      ( is_Arr43961803e_indi(X4)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),top_to1576102282i_bool))
       => hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,X75),hAPP_A1637648121di_nat(X75,X4)) = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_inv__f__f) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow,axiom,
    ! [X1,X2,X3] :
      ( ( is_fun961089132t_bool(X1)
        & is_Arr1861959080le_alt(X2)
        & is_Arr1861959080le_alt(X3) )
     => is_fun961089132t_bool(arrow_1539419881_below(X1,X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow) ).

fof(fact_186_inv__f__eq,axiom,
    ! [X4,X5,X75] :
      ( is_Arr43961803e_indi(X4)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),top_to1576102282i_bool))
       => ( hAPP_A1637648121di_nat(X75,X4) = X5
         => hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,X75),X5) = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inv__f__eq) ).

fof(fact_1117_gr0__implies__Suc,axiom,
    ! [X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X197))
     => ? [X30] : X197 = hAPP_nat_nat(suc,X30) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_gr0__implies__Suc) ).

fof(fact_1094_gr0__conv__Suc,axiom,
    ! [X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X27))
    <=> ? [X30] : X27 = hAPP_nat_nat(suc,X30) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_gr0__conv__Suc) ).

fof(fact_66_less__top,axiom,
    ! [X12] :
      ( ~ ( hBOOL(X12)
        <=> hBOOL(top_top_bool) )
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X12),top_top_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__top) ).

fof(fact_189_inv__f__f,axiom,
    ! [X4,X75] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),top_top_fun_nat_bool))
     => hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,X75),hAPP_nat_nat(X75,X4)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_inv__f__f) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_074,axiom,
    ! [X227,X228,X229] : hAPP_A1102281708t_bool(hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,X227),X228),X229) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_074) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065,axiom,
    ! [X227,X228,X229] : hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,X227),X228),X229) = hAPP_A1941004017t_bool(hAPP_A621939144t_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062,axiom,
    ! [X227,X228,X229] : hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,X227),X228),X229) = hAPP_f1663053423t_bool(hAPP_A572596845t_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U,axiom,
    ! [X227,X228,X229] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,X227),X228),X229) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) ).

fof(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_,axiom,
    ! [X227,X228,X229] : hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,X227),X228),X229) = hAPP_f592646513l_bool(hAPP_P229966473l_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
    ! [X227,X228,X229] : hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,X227),X228),X229) = hAPP_f1749234559l_bool(hAPP_f566237389l_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn,axiom,
    ! [X227,X228,X229] : hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,X227),X228),X229) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    ! [X227,X228,X229] : hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,X227),X228),X229) = hAPP_f777333846l_bool(hAPP_f461621971l_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [X227,X228,X229] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,X227),X228),X229) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
    ! [X227,X228,X229] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,X227),X228),X229) = hAPP_nat_bool(hAPP_n1699378549t_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_066,axiom,
    ! [X227,X228,X229] : hAPP_A1677245848t_bool(hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,X227),X228),X229) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_066) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059,axiom,
    ! [X227,X228,X229] : hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,X227),X228),X229) = hAPP_A568203993t_bool(hAPP_A1625428400t_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000,axiom,
    ! [X227,X228,X229] : hAPP_A1785763630i_bool(hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,X227),X228),X229) = hAPP_nat_bool(hAPP_A2046586321t_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t,axiom,
    ! [X227,X228,X229] : hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,X227),X228),X229) = hAPP_f592646513l_bool(hAPP_A187815023l_bool(X227,X229),X228),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t) ).

fof(fact_67_less__top,axiom,
    ! [X12] :
      ( is_fun961089132t_bool(X12)
     => ( X12 != top_to565915683t_bool
      <=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X12),top_to565915683t_bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__top) ).

fof(fact_63_less__top,axiom,
    ! [X12] :
      ( is_fun279392540l_bool(X12)
     => ( X12 != top_to1853035173l_bool
      <=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X12),top_to1853035173l_bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__top) ).

fof(fact_65_less__top,axiom,
    ! [X12] :
      ( is_fun158382675l_bool(X12)
     => ( X12 != top_to1714702858l_bool
      <=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X12),top_to1714702858l_bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__top) ).

fof(fact_64_less__top,axiom,
    ! [X12] :
      ( is_fun288122577l_bool(X12)
     => ( X12 != top_to522745736l_bool
      <=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X12),top_to522745736l_bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__top) ).

fof(fact_70_less__top,axiom,
    ! [X12] :
      ( is_fun1568535512t_bool(X12)
     => ( X12 != top_to1257323279t_bool
      <=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),top_to1257323279t_bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__top) ).

fof(fact_68_less__top,axiom,
    ! [X12] :
      ( is_fun1236654035i_bool(X12)
     => ( X12 != top_to1576102282i_bool
      <=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),top_to1576102282i_bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__top) ).

fof(fact_187_inv__f__eq,axiom,
    ! [X4,X5,X75] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),top_top_fun_nat_bool))
     => ( hAPP_nat_nat(X75,X4) = X5
       => hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,X75),X5) = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_inv__f__eq) ).

fof(fact_150_less__imp__neq,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => X4 != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_less__imp__neq) ).

fof(fact_138_order__less__imp__not__eq,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => X4 != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__less__imp__not__eq) ).

fof(fact_134_order__less__imp__not__eq2,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => X5 != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_order__less__imp__not__eq2) ).

fof(fact_149_less__imp__neq,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => X4 != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_less__imp__neq) ).

fof(fact_137_order__less__imp__not__eq,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => X4 != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_order__less__imp__not__eq) ).

fof(fact_133_order__less__imp__not__eq2,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => X5 != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_order__less__imp__not__eq2) ).

fof(fact_151_less__imp__neq,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => X4 != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_less__imp__neq) ).

fof(fact_139_order__less__imp__not__eq,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => X4 != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order__less__imp__not__eq) ).

fof(fact_135_order__less__imp__not__eq2,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => X5 != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_order__less__imp__not__eq2) ).

fof(fact_986_less__not__refl3,axiom,
    ! [X203,X204] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X203),X204))
     => X203 != X204 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_986_less__not__refl3) ).

fof(fact_985_less__not__refl2,axiom,
    ! [X197,X195] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),X195))
     => X195 != X197 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_less__not__refl2) ).

fof(fact_152_less__imp__neq,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X65),X66))
     => X65 != X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_less__imp__neq) ).

fof(fact_140_order__less__imp__not__eq,axiom,
    ! [X59,X60] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X59),X60))
     => X59 != X60 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_order__less__imp__not__eq) ).

fof(fact_136_order__less__imp__not__eq2,axiom,
    ! [X57,X58] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X57),X58))
     => X58 != X57 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_order__less__imp__not__eq2) ).

fof(fact_614_injD,axiom,
    ! [X4,X5,X75] :
      ( ( is_Arr43961803e_indi(X4)
        & is_Arr43961803e_indi(X5) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),top_to1576102282i_bool))
       => ( hAPP_A1637648121di_nat(X75,X4) = hAPP_A1637648121di_nat(X75,X5)
         => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_injD) ).

fof(fact_612_inj__eq,axiom,
    ! [X4,X5,X75] :
      ( ( is_Arr43961803e_indi(X4)
        & is_Arr43961803e_indi(X5) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),top_to1576102282i_bool))
       => ( hAPP_A1637648121di_nat(X75,X4) = hAPP_A1637648121di_nat(X75,X5)
        <=> X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_inj__eq) ).

fof(fact_1047_gr__implies__not0,axiom,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
     => X197 != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1047_gr__implies__not0) ).

fof(fact_1059_lessI,axiom,
    ! [X197] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),hAPP_nat_nat(suc,X197))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_lessI) ).

fof(fact_533_top__le,axiom,
    ! [X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X12))
     => ( hBOOL(X12)
      <=> hBOOL(top_top_bool) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_top__le) ).

fof(fact_524_top__unique,axiom,
    ! [X12] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X12))
    <=> ( hBOOL(X12)
      <=> hBOOL(top_top_bool) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_top__unique) ).

fof(fact_534_top__le,axiom,
    ! [X12] :
      ( is_fun961089132t_bool(X12)
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),X12))
       => X12 = top_to565915683t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_top__le) ).

fof(fact_525_top__unique,axiom,
    ! [X12] :
      ( is_fun961089132t_bool(X12)
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),X12))
      <=> X12 = top_to565915683t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_top__unique) ).

fof(fact_530_top__le,axiom,
    ! [X12] :
      ( is_fun279392540l_bool(X12)
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),X12))
       => X12 = top_to1853035173l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_top__le) ).

fof(fact_521_top__unique,axiom,
    ! [X12] :
      ( is_fun279392540l_bool(X12)
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),X12))
      <=> X12 = top_to1853035173l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_top__unique) ).

fof(fact_532_top__le,axiom,
    ! [X12] :
      ( is_fun158382675l_bool(X12)
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),X12))
       => X12 = top_to1714702858l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_top__le) ).

fof(fact_523_top__unique,axiom,
    ! [X12] :
      ( is_fun158382675l_bool(X12)
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),X12))
      <=> X12 = top_to1714702858l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_top__unique) ).

fof(fact_531_top__le,axiom,
    ! [X12] :
      ( is_fun288122577l_bool(X12)
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),X12))
       => X12 = top_to522745736l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_top__le) ).

fof(fact_522_top__unique,axiom,
    ! [X12] :
      ( is_fun288122577l_bool(X12)
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),X12))
      <=> X12 = top_to522745736l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_top__unique) ).

fof(fact_538_top__le,axiom,
    ! [X12] :
      ( is_fun1568535512t_bool(X12)
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),X12))
       => X12 = top_to1257323279t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_top__le) ).

fof(fact_529_top__unique,axiom,
    ! [X12] :
      ( is_fun1568535512t_bool(X12)
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),X12))
      <=> X12 = top_to1257323279t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_top__unique) ).

fof(fact_536_top__le,axiom,
    ! [X12] :
      ( is_fun1236654035i_bool(X12)
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),X12))
       => X12 = top_to1576102282i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_top__le) ).

fof(fact_527_top__unique,axiom,
    ! [X12] :
      ( is_fun1236654035i_bool(X12)
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),X12))
      <=> X12 = top_to1576102282i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_top__unique) ).

fof(fact_535_top__le,axiom,
    ! [X12] :
      ( is_fun2093718614t_bool(X12)
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),X12))
       => X12 = top_to178429151t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_top__le) ).

fof(fact_526_top__unique,axiom,
    ! [X12] :
      ( is_fun2093718614t_bool(X12)
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),X12))
      <=> X12 = top_to178429151t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_top__unique) ).

fof(fact_992_nat__add__right__cancel,axiom,
    ! [X200,X206,X27] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X200),X206) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X27),X206)
    <=> X200 = X27 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_nat__add__right__cancel) ).

fof(fact_731_add__right__cancel,axiom,
    ! [X13,X12,X15] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X12)
    <=> X13 = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_add__right__cancel) ).

fof(fact_728_add__right__imp__eq,axiom,
    ! [X151,X152,X153] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X151),X152) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X153),X152)
     => X151 = X153 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_add__right__imp__eq) ).

fof(fact_991_nat__add__left__cancel,axiom,
    ! [X206,X200,X27] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X206),X200) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X206),X27)
    <=> X200 = X27 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_nat__add__left__cancel) ).

fof(fact_732_add__left__cancel,axiom,
    ! [X12,X13,X15] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X15)
    <=> X13 = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_add__left__cancel) ).

fof(fact_730_add__left__imp__eq,axiom,
    ! [X157,X158,X159] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X157),X158) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X157),X159)
     => X158 = X159 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_add__left__imp__eq) ).

fof(fact_729_add__imp__eq,axiom,
    ! [X154,X155,X156] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X154),X155) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X154),X156)
     => X155 = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_add__imp__eq) ).

fof(fact_1164_mult__Suc__right,axiom,
    ! [X195,X197] : hAPP_nat_nat(times_times_nat(X195),hAPP_nat_nat(suc,X197)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),hAPP_nat_nat(times_times_nat(X195),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1164_mult__Suc__right) ).

fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_075,axiom,
    ! [X227,X228,X229] : hAPP_A1102281708t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(X227),X228),X229) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(X227,X229),hAPP_A1677245848t_bool(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_075) ).

fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [X227,X228,X229] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBS_nat_bool_bool(X227),X228),X229) = hAPP_bool_bool(hAPP_n1006566506l_bool(X227,X229),hAPP_nat_bool(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000,axiom,
    ! [X227,X228,X229] : hAPP_A1677245848t_bool(hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(X227),X228),X229) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(X227,X229),hAPP_A1677245848t_bool(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000) ).

fof(fact_69_less__top,axiom,
    ! [X12] :
      ( X12 != top_top_fun_nat_bool
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),top_top_fun_nat_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__top) ).

fof(fact_1053_le__0__eq,axiom,
    ! [X27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),zero_zero_nat))
    <=> X27 = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_le__0__eq) ).

fof(fact_1061_zero__less__Suc,axiom,
    ! [X197] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X197))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_zero__less__Suc) ).

fof(fact_1045_neq0__conv,axiom,
    ! [X27] :
      ( X27 != zero_zero_nat
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_neq0__conv) ).

fof(fact_537_top__le,axiom,
    ! [X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),X12))
     => X12 = top_top_fun_nat_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_top__le) ).

fof(fact_528_top__unique,axiom,
    ! [X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),X12))
    <=> X12 = top_top_fun_nat_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_top__unique) ).

fof(fact_615_injD,axiom,
    ! [X4,X5,X75] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),top_top_fun_nat_bool))
     => ( hAPP_nat_nat(X75,X4) = hAPP_nat_nat(X75,X5)
       => X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_injD) ).

fof(fact_613_inj__eq,axiom,
    ! [X4,X5,X75] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),top_top_fun_nat_bool))
     => ( hAPP_nat_nat(X75,X4) = hAPP_nat_nat(X75,X5)
      <=> X4 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_inj__eq) ).

fof(fact_1189_finite__atLeastAtMost,axiom,
    ! [X223,X215] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(X223),X215))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1189_finite__atLeastAtMost) ).

fof(fact_1138_finite__greaterThanLessThan,axiom,
    ! [X223,X215] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(X223),X215))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_finite__greaterThanLessThan) ).

fof(fact_1137_finite__greaterThanAtMost,axiom,
    ! [X223,X215] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(X223),X215))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_finite__greaterThanAtMost) ).

fof(fact_1128_finite__atLeastLessThan,axiom,
    ! [X223,X215] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(X223),X215))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1128_finite__atLeastLessThan) ).

fof(fact_1097_add__is__1,axiom,
    ! [X200,X27] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X200),X27) = hAPP_nat_nat(suc,zero_zero_nat)
    <=> ( ( X200 = hAPP_nat_nat(suc,zero_zero_nat)
          & X27 = zero_zero_nat )
        | ( X200 = zero_zero_nat
          & X27 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1097_add__is__1) ).

fof(fact_1098_one__is__add,axiom,
    ! [X200,X27] :
      ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X200),X27)
    <=> ( ( X200 = hAPP_nat_nat(suc,zero_zero_nat)
          & X27 = zero_zero_nat )
        | ( X200 = zero_zero_nat
          & X27 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_one__is__add) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_,axiom,
    ! [X227,X228,X229] : hAPP_A1455239488t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(X227),X228),X229) = hAPP_b1588041841t_bool(X227,hAPP_A1785763630i_bool(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    ! [X227,X228,X229] : hAPP_A1553574765l_bool(hAPP_f156764033l_bool(cOMBB_2112722489le_alt(X227),X228),X229) = hAPP_f1539445765l_bool(X227,hAPP_A1505516597le_alt(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_073,axiom,
    ! [X227,X228,X229] : hAPP_A621939144t_bool(hAPP_f210227915t_bool(cOMBB_1769989562e_indi(X227),X228),X229) = hAPP_f344580165t_bool(X227,hAPP_A1677245848t_bool(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_073) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___076,axiom,
    ! [X227,X228,X229] : hAPP_A572596845t_bool(hAPP_f1324249913t_bool(cOMBB_747702273le_alt(X227),X228),X229) = hAPP_f653880381t_bool(X227,hAPP_A1553574765l_bool(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___076) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
    ! [X227,X228,X229] : hAPP_A1625428400t_bool(hAPP_f721938099t_bool(cOMBB_2032668066e_indi(X227),X228),X229) = hAPP_f393984045t_bool(X227,hAPP_A1677245848t_bool(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [X227,X228,X229] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(X227),X228),X229) = hAPP_b589554111l_bool(X227,hAPP_nat_bool(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__049,axiom,
    ! [X227,X228,X229] : hAPP_A2046586321t_bool(hAPP_f224734595t_bool(cOMBB_1883918730e_indi(X227),X228),X229) = hAPP_n1699378549t_bool(X227,hAPP_A1637648121di_nat(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__049) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,axiom,
    ! [X227,X228,X229] : hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(X227),X228),X229) = hAPP_n215258509l_bool(X227,hAPP_nat_nat(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [X227,X228,X229] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(X227),X228),X229) = hAPP_n1699378549t_bool(X227,hAPP_nat_nat(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_,axiom,
    ! [X227,X228,X229] : hAPP_A187815023l_bool(hAPP_f1539445765l_bool(cOMBB_84213429le_alt(X227),X228),X229) = hAPP_P229966473l_bool(X227,hAPP_A702847159le_alt(X228,X229)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_) ).

fof(fact_349_order__eq__refl,axiom,
    ! [X5,X4] :
      ( ( hBOOL(X4)
      <=> hBOOL(X5) )
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_order__eq__refl) ).

fof(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp,axiom,
    ! [X201,X202] :
      ( is_fun961089132t_bool(X201)
     => hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),X201),X202) = X201 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) ).

fof(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp,axiom,
    ! [X201,X202] :
      ( is_fun961089132t_bool(X202)
     => hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fFalse),X201),X202) = X202 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) ).

fof(fact_1194_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [X223,X215] : hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,X223)),X215) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(X223),X215),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1194_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_1139_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [X223,X215] : hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,X223)),X215) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(X223),X215),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1139_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_657_injI,axiom,
    ! [X75] :
      ( ! [X24,X149] :
          ( hAPP_nat_nat(X75,X24) = hAPP_nat_nat(X75,X149)
         => X24 = X149 )
     => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X75),top_top_fun_nat_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_injI) ).

fof(fact_656_injI,axiom,
    ! [X75] :
      ( ! [X24,X149] :
          ( ( is_Arr43961803e_indi(X24)
            & is_Arr43961803e_indi(X149) )
         => ( hAPP_A1637648121di_nat(X75,X24) = hAPP_A1637648121di_nat(X75,X149)
           => X24 = X149 ) )
     => hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X75),top_to1576102282i_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_injI) ).

fof(fact_348_order__eq__refl,axiom,
    ! [X4,X5] :
      ( X4 = X5
     => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_order__eq__refl) ).

fof(fact_345_order__eq__refl,axiom,
    ! [X4,X5] :
      ( X4 = X5
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_order__eq__refl) ).

fof(fact_346_order__eq__refl,axiom,
    ! [X4,X5] :
      ( X4 = X5
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_order__eq__refl) ).

fof(fact_347_order__eq__refl,axiom,
    ! [X4,X5] :
      ( X4 = X5
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_order__eq__refl) ).

fof(fact_351_order__eq__refl,axiom,
    ! [X4,X5] :
      ( X4 = X5
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_order__eq__refl) ).

fof(fact_972_equalityD1,axiom,
    ! [X72,X76] :
      ( X72 = X76
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_equalityD1) ).

fof(fact_354_order__eq__refl,axiom,
    ! [X4,X5] :
      ( X4 = X5
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_order__eq__refl) ).

fof(fact_971_equalityD2,axiom,
    ! [X72,X76] :
      ( X72 = X76
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X76),X72)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_equalityD2) ).

fof(fact_350_order__eq__refl,axiom,
    ! [X4,X5] :
      ( X4 = X5
     => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_order__eq__refl) ).

fof(fact_352_order__eq__refl,axiom,
    ! [X4,X5] :
      ( X4 = X5
     => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_order__eq__refl) ).

fof(fact_995_eq__imp__le,axiom,
    ! [X195,X197] :
      ( X195 = X197
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_eq__imp__le) ).

fof(fact_353_order__eq__refl,axiom,
    ! [X104,X105] :
      ( X104 = X105
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X104),X105)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_order__eq__refl) ).

fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X201,X202] :
      ( X201 != X202
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X201),X202)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

fof(fact_229_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_order__refl) ).

fof(fact_226_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_order__refl) ).

fof(fact_227_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_order__refl) ).

fof(fact_228_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_order__refl) ).

fof(fact_232_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_order__refl) ).

fof(fact_975_subset__refl,axiom,
    ! [X72] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_subset__refl) ).

fof(fact_235_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_order__refl) ).

fof(fact_231_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_order__refl) ).

fof(fact_233_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_order__refl) ).

fof(fact_993_le__refl,axiom,
    ! [X197] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X197),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_le__refl) ).

fof(fact_234_order__refl,axiom,
    ! [X77] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X77),X77)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_order__refl) ).

fof(fact_230_order__refl,axiom,
    ! [X4] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_order__refl) ).

fof(fact_988_nat__add__commute,axiom,
    ! [X195,X197] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X197) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X197),X195),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_nat__add__commute) ).

fof(fact_43_iso__tuple__UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),top_to565915683t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).

fof(fact_35_UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),top_to565915683t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_UNIV__I) ).

fof(fact_722_subset__UNIV,axiom,
    ! [X72] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X72),top_to565915683t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_subset__UNIV) ).

fof(fact_516_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X12),top_to565915683t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_top__greatest) ).

fof(fact_719_subset__UNIV,axiom,
    ! [X72] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X72),top_to1853035173l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_subset__UNIV) ).

fof(fact_512_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X12),top_to1853035173l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_top__greatest) ).

fof(fact_46_iso__tuple__UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),top_to1853035173l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_iso__tuple__UNIV__I) ).

fof(fact_38_UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),top_to1853035173l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_UNIV__I) ).

fof(fact_721_subset__UNIV,axiom,
    ! [X72] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X72),top_to1714702858l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_721_subset__UNIV) ).

fof(fact_514_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X12),top_to1714702858l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_top__greatest) ).

fof(fact_45_iso__tuple__UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),top_to1714702858l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).

fof(fact_37_UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),top_to1714702858l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_UNIV__I) ).

fof(fact_720_subset__UNIV,axiom,
    ! [X72] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X72),top_to522745736l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_720_subset__UNIV) ).

fof(fact_513_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X12),top_to522745736l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_top__greatest) ).

fof(fact_44_iso__tuple__UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),top_to522745736l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).

fof(fact_36_UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),top_to522745736l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_UNIV__I) ).

fof(fact_725_subset__UNIV,axiom,
    ! [X72] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X72),top_to1257323279t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_subset__UNIV) ).

fof(fact_520_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X12),top_to1257323279t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_top__greatest) ).

fof(fact_42_iso__tuple__UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),top_to1257323279t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_iso__tuple__UNIV__I) ).

fof(fact_34_UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),top_to1257323279t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_UNIV__I) ).

fof(fact_724_subset__UNIV,axiom,
    ! [X72] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),top_top_fun_nat_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_subset__UNIV) ).

fof(fact_519_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),top_top_fun_nat_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_top__greatest) ).

fof(fact_47_iso__tuple__UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),top_top_fun_nat_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_iso__tuple__UNIV__I) ).

fof(fact_39_UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),top_top_fun_nat_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_UNIV__I) ).

fof(fact_40_iso__tuple__UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),top_to1647826457l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).

fof(fact_32_UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),top_to1647826457l_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_UNIV__I) ).

fof(fact_723_subset__UNIV,axiom,
    ! [X72] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X72),top_to1576102282i_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_subset__UNIV) ).

fof(fact_518_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X12),top_to1576102282i_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_top__greatest) ).

fof(fact_41_iso__tuple__UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),top_to1576102282i_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).

fof(fact_33_UNIV__I,axiom,
    ! [X4] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),top_to1576102282i_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_UNIV__I) ).

fof(fact_517_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X12),top_to178429151t_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_top__greatest) ).

fof(fact_515_top__greatest,axiom,
    ! [X12] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X12),top_top_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_top__greatest) ).

fof(fact_1048_gr0I,axiom,
    ! [X197] :
      ( X197 != zero_zero_nat
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X197)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_gr0I) ).

fof(fact_1054_less__eq__nat_Osimps_I1_J,axiom,
    ! [X197] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_less__eq__nat_Osimps_I1_J) ).

fof(fact_1043_le0,axiom,
    ! [X197] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X197)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_le0) ).

fof(fact_1157_mult__eq__1__iff,axiom,
    ! [X200,X27] :
      ( hAPP_nat_nat(times_times_nat(X200),X27) = hAPP_nat_nat(suc,zero_zero_nat)
    <=> ( X200 = hAPP_nat_nat(suc,zero_zero_nat)
        & X27 = hAPP_nat_nat(suc,zero_zero_nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1157_mult__eq__1__iff) ).

fof(fact_1152_mult__cancel2,axiom,
    ! [X200,X206,X27] :
      ( hAPP_nat_nat(times_times_nat(X200),X206) = hAPP_nat_nat(times_times_nat(X27),X206)
    <=> ( X200 = X27
        | X206 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_mult__cancel2) ).

fof(fact_1179_nat__mult__eq__cancel__disj,axiom,
    ! [X206,X200,X27] :
      ( hAPP_nat_nat(times_times_nat(X206),X200) = hAPP_nat_nat(times_times_nat(X206),X27)
    <=> ( X206 = zero_zero_nat
        | X200 = X27 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1179_nat__mult__eq__cancel__disj) ).

fof(fact_1153_mult__cancel1,axiom,
    ! [X206,X200,X27] :
      ( hAPP_nat_nat(times_times_nat(X206),X200) = hAPP_nat_nat(times_times_nat(X206),X27)
    <=> ( X200 = X27
        | X206 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_mult__cancel1) ).

fof(fact_1030_linear__alt,axiom,
    ? [X214] :
      ( is_fun961089132t_bool(X214)
      & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X214),arrow_1681063817le_Lin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_linear__alt) ).

fof(fact_1190_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [X223,X215] : hAPP_n1699378549t_bool(ord_at4362885an_nat(X223),hAPP_nat_nat(suc,X215)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(X223),X215),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1190_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_1052_add__eq__self__zero,axiom,
    ! [X195,X197] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X197) = X195
     => X197 = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_add__eq__self__zero) ).

fof(fact_1051_add__is__0,axiom,
    ! [X200,X27] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X200),X27) = zero_zero_nat
    <=> ( X200 = zero_zero_nat
        & X27 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_add__is__0) ).

fof(fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12,axiom,
    ~ ! [X224] :
        ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X224),top_to1576102282i_bool))
       => hAPP_f2026336507t_bool(image_579431497di_nat(X224),top_to1576102282i_bool) != hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12) ).

fof(fact_1198_atLeast__Suc__greaterThan,axiom,
    ! [X206] : hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,X206)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,X206),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1198_atLeast__Suc__greaterThan) ).

fof(fact_1118_Suc__eq__plus1,axiom,
    ! [X197] : hAPP_nat_nat(suc,X197) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X197),one_one_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1118_Suc__eq__plus1) ).

fof(fact_1110_less__eq__Suc__le__raw,axiom,
    ! [X24] : hAPP_n1699378549t_bool(ord_less_nat,X24) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_less__eq__Suc__le__raw) ).

fof(fact_1119_Suc__eq__plus1__left,axiom,
    ! [X197] : hAPP_nat_nat(suc,X197) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X197),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_Suc__eq__plus1__left) ).

fof(fact_51_top__apply,axiom,
    ! [X4] :
      ( hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X4))
    <=> hBOOL(top_top_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_top__apply) ).

fof(fact_48_top__apply,axiom,
    ! [X4] :
      ( hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X4))
    <=> hBOOL(top_top_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_top__apply) ).

fof(fact_50_top__apply,axiom,
    ! [X4] :
      ( hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X4))
    <=> hBOOL(top_top_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_top__apply) ).

fof(fact_49_top__apply,axiom,
    ! [X4] :
      ( hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X4))
    <=> hBOOL(top_top_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_top__apply) ).

fof(fact_54_top__apply,axiom,
    ! [X4] :
      ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X4))
    <=> hBOOL(top_top_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_top__apply) ).

fof(fact_53_top__apply,axiom,
    ! [X4] :
      ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X4))
    <=> hBOOL(top_top_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_top__apply) ).

fof(fact_52_top__apply,axiom,
    ! [X4] :
      ( hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X4))
    <=> hBOOL(top_top_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_top__apply) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_050,axiom,
    ! [X227,X228] :
      ( is_fun1568535512t_bool(X227)
     => hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_050) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___052,axiom,
    ! [X227,X228] :
      ( is_fun1236654035i_bool(X227)
     => hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___052) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [X227,X228] :
      ( is_bool(X227)
     => hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_alt,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_054,axiom,
    ! [X227,X228] :
      ( is_fun1568535512t_bool(X227)
     => hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_054) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___056,axiom,
    ! [X227,X228] :
      ( is_fun1236654035i_bool(X227)
     => hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___056) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
    ! [X227,X228] :
      ( is_bool(X227)
     => hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_069,axiom,
    ! [X227,X228] :
      ( is_fun1568535512t_bool(X227)
     => hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_069) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___071,axiom,
    ! [X227,X228] :
      ( is_fun1236654035i_bool(X227)
     => hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___071) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
    ! [X227,X228] :
      ( is_bool(X227)
     => hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_067,axiom,
    ! [X227,X228] :
      ( is_fun279392540l_bool(X227)
     => hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_067) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_060,axiom,
    ! [X227,X228] :
      ( is_fun1568535512t_bool(X227)
     => hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_060) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___063,axiom,
    ! [X227,X228] :
      ( is_fun1236654035i_bool(X227)
     => hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___063) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [X227,X228] :
      ( is_bool(X227)
     => hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051,axiom,
    ! [X227,X228] :
      ( is_fun961089132t_bool(X227)
     => hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_055,axiom,
    ! [X227,X228] :
      ( is_fun279392540l_bool(X227)
     => hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_055) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_070,axiom,
    ! [X227,X228] :
      ( is_fun158382675l_bool(X227)
     => hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_070) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_061,axiom,
    ! [X227,X228] :
      ( is_fun288122577l_bool(X227)
     => hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_061) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U,axiom,
    ! [X227,X228] :
      ( is_bool(X227)
     => hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00,axiom,
    ! [X227,X228] :
      ( is_fun1568535512t_bool(X227)
     => hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    ! [X227,X228] :
      ( is_fun1236654035i_bool(X227)
     => hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [X227,X228] :
      ( is_bool(X227)
     => hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
    ! [X227,X228] :
      ( is_fun961089132t_bool(X227)
     => hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [X227,X228] :
      ( is_fun279392540l_bool(X227)
     => hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [X227,X228] :
      ( is_fun158382675l_bool(X227)
     => hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn,axiom,
    ! [X227,X228] :
      ( is_fun288122577l_bool(X227)
     => hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_053,axiom,
    ! [X227,X228] :
      ( is_fun961089132t_bool(X227)
     => hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_053) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057,axiom,
    ! [X227,X228] :
      ( is_fun279392540l_bool(X227)
     => hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_072,axiom,
    ! [X227,X228] :
      ( is_fun158382675l_bool(X227)
     => hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_072) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_064,axiom,
    ! [X227,X228] :
      ( is_fun288122577l_bool(X227)
     => hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_064) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn,axiom,
    ! [X227,X228] :
      ( is_bool(X227)
     => hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,X227),X228) = X227 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039,hypothesis,
    ! [X1,X2] :
      ( ( is_fun279392540l_bool(X1)
        & is_fun961089132t_bool(X2) )
     => is_bool(hAPP_f592646513l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O,axiom,
    ! [X1,X2] :
      ( ( is_fun1236654035i_bool(X1)
        & is_Arr43961803e_indi(X2) )
     => is_bool(hAPP_A1785763630i_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O) ).

fof(fact_1063_nat_Oinject,axiom,
    ! [X216,X217] :
      ( hAPP_nat_nat(suc,X216) = hAPP_nat_nat(suc,X217)
    <=> X216 = X217 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_nat_Oinject) ).

fof(fact_1062_Suc__inject,axiom,
    ! [X201,X202] :
      ( hAPP_nat_nat(suc,X201) = hAPP_nat_nat(suc,X202)
     => X201 = X202 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1062_Suc__inject) ).

fof(fact_1174_nat__mult__commute,axiom,
    ! [X195,X197] : hAPP_nat_nat(times_times_nat(X195),X197) = hAPP_nat_nat(times_times_nat(X197),X195),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_nat__mult__commute) ).

fof(fact_1034_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1034_infinite__UNIV__nat) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__On,axiom,
    ! [X227,X228] : hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,X227),X228) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__On) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
    ! [X227,X228] : hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,X227),X228) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_068,axiom,
    ! [X227,X228] : hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,X227),X228) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_068) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_058,axiom,
    ! [X227,X228] : hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,X227),X228) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_058) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product_,axiom,
    ! [X227,X228] : hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,X227),X228) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product_) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___,axiom,
    ! [X227,X228] : hAPP_A2046586321t_bool(hAPP_f1491725936t_bool(cOMBK_847149194e_indi,X227),X228) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It,axiom,
    ! [X227,X228] : hAPP_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_alt,X227),X228) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
    ! [X227,X228] : hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,X227),X228) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

fof(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu,axiom,
    ! [X1,X2] :
      ( is_fun1236654035i_bool(X1)
     => is_fun1217980910e_indi(hilber693666498di_nat(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___042,axiom,
    ! [X1,X2] :
      ( is_fun961089132t_bool(X2)
     => is_fun1568535512t_bool(hAPP_f1710744577t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___042) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I,axiom,
    ! [X1,X2] :
      ( is_fun1568535512t_bool(X2)
     => is_fun1568535512t_bool(hAPP_f427533077t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob,axiom,
    ! [X1,X2] :
      ( is_bool(X2)
     => is_fun1568535512t_bool(hAPP_b1096750261t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040,axiom,
    ! [X1,X2] :
      ( is_fun961089132t_bool(X2)
     => is_fun2093718614t_bool(hAPP_f1617919085t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__045,axiom,
    ! [X1,X2] :
      ( is_fun961089132t_bool(X1)
     => is_bool(hAPP_P606313927t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__045) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_036,axiom,
    ! [X1,X2] :
      ( is_fun279392540l_bool(X2)
     => is_bool(hAPP_f1749234559l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_036) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_030,axiom,
    ! [X1,X2] :
      ( is_fun158382675l_bool(X2)
     => is_bool(hAPP_f250445784l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_030) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_024,axiom,
    ! [X1,X2] :
      ( is_fun158382675l_bool(X1)
     => is_bool(hAPP_f312250286l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_024) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_021,axiom,
    ! [X1,X2] :
      ( is_fun288122577l_bool(X2)
     => is_bool(hAPP_f777333846l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_021) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__,axiom,
    ! [X1,X2] :
      ( is_fun1568535512t_bool(X2)
     => is_bool(hAPP_f2028818269l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__011,axiom,
    ! [X1,X2] :
      ( is_fun288122577l_bool(X1)
     => is_bool(hAPP_f965095724l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__011) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_,axiom,
    ! [X1,X2] :
      ( is_fun1236654035i_bool(X2)
     => is_bool(hAPP_f1599966040l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___008,axiom,
    ! [X1,X2] :
      ( is_fun2093718614t_bool(X2)
     => is_bool(hAPP_f324780729l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___008) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool,axiom,
    ! [X1,X2] :
      ( is_fun1568535512t_bool(X1)
     => is_bool(hAPP_P1676879539t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
    ! [X1,X2] :
      ( is_bool(X2)
     => is_bool(hAPP_bool_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob,axiom,
    ! [X1,X2] :
      ( is_Arr1861959080le_alt(X2)
     => is_bool(hAPP_A862370221t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    ! [X1,X2] :
      ( is_fun961089132t_bool(X2)
     => is_Arr43961803e_indi(hAPP_f1582908258e_indi(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oi,axiom,
    ! [X1,X2] :
      ( is_fun1217980910e_indi(X1)
     => is_Arr43961803e_indi(hAPP_n1951273283e_indi(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oi) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___041,axiom,
    ! [X1,X2] :
      ( is_fun961089132t_bool(X2)
     => is_fun1236654035i_bool(hAPP_f244157820i_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___041) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__009,axiom,
    ! [X1,X2] :
      ( is_fun1236654035i_bool(X2)
     => is_fun1236654035i_bool(hAPP_f580451669i_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__009) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnf,axiom,
    ! [X1,X2] :
      ( is_bool(X2)
     => is_fun1236654035i_bool(hAPP_b1337486384i_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnf) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___044,axiom,
    ! [X1,X2] :
      ( is_fun961089132t_bool(X2)
     => is_fun961089132t_bool(hAPP_f515126293t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___044) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,axiom,
    ! [X1,X2] :
      ( is_bool(X2)
     => is_fun961089132t_bool(hAPP_b1703662281t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_006,axiom,
    ! [X1,X2] :
      ( is_Arr43961803e_indi(X2)
     => is_fun961089132t_bool(hAPP_A1677245848t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_006) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003,axiom,
    ! [X1,X2] :
      ( is_Arr1861959080le_alt(X2)
     => is_fun961089132t_bool(hAPP_A568203993t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_022,axiom,
    ! [X1,X2] :
      ( is_fun288122577l_bool(X2)
     => is_fun288122577l_bool(hAPP_f146009813l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_022) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,axiom,
    ! [X1,X2] :
      ( is_bool(X2)
     => is_fun288122577l_bool(hAPP_b1048178734l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It,axiom,
    ! [X1,X2] :
      ( is_Arr43961803e_indi(X2)
     => is_fun288122577l_bool(hAPP_A1952883197l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It) ).

fof(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc_,axiom,
    ! [X1,X2] :
      ( is_fun1236654035i_bool(X1)
     => is_fun288122577l_bool(pi_Arr990697634t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___043,axiom,
    ! [X1,X2] :
      ( is_fun961089132t_bool(X2)
     => is_fun279392540l_bool(hAPP_f863359027l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___043) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_037,axiom,
    ! [X1,X2] :
      ( is_fun279392540l_bool(X2)
     => is_fun279392540l_bool(hAPP_f111185985l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_037) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__,axiom,
    ! [X1,X2] :
      ( is_bool(X2)
     => is_fun279392540l_bool(hAPP_b1812770943l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_005,axiom,
    ! [X1,X2] :
      ( is_Arr43961803e_indi(X2)
     => is_fun279392540l_bool(hAPP_A60074736l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_005) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc,axiom,
    ! [X1,X2] :
      ( is_Arr1861959080le_alt(X2)
     => is_fun279392540l_bool(hAPP_A187815023l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc) ).

fof(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa,axiom,
    ! [X1,X2] :
      ( is_fun961089132t_bool(X1)
     => is_fun279392540l_bool(pi_Pro666468413t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_031,axiom,
    ! [X1,X2] :
      ( is_fun158382675l_bool(X2)
     => is_fun158382675l_bool(hAPP_f1765205l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_031) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___,axiom,
    ! [X1,X2] :
      ( is_bool(X2)
     => is_fun158382675l_bool(hAPP_b517355696l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_004,axiom,
    ! [X1,X2] :
      ( is_Arr43961803e_indi(X2)
     => is_fun158382675l_bool(hAPP_A1112981887l_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_004) ).

fof(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oin,axiom,
    ! [X1,X2] :
      ( is_fun288122577l_bool(X1)
     => is_fun158382675l_bool(pi_fun150026276t_bool(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oin) ).

fof(fact_1167_mult__eq__self__implies__10,axiom,
    ! [X195,X197] :
      ( X195 = hAPP_nat_nat(times_times_nat(X195),X197)
     => ( X197 = one_one_nat
        | X195 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_mult__eq__self__implies__10) ).

fof(fact_1093_inj__Suc,axiom,
    ! [X209] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),X209)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_inj__Suc) ).

fof(fact_580_inj__on__id2,axiom,
    ! [X72] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_inj__on__id2) ).

fof(fact_1050_Nat_Oadd__0__right,axiom,
    ! [X195] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),zero_zero_nat) = X195,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_Nat_Oadd__0__right) ).

fof(fact_1154_mult__is__0,axiom,
    ! [X200,X27] :
      ( hAPP_nat_nat(times_times_nat(X200),X27) = zero_zero_nat
    <=> ( X200 = zero_zero_nat
        | X27 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_mult__is__0) ).

fof(fact_1049_plus__nat_Oadd__0,axiom,
    ! [X197] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X197) = X197,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_plus__nat_Oadd__0) ).

fof(fact_222_Pi__UNIV,axiom,
    ! [X72] : pi_Pro666468413t_bool(X72,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool)) = top_to1853035173l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Pi__UNIV) ).

fof(fact_223_Pi__UNIV,axiom,
    ! [X72] : pi_fun150026276t_bool(X72,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Pi__UNIV) ).

fof(fact_224_Pi__UNIV,axiom,
    ! [X72] : pi_Arr990697634t_bool(X72,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Pi__UNIV) ).

fof(fact_1145_nat__mult__eq__1__iff,axiom,
    ! [X200,X27] :
      ( hAPP_nat_nat(times_times_nat(X200),X27) = one_one_nat
    <=> ( X200 = one_one_nat
        & X27 = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_nat__mult__eq__1__iff) ).

fof(fact_1147_nat__1__eq__mult__iff,axiom,
    ! [X200,X27] :
      ( one_one_nat = hAPP_nat_nat(times_times_nat(X200),X27)
    <=> ( X200 = one_one_nat
        & X27 = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_nat__1__eq__mult__iff) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__047,axiom,
    ! [X1,X2] : is_fun1568535512t_bool(hAPP_P332578347t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__047) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_026,axiom,
    ! [X1,X2] : is_fun1568535512t_bool(hAPP_f1866147972t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_026) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Product__,axiom,
    ! [X1,X2] : is_fun1568535512t_bool(hAPP_f1061584978t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Product__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__013,axiom,
    ! [X1,X2] : is_fun1568535512t_bool(hAPP_f1891021702t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__013) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo,axiom,
    ! [X1,X2] : is_fun1568535512t_bool(hAPP_n454528608t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow____,axiom,
    ! [X1,X2] : is_fun2093718614t_bool(hAPP_f861874780t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow____) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn,axiom,
    ! [X1,X2] : is_fun2093718614t_bool(hAPP_n539120590t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_038,axiom,
    ! [X1,X2] : is_bool(hAPP_f22590837l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_038) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn,axiom,
    ! [X1,X2] : is_bool(hAPP_f1306865520l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_035,axiom,
    ! [X1,X2] : is_bool(hAPP_f866275871l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_035) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_034,axiom,
    ! [X1,X2] : is_bool(hAPP_f167218729l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_034) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,axiom,
    ! [X1,X2] : is_bool(hAPP_f560831258l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_033,axiom,
    ! [X1,X2] : is_bool(hAPP_f1644647260l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_033) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_032,axiom,
    ! [X1,X2] : is_bool(hAPP_f859154022l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_032) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,axiom,
    ! [X1,X2] : is_bool(hAPP_f10461143l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_029,axiom,
    ! [X1,X2] : is_bool(hAPP_f770608346l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_029) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_028,axiom,
    ! [X1,X2] : is_bool(hAPP_f597137892l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_028) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf,axiom,
    ! [X1,X2] : is_bool(hAPP_f1725204053l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_,axiom,
    ! [X1,X2] : is_bool(hAPP_f415146997l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It,axiom,
    ! [X1,X2] : is_bool(hAPP_f1846209297l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc,axiom,
    ! [X1,X2] : is_bool(hAPP_f1508442332l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__,axiom,
    ! [X1,X2] : is_bool(hAPP_f844512602l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_,axiom,
    ! [X1,X2] : is_bool(hAPP_f339859954l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_,axiom,
    ! [X1,X2] : is_bool(hAPP_f537623936l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
    ! [X1,X2] : is_bool(hAPP_f1637334154l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__,axiom,
    ! [X1,X2] : is_bool(hAPP_f795156475l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____,axiom,
    ! [X1,X2] : is_bool(hAPP_f1351174655l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____,axiom,
    ! [X1,X2] : is_bool(hAPP_f817604743l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O,axiom,
    ! [X1,X2] : is_bool(hAPP_f651410150l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M,axiom,
    ! [X1,X2] : is_bool(hAPP_f599145828l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_,axiom,
    ! [X1,X2] : is_bool(hAPP_f67777128l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_027,axiom,
    ! [X1,X2] : is_bool(hAPP_f1837019376l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_027) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_020,axiom,
    ! [X1,X2] : is_bool(hAPP_f785974231l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_020) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_019,axiom,
    ! [X1,X2] : is_bool(hAPP_f1252760917l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_019) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O,axiom,
    ! [X1,X2] : is_bool(hAPP_f1632652727l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
    ! [X1,X2] : is_bool(hAPP_f54304608l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
    ! [X1,X2] : is_bool(hAPP_f387058535l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__,axiom,
    ! [X1,X2] : is_bool(hAPP_f2013399995l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
    ! [X1,X2] : is_bool(hAPP_nat_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_,axiom,
    ! [X1,X2] : is_Arr43961803e_indi(hAPP_P710098616e_indi(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_023,axiom,
    ! [X1,X2] : is_Arr43961803e_indi(hAPP_f1693298207e_indi(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_023) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__010,axiom,
    ! [X1,X2] : is_Arr43961803e_indi(hAPP_f836059805e_indi(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__010) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__046,axiom,
    ! [X1,X2] : is_fun1236654035i_bool(hAPP_P1875867302i_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__046) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025,axiom,
    ! [X1,X2] : is_fun1236654035i_bool(hAPP_f1552576127i_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow_____016,axiom,
    ! [X1,X2] : is_fun1236654035i_bool(hAPP_f632777549i_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow_____016) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__012,axiom,
    ! [X1,X2] : is_fun1236654035i_bool(hAPP_f1948454017i_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__012) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007,axiom,
    ! [X1,X2] : is_fun1236654035i_bool(hAPP_n821919323i_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc_,axiom,
    ! [X1,X2] : is_fun961089132t_bool(hAPP_f899613158t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__015,hypothesis,
    ! [X1,X2] : is_fun961089132t_bool(hAPP_f412050202t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__015) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde,axiom,
    ! [X1,X2] : is_fun961089132t_bool(hAPP_P1341894483t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell,axiom,
    ! [X1,X2] : is_fun961089132t_bool(hAPP_n588788980t_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__,axiom,
    ! [X1,X2] : is_fun288122577l_bool(hAPP_f226010187l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order,axiom,
    ! [X1,X2] : is_fun288122577l_bool(hAPP_P254387896l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle,axiom,
    ! [X1,X2] : is_fun288122577l_bool(hAPP_n2095207769l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048,hypothesis,
    ! [X1,X2] : is_fun279392540l_bool(hAPP_P229966473l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___018,axiom,
    ! [X1,X2] : is_fun279392540l_bool(hAPP_f769545506l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___018) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__014,axiom,
    ! [X1,X2] : is_fun279392540l_bool(hAPP_f1277514478l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__014) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro,axiom,
    ! [X1,X2] : is_fun279392540l_bool(hAPP_P1294997365l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___,axiom,
    ! [X1,X2] : is_fun279392540l_bool(hAPP_n1674354836l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___017,axiom,
    ! [X1,X2] : is_fun158382675l_bool(hAPP_f1449238989l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___017) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow,axiom,
    ! [X1,X2] : is_fun158382675l_bool(hAPP_P1171466554l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____,axiom,
    ! [X1,X2] : is_fun158382675l_bool(hAPP_n295497947l_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____) ).

fof(fact_28_top1I,axiom,
    ! [X4] : hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_top1I) ).

fof(fact_25_top1I,axiom,
    ! [X4] : hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_top1I) ).

fof(fact_27_top1I,axiom,
    ! [X4] : hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_top1I) ).

fof(fact_26_top1I,axiom,
    ! [X4] : hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_top1I) ).

fof(fact_31_top1I,axiom,
    ! [X4] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_top1I) ).

fof(fact_30_top1I,axiom,
    ! [X4] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_top1I) ).

fof(fact_29_top1I,axiom,
    ! [X4] : hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_top1I) ).

fof(fact_1064_Suc__n__not__n,axiom,
    ! [X197] : hAPP_nat_nat(suc,X197) != X197,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_Suc__n__not__n) ).

fof(fact_1065_n__not__Suc__n,axiom,
    ! [X197] : X197 != hAPP_nat_nat(suc,X197),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1065_n__not__Suc__n) ).

fof(fact_1124_nat_Oexhaust,axiom,
    ! [X202] :
      ( X202 != zero_zero_nat
     => ~ ! [X222] : X202 != hAPP_nat_nat(suc,X222) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_nat_Oexhaust) ).

fof(fact_1123_not0__implies__Suc,axiom,
    ! [X197] :
      ( X197 != zero_zero_nat
     => ? [X30] : X197 = hAPP_nat_nat(suc,X30) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_not0__implies__Suc) ).

fof(fact_170_Collect__def,axiom,
    ! [X9] :
      ( is_fun1568535512t_bool(X9)
     => hAPP_f427533077t_bool(collect_Product_unit,X9) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Collect__def) ).

fof(fact_171_Collect__def,axiom,
    ! [X9] :
      ( is_fun1236654035i_bool(X9)
     => hAPP_f580451669i_bool(collec1611109369e_indi,X9) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Collect__def) ).

fof(fact_1069_Suc__not__Zero,axiom,
    ! [X195] : hAPP_nat_nat(suc,X195) != zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1069_Suc__not__Zero) ).

fof(fact_1068_nat_Osimps_I3_J,axiom,
    ! [X218] : hAPP_nat_nat(suc,X218) != zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_nat_Osimps_I3_J) ).

fof(fact_1066_Suc__neq__Zero,axiom,
    ! [X195] : hAPP_nat_nat(suc,X195) != zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_Suc__neq__Zero) ).

fof(fact_1071_Zero__not__Suc,axiom,
    ! [X195] : zero_zero_nat != hAPP_nat_nat(suc,X195),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1071_Zero__not__Suc) ).

fof(fact_1070_nat_Osimps_I2_J,axiom,
    ! [X219] : zero_zero_nat != hAPP_nat_nat(suc,X219),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_nat_Osimps_I2_J) ).

fof(fact_1067_Zero__neq__Suc,axiom,
    ! [X195] : zero_zero_nat != hAPP_nat_nat(suc,X195),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_Zero__neq__Suc) ).

fof(fact_1146_nat__mult__1__right,axiom,
    ! [X197] : hAPP_nat_nat(times_times_nat(X197),one_one_nat) = X197,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1146_nat__mult__1__right) ).

fof(fact_1155_mult__0__right,axiom,
    ! [X195] : hAPP_nat_nat(times_times_nat(X195),zero_zero_nat) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_mult__0__right) ).

fof(fact_1148_nat__mult__1,axiom,
    ! [X197] : hAPP_nat_nat(times_times_nat(one_one_nat),X197) = X197,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_nat__mult__1) ).

fof(fact_1156_mult__0,axiom,
    ! [X197] : hAPP_nat_nat(times_times_nat(zero_zero_nat),X197) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_mult__0) ).

fof(fact_1184_nat__size,axiom,
    ! [X197] : hAPP_nat_nat(size_size_nat,X197) = X197,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1184_nat__size) ).

fof(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
    ! [X227] : hAPP_nat_nat(cOMBI_nat,X227) = X227,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

fof(fact_172_Collect__def,axiom,
    ! [X9] : hAPP_f800510211t_bool(collect_nat,X9) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Collect__def) ).

fof(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp,axiom,
    ! [X227] :
      ( is_bool(X227)
     => ( X227 = fTrue
        | X227 = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) ).

fof(help_fFalse_1_1_T,axiom,
    ! [X227] :
      ( is_bool(X227)
     => ( X227 = fTrue
        | X227 = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

fof(help_fTrue_1_1_T,axiom,
    ! [X227] :
      ( is_bool(X227)
     => ( X227 = fTrue
        | X227 = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

fof(help_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

fof(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))),arrow_1721807329e_Prof)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).

fof(fact_183_n_I3_J,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_n_I3_J) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
    is_fun158382675l_bool(undefi1466315554l_bool(fun(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn,axiom,
    is_fun288122577l_bool(undefi203294880l_bool(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) ).

fof(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,h),n)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).

fof(fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

fof(fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
    is_fun279392540l_bool(undefi871250829l_bool(fun(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool),bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

fof(fact_71_assms_I1_J,axiom,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,f),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_assms_I1_J) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
    is_fun961089132t_bool(undefi1481304379t_bool(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    is_fun2093718614t_bool(undefi1931156935t_bool(fun(arrow_107136085le_alt,fun(arrow_107136085le_alt,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(fact_19_n_I1_J,axiom,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n_I1_J) ).

fof(fact_75__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lba),arrow_1681063817le_Lin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75__096Lba_A_058_ALin_096) ).

fof(fact_74__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lab),arrow_1681063817le_Lin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74__096Lab_A_058_ALin_096) ).

fof(fact_3__096P_A_058_AProf_096,axiom,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,p),arrow_1721807329e_Prof)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

fof(fact_1127_surjh,axiom,
    hAPP_f2026336507t_bool(image_579431497di_nat(h),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_surjh) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J,axiom,
    is_fun1568535512t_bool(undefi312741927t_bool(fun(product_unit,bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___001,axiom,
    is_fun1236654035i_bool(undefi1547870882i_bool(fun(arrow_1271263838e_indi,bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___001) ).

fof(fact_20_injh,axiom,
    hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(h),top_to1576102282i_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_injh) ).

fof(fact_179_UNIV__def,axiom,
    top_top_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_UNIV__def) ).

fof(fact_176_UNIV__def,axiom,
    top_to565915683t_bool = hAPP_f515126293t_bool(collec2096990994le_alt,hAPP_b1703662281t_bool(cOMBK_306730240le_alt,fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_UNIV__def) ).

fof(fact_173_UNIV__def,axiom,
    top_to1853035173l_bool = hAPP_f111185985l_bool(collec1553055422t_bool,hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_UNIV__def) ).

fof(fact_175_UNIV__def,axiom,
    top_to1714702858l_bool = hAPP_f1765205l_bool(collec418781817t_bool,hAPP_b517355696l_bool(cOMBK_1626390631t_bool,fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_UNIV__def) ).

fof(fact_174_UNIV__def,axiom,
    top_to522745736l_bool = hAPP_f146009813l_bool(collec1063742455t_bool,hAPP_b1048178734l_bool(cOMBK_272667621t_bool,fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_UNIV__def) ).

fof(fact_178_UNIV__def,axiom,
    top_to1257323279t_bool = hAPP_f427533077t_bool(collect_Product_unit,hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_UNIV__def) ).

fof(fact_177_UNIV__def,axiom,
    top_to1576102282i_bool = hAPP_f580451669i_bool(collec1611109369e_indi,hAPP_b1337486384i_bool(cOMBK_575487463e_indi,fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_UNIV__def) ).

fof(fact_579_Prof__def,axiom,
    arrow_1721807329e_Prof = pi_Arr990697634t_bool(top_to1576102282i_bool,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,arrow_1681063817le_Lin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_Prof__def) ).

fof(fact_1135_greaterThan__0,axiom,
    hAPP_n1699378549t_bool(ord_greaterThan_nat,zero_zero_nat) = hAPP_f800510211t_bool(image_nat_nat(suc),top_top_fun_nat_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1135_greaterThan__0) ).

fof(fact_1_u,axiom,
    hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,f)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_u) ).

fof(fact_0_assms_I3_J,axiom,
    hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,f)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).

fof(fact_1031_finite__indi,axiom,
    hBOOL(hAPP_f1599966040l_bool(finite106199483e_indi,top_to1576102282i_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_finite__indi) ).

fof(fact_1035_card__UNIV__unit,axiom,
    hAPP_f2030293770ol_nat(finite1949902593t_unit,top_to1257323279t_bool) = one_one_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1035_card__UNIV__unit) ).

fof(fact_1187_bool_Osize_I1_J,axiom,
    hAPP_bool_nat(bool_size,fTrue) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_bool_Osize_I1_J) ).

fof(fact_1188_bool_Osize_I2_J,axiom,
    hAPP_bool_nat(bool_size,fFalse) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_bool_Osize_I2_J) ).

fof(fact_1185_nat_Osize_I3_J,axiom,
    hAPP_nat_nat(size_size_nat,zero_zero_nat) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_nat_Osize_I3_J) ).

fof(fact_1182_nat_Osize_I1_J,axiom,
    hAPP_nat_nat(nat_size,zero_zero_nat) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_nat_Osize_I1_J) ).

fof(fact_1197_atLeast__0,axiom,
    hAPP_n1699378549t_bool(ord_atLeast_nat,zero_zero_nat) = top_top_fun_nat_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_atLeast__0) ).

fof(fact_1109_One__nat__def,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1109_One__nat__def) ).

fof(gsy_c_HOL_Oundefined_000tc__HOL__Obool,axiom,
    is_bool(undefined_bool(bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__HOL__Obool) ).

fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi,axiom,
    is_Arr43961803e_indi(undefi237088188e_indi(arrow_1271263838e_indi)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi) ).

fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt,axiom,
    is_Arr1861959080le_alt(undefi462180727le_alt(arrow_107136085le_alt)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt) ).

fof(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL,axiom,
    is_fun1568535512t_bool(top_to1257323279t_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____,axiom,
    is_fun2093718614t_bool(top_to178429151t_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____) ).

fof(gsy_c_fTrue,axiom,
    is_bool(fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fTrue) ).

fof(gsy_c_fFalse,axiom,
    is_bool(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool,axiom,
    is_bool(top_top_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____002,axiom,
    is_fun1236654035i_bool(top_to1576102282i_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____002) ).

fof(gsy_v_e____,axiom,
    is_Arr1861959080le_alt(e),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_e____) ).

fof(gsy_v_d____,hypothesis,
    is_Arr1861959080le_alt(d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_d____) ).

fof(gsy_v_c____,hypothesis,
    is_Arr1861959080le_alt(c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_c____) ).

fof(gsy_v_b____,axiom,
    is_Arr1861959080le_alt(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_b____) ).

fof(gsy_v_a____,axiom,
    is_Arr1861959080le_alt(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_a____) ).

fof(gsy_v_Lba____,axiom,
    is_fun961089132t_bool(lba),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_Lba____) ).

fof(gsy_v_Lab____,axiom,
    is_fun961089132t_bool(lab),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_Lab____) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir,axiom,
    is_fun961089132t_bool(top_to565915683t_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira,axiom,
    is_fun288122577l_bool(top_to522745736l_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OProf,axiom,
    is_fun288122577l_bool(arrow_1721807329e_Prof),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OProf) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord,axiom,
    is_fun279392540l_bool(top_to1853035173l_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OLin,axiom,
    is_fun279392540l_bool(arrow_1681063817le_Lin),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OLin) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde,axiom,
    is_fun158382675l_bool(top_to1714702858l_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Ounanimity,axiom,
    is_fun158382675l_bool(arrow_1587283740nimity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Ounanimity) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OIIA,axiom,
    is_fun158382675l_bool(arrow_1654180089le_IIA),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OIIA) ).

fof(fact_2__096c_A_126_061_Ad_096,axiom,
    c != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).

fof(fact_76__096a_A_126_061_Ab_096,axiom,
    a != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76__096a_A_126_061_Ab_096) ).

fof(i_0_1362,plain,
    ! [X14] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X14)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => ( ( hAPP_A1637648121di_nat(h,X14) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X14)),c),e))) )
            & ( hAPP_A1637648121di_nat(h,X14) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X14)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_1363,plain,
    ~ ! [X78] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X78),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)))
       => ( ! [X30] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X78))
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X30))),lab)),lba)))) )
         => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X78),one_one_nat)))),lab)),lba)))) ) ),
    inference(fof_simplification,[status(thm)],[fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_]) ).

fof(i_0_1364,plain,
    ! [X26,X220] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X220))
     => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),X220))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X26)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X220))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X26))))) ),
    inference(fof_simplification,[status(thm)],[fact_1114_card__less__Suc2]) ).

fof(i_0_1365,plain,
    ! [X14] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X14)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => ( ( hAPP_A1637648121di_nat(h,X14) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X14)),c),e))) )
            & ( hAPP_A1637648121di_nat(h,X14) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X14)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am]) ).

fof(i_0_1366,plain,
    ! [X14] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X14)))
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X14)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X14)),n))
         => ( ( hAPP_A1637648121di_nat(h,X14) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X14)),c),e))) )
            & ( hAPP_A1637648121di_nat(h,X14) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X14)),e))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J]) ).

fof(i_0_1367,plain,
    ! [X4561] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | hAPP_A1637648121di_nat(h,X4561) != n
        | hAPP_A1637648121di_nat(h,X4561) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | hAPP_A1637648121di_nat(h,X4561) != n
        | hAPP_A1637648121di_nat(h,X4561) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | hAPP_A1637648121di_nat(h,X4561) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | hAPP_A1637648121di_nat(h,X4561) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | hAPP_A1637648121di_nat(h,X4561) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | hAPP_A1637648121di_nat(h,X4561) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | hAPP_A1637648121di_nat(h,X4561) != n
        | hAPP_A1637648121di_nat(h,X4561) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | hAPP_A1637648121di_nat(h,X4561) != n
        | hAPP_A1637648121di_nat(h,X4561) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | hAPP_A1637648121di_nat(h,X4561) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | hAPP_A1637648121di_nat(h,X4561) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | hAPP_A1637648121di_nat(h,X4561) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | hAPP_A1637648121di_nat(h,X4561) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hAPP_A1637648121di_nat(h,X4561) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hAPP_A1637648121di_nat(h,X4561) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hAPP_A1637648121di_nat(h,X4561) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( hAPP_A1637648121di_nat(h,X4561) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) )
      & ( hAPP_A1637648121di_nat(h,X4561) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) )
      & ( hAPP_A1637648121di_nat(h,X4561) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4561)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) )
      & ( hAPP_A1637648121di_nat(h,X4561) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4561)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) )
      & ( hAPP_A1637648121di_nat(h,X4561) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4561)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4561)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1362])])]) ).

fof(i_0_1368,plain,
    ! [X4,X5,X6] :
      ( ( is_Arr1861959080le_alt(X4)
        & is_Arr1861959080le_alt(X5) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
       => ( X4 != X5
         => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),X6))
          <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X5),X4)),X6)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_86_notin__Lin__iff]) ).

fof(i_0_1369,plain,
    ! [X12,X13,X6] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6),arrow_1681063817le_Lin))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X12),X13)),X6))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X13),X12)),X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_87_Lin__irrefl]) ).

fof(i_0_1370,plain,
    ! [X195,X196,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X195),X196)),X197))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X196),X197)) ) ),
    inference(fof_simplification,[status(thm)],[fact_904_add__leE]) ).

fof(i_0_1371,plain,
    ! [X207,X208] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X207),X208)),X207)),
    inference(fof_simplification,[status(thm)],[fact_999_not__add__less1]) ).

fof(i_0_1372,plain,
    ! [X208,X207] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X208),X207)),X207)),
    inference(fof_simplification,[status(thm)],[fact_1000_not__add__less2]) ).

fof(i_0_1373,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X75),pi_Pro1928973619le_alt(X72,X76)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X75,X4)),hAPP_P1341894483t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_193_PiE]) ).

fof(i_0_1374,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X75),pi_boo115158845le_alt(X72,X76)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X75,X4)),hAPP_b1703662281t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_192_PiE]) ).

fof(i_0_1375,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X75),pi_Arr1199386158le_alt(X72,X76)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X75,X4)),hAPP_A1677245848t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_191_PiE]) ).

fof(i_0_1376,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X75),pi_fun150026276t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X75,X4)),hAPP_f1277514478l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_219_PiE]) ).

fof(i_0_1377,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X75),pi_Pro718203741t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X75,X4)),hAPP_P1294997365l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_201_PiE]) ).

fof(i_0_1378,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X75),pi_boo538701011t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X75,X4)),hAPP_b1812770943l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_200_PiE]) ).

fof(i_0_1379,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X75),pi_Arr990697634t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X75,X4)),hAPP_A60074736l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_220_PiE]) ).

fof(i_0_1380,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X75),pi_Pro1880661658t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X75,X4)),hAPP_P1171466554l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_199_PiE]) ).

fof(i_0_1381,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X75),pi_boo1117000868t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X75,X4)),hAPP_b517355696l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_198_PiE]) ).

fof(i_0_1382,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X75),pi_Arr1936979349t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X75,X4)),hAPP_A1112981887l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_197_PiE]) ).

fof(i_0_1383,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X75),pi_Pro610293528t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X75,X4)),hAPP_P254387896l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_196_PiE]) ).

fof(i_0_1384,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X75),pi_boo175444770t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X75,X4)),hAPP_b1048178734l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_195_PiE]) ).

fof(i_0_1385,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X75),pi_Arr2020412179t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X75,X4)),hAPP_A1952883197l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_194_PiE]) ).

fof(i_0_1386,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X75),pi_nat_Product_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X75,X4)),hAPP_n454528608t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_218_PiE]) ).

fof(i_0_1387,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X75),pi_fun308431217t_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X75,X4)),hAPP_f1710744577t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_215_PiE]) ).

fof(i_0_1388,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X75),pi_fun321364250t_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X75,X4)),hAPP_f1866147972t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_212_PiE]) ).

fof(i_0_1389,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X75),pi_fun1877263000t_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X75,X4)),hAPP_f1891021702t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_209_PiE]) ).

fof(i_0_1390,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X75),pi_Pro1122146355t_unit(X72,X76)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X75,X4)),hAPP_P332578347t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_206_PiE]) ).

fof(i_0_1391,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X75),pi_Product_unit_nat(X72,X76)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X75,X4)),hAPP_P32877782t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_204_PiE]) ).

fof(i_0_1392,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X75),pi_bool_nat(X72,X76)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X75,X4)),hAPP_b1013836512t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_203_PiE]) ).

fof(i_0_1393,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X75),pi_Arr346900227di_nat(X72,X76)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X75,X4)),hAPP_A2046586321t_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_202_PiE]) ).

fof(i_0_1394,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X75),pi_Pro666468413t_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X75,X4)),hAPP_P324742453l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_190_PiE]) ).

fof(i_0_1395,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X75),pi_fun1575168891l_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X75,X4)),hAPP_f210572555l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_214_PiE]) ).

fof(i_0_1396,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X75),pi_fun52649508l_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X75,X4)),hAPP_f1624277646l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_211_PiE]) ).

fof(i_0_1397,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X75),pi_fun823343522l_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X75,X4)),hAPP_f839832464l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_208_PiE]) ).

fof(i_0_1398,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X75),pi_nat_bool(X72,X76)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X75,X4)),hAPP_n1006566506l_bool(X76,X4)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_217_PiE]) ).

fof(i_0_1399,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X75),pi_Pro1270767662e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X75,X4)),hAPP_P1875867302i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_205_PiE]) ).

fof(i_0_1400,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X75),pi_fun896360044e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X75,X4)),hAPP_f244157820i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_213_PiE]) ).

fof(i_0_1401,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X75),pi_fun1002945429e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X75,X4)),hAPP_f1552576127i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_210_PiE]) ).

fof(i_0_1402,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X75),pi_fun753830419e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X75,X4)),hAPP_f1948454017i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_207_PiE]) ).

fof(i_0_1403,plain,
    ! [X4,X75,X72,X76] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X75),pi_nat660525389e_indi(X72,X76)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X75,X4)),hAPP_n821919323i_bool(X76,X4)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_216_PiE]) ).

fof(i_0_1404,plain,
    ! [X27,X9] :
      ( ~ hBOOL(hAPP_nat_bool(X9,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X9,X27))
       => ? [X211] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X211),X27))
            & ! [X14] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X211))
               => ~ hBOOL(hAPP_nat_bool(X9,X14)) )
            & hBOOL(hAPP_nat_bool(X9,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X211),one_one_nat))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_1056_ex__least__nat__less]) ).

fof(i_0_1405,plain,
    ! [X200,X27] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X27))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X27)),X200)) ),
    inference(fof_simplification,[status(thm)],[fact_1091_not__less__eq__eq]) ).

fof(i_0_1406,plain,
    ! [X27,X9] :
      ( ~ hBOOL(hAPP_nat_bool(X9,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X9,X27))
       => ? [X211] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X211),X27))
            & ! [X14] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X211))
               => ~ hBOOL(hAPP_nat_bool(X9,X14)) )
            & hBOOL(hAPP_nat_bool(X9,X211)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_1057_ex__least__nat__le]) ).

fof(i_0_1407,plain,
    ~ ! [X29] :
        ( is_fun961089132t_bool(X29)
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),X29))
         => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X29),arrow_1681063817le_Lin)) ) ),
    inference(fof_simplification,[status(thm)],[fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_]) ).

fof(i_0_1408,plain,
    ~ ! [X28] :
        ( is_fun961089132t_bool(X28)
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),X28))
         => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X28),arrow_1681063817le_Lin)) ) ),
    inference(fof_simplification,[status(thm)],[fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_]) ).

fof(i_0_1409,plain,
    ! [X200,X27] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X200),X27))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),hAPP_nat_nat(suc,X200))) ),
    inference(fof_simplification,[status(thm)],[fact_1082_not__less__eq]) ).

fof(i_0_1410,plain,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),hAPP_nat_nat(suc,X197)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X195),X197))
       => X195 = hAPP_nat_nat(suc,X197) ) ),
    inference(fof_simplification,[status(thm)],[fact_1087_le__SucE]) ).

fof(i_0_1411,plain,
    ! [X75,X81] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X75),X81))
    <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X75),X81))
        & ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X81),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_712_less__fun__def]) ).

fof(i_0_1412,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X5))
        & ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_392_less__le__not__le]) ).

fof(i_0_1413,plain,
    ! [X75,X81] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X75),X81))
    <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X75),X81))
        & ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X81),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_709_less__fun__def]) ).

fof(i_0_1414,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4),X5))
    <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X5))
        & ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_389_less__le__not__le]) ).

fof(i_0_1415,plain,
    ! [X75,X81] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X75),X81))
    <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X75),X81))
        & ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X81),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_710_less__fun__def]) ).

fof(i_0_1416,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4),X5))
    <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X5))
        & ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_390_less__le__not__le]) ).

fof(i_0_1417,plain,
    ! [X75,X81] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X75),X81))
    <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X75),X81))
        & ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X81),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_711_less__fun__def]) ).

fof(i_0_1418,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4),X5))
    <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X5))
        & ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_391_less__le__not__le]) ).

fof(i_0_1419,plain,
    ! [X75,X81] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X75),X81))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X75),X81))
        & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X81),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_707_less__fun__def]) ).

fof(i_0_1420,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X5))
        & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_387_less__le__not__le]) ).

fof(i_0_1421,plain,
    ! [X75,X81] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X75),X81))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X75),X81))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X81),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_714_less__fun__def]) ).

fof(i_0_1422,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X5))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_395_less__le__not__le]) ).

fof(i_0_1423,plain,
    ! [X75,X81] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X75),X81))
    <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X75),X81))
        & ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X81),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_708_less__fun__def]) ).

fof(i_0_1424,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
    <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X5))
        & ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_388_less__le__not__le]) ).

fof(i_0_1425,plain,
    ! [X75,X81] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X75),X81))
    <=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X75),X81))
        & ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X81),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_713_less__fun__def]) ).

fof(i_0_1426,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X4),X5))
    <=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X5))
        & ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_394_less__le__not__le]) ).

fof(i_0_1427,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_396_less__le__not__le]) ).

fof(i_0_1428,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4),X5))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X5))
        & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5),X4)) ) ),
    inference(fof_simplification,[status(thm)],[fact_393_less__le__not__le]) ).

fof(i_0_1429,plain,
    ! [X27,X200] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),X200))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),hAPP_nat_nat(suc,X200)))
      <=> X27 = X200 ) ),
    inference(fof_simplification,[status(thm)],[fact_1079_not__less__less__Suc__eq]) ).

fof(i_0_1430,plain,
    ! [X197,X195] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),X195))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),hAPP_nat_nat(suc,X195)))
       => X195 = X197 ) ),
    inference(fof_simplification,[status(thm)],[fact_1078_less__antisym]) ).

fof(i_0_1431,plain,
    ! [X195,X197] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),hAPP_nat_nat(suc,X197)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X195),X197))
       => X195 = X197 ) ),
    inference(fof_simplification,[status(thm)],[fact_1074_less__SucE]) ).

fof(i_0_1432,plain,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X197)),X197)),
    inference(fof_simplification,[status(thm)],[fact_1092_Suc__n__not__le__n]) ).

fof(i_0_1433,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
      <=> X4 = X5 ) ),
    inference(fof_simplification,[status(thm)],[fact_441_linorder__antisym__conv2]) ).

fof(i_0_1434,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_146_order__less__not__sym]) ).

fof(i_0_1435,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_142_order__less__imp__not__less]) ).

fof(i_0_1436,plain,
    ! [X12,X13] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),X13))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_126_order__less__asym_H]) ).

fof(i_0_1437,plain,
    ! [X13,X12] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X13),X12))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X12),X13)) ),
    inference(fof_simplification,[status(thm)],[fact_122_xt1_I9_J]) ).

fof(i_0_1438,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X5))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_94_order__less__asym]) ).

fof(i_0_1439,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_145_order__less__not__sym]) ).

fof(i_0_1440,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_141_order__less__imp__not__less]) ).

fof(i_0_1441,plain,
    ! [X12,X13] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),X13))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_125_order__less__asym_H]) ).

fof(i_0_1442,plain,
    ! [X13,X12] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X13),X12))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X12),X13)) ),
    inference(fof_simplification,[status(thm)],[fact_121_xt1_I9_J]) ).

fof(i_0_1443,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X5))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_93_order__less__asym]) ).

fof(i_0_1444,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_147_order__less__not__sym]) ).

fof(i_0_1445,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_143_order__less__imp__not__less]) ).

fof(i_0_1446,plain,
    ! [X12,X13] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),X13))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_127_order__less__asym_H]) ).

fof(i_0_1447,plain,
    ! [X13,X12] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X13),X12))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X12),X13)) ),
    inference(fof_simplification,[status(thm)],[fact_123_xt1_I9_J]) ).

fof(i_0_1448,plain,
    ! [X4,X5] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X5))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_95_order__less__asym]) ).

fof(i_0_1449,plain,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_375_linorder__not__le]) ).

fof(i_0_1450,plain,
    ! [X118,X119] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X118),X119))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X119),X118)) ),
    inference(fof_simplification,[status(thm)],[fact_430_leD]) ).

fof(i_0_1451,plain,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X4)) ),
    inference(fof_simplification,[status(thm)],[fact_374_linorder__not__less]) ).

fof(i_0_1452,plain,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X4))
        | X4 = X5 ) ),
    inference(fof_simplification,[status(thm)],[fact_156_not__less__iff__gr__or__eq]) ).

fof(i_0_1453,plain,
    ! [X63,X64] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X63),X64))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X64),X63)) ),
    inference(fof_simplification,[status(thm)],[fact_148_order__less__not__sym]) ).

fof(i_0_1454,plain,
    ! [X61,X62] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X61),X62))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X62),X61)) ),
    inference(fof_simplification,[status(thm)],[fact_144_order__less__imp__not__less]) ).

fof(i_0_1455,plain,
    ! [X55,X56] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X55),X56))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X55)) ),
    inference(fof_simplification,[status(thm)],[fact_128_order__less__asym_H]) ).

fof(i_0_1456,plain,
    ! [X53,X54] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X53),X54))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X54),X53)) ),
    inference(fof_simplification,[status(thm)],[fact_124_xt1_I9_J]) ).

fof(i_0_1457,plain,
    ! [X33,X34] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X33),X34))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X34),X33)) ),
    inference(fof_simplification,[status(thm)],[fact_96_order__less__asym]) ).

fof(i_0_1458,plain,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X5))
      <=> X4 = X5 ) ),
    inference(fof_simplification,[status(thm)],[fact_409_linorder__antisym__conv1]) ).

fof(i_0_1459,plain,
    ! [X201,X202] :
      ( X201 != X202
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X201),X202))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X202),X201)) ) ),
    inference(fof_simplification,[status(thm)],[fact_983_linorder__neqE__nat]) ).

fof(i_0_1460,plain,
    ! [X5,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X4))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X5))
      <=> X4 = X5 ) ),
    inference(fof_simplification,[status(thm)],[fact_154_linorder__antisym__conv3]) ).

fof(i_0_1461,plain,
    ! [X67,X68] :
      ( X67 != X68
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X67),X68))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X68),X67)) ) ),
    inference(fof_simplification,[status(thm)],[fact_153_linorder__neqE]) ).

fof(i_0_1462,plain,
    ! [X31,X32] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X31),X32))
     => ( X31 != X32
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X31)) ) ),
    inference(fof_simplification,[status(thm)],[fact_92_linorder__cases]) ).

fof(i_0_1463,plain,
    ! [X79,X80] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X79),X80))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X80),X79)) ),
    inference(fof_simplification,[status(thm)],[fact_238_linorder__le__cases]) ).

fof(i_0_1464,plain,
    ! [X110,X111] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X110),X111))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X111),X110)) ),
    inference(fof_simplification,[status(thm)],[fact_407_leI]) ).

fof(i_0_1465,plain,
    ! [X112,X113] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X112),X113))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X113),X112)) ),
    inference(fof_simplification,[status(thm)],[fact_408_not__leE]) ).

fof(i_0_1466,plain,
    ! [X227,X228] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X227),X228))
      | hBOOL(X227) ),
    inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).

fof(i_0_1467,plain,
    ! [X227,X228] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X227),X228))
      | hBOOL(X228) ),
    inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).

fof(i_0_1468,plain,
    ! [X201,X202] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X201),X202))
      | X201 = X202 ),
    inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000tc__Nat__Onat_T]) ).

fof(i_0_1469,plain,
    ! [X4] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X4)),
    inference(fof_simplification,[status(thm)],[fact_159_order__less__irrefl]) ).

fof(i_0_1470,plain,
    ! [X4] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X4)),
    inference(fof_simplification,[status(thm)],[fact_158_order__less__irrefl]) ).

fof(i_0_1471,plain,
    ! [X4] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X4)),
    inference(fof_simplification,[status(thm)],[fact_160_order__less__irrefl]) ).

fof(i_0_1472,plain,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),X197)),
    inference(fof_simplification,[status(thm)],[fact_984_less__irrefl__nat]) ).

fof(i_0_1473,plain,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),X197)),
    inference(fof_simplification,[status(thm)],[fact_981_less__not__refl]) ).

fof(i_0_1474,plain,
    ! [X71] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X71),X71)),
    inference(fof_simplification,[status(thm)],[fact_161_order__less__irrefl]) ).

fof(i_0_1475,plain,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),zero_zero_nat)),
    inference(fof_simplification,[status(thm)],[fact_1046_less__nat__zero__code]) ).

fof(i_0_1476,plain,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),zero_zero_nat)),
    inference(fof_simplification,[status(thm)],[fact_1044_not__less0]) ).

fof(i_0_1477,plain,
    ! [X197] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X197),zero_zero_nat)),
    inference(fof_simplification,[status(thm)],[fact_1042_less__zeroE]) ).

fof(i_0_1478,plain,
    ! [X12] : ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),X12)),
    inference(fof_simplification,[status(thm)],[fact_59_not__top__less]) ).

fof(i_0_1479,plain,
    ! [X12] : ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),X12)),
    inference(fof_simplification,[status(thm)],[fact_55_not__top__less]) ).

fof(i_0_1480,plain,
    ! [X12] : ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),X12)),
    inference(fof_simplification,[status(thm)],[fact_57_not__top__less]) ).

fof(i_0_1481,plain,
    ! [X12] : ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),X12)),
    inference(fof_simplification,[status(thm)],[fact_56_not__top__less]) ).

fof(i_0_1482,plain,
    ! [X12] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),X12)),
    inference(fof_simplification,[status(thm)],[fact_62_not__top__less]) ).

fof(i_0_1483,plain,
    ! [X12] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),X12)),
    inference(fof_simplification,[status(thm)],[fact_61_not__top__less]) ).

fof(i_0_1484,plain,
    ! [X12] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),X12)),
    inference(fof_simplification,[status(thm)],[fact_60_not__top__less]) ).

fof(i_0_1485,plain,
    ! [X12] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),X12)),
    inference(fof_simplification,[status(thm)],[fact_58_not__top__less]) ).

fof(i_0_1486,plain,
    ! [X228,X227] :
      ( ~ hBOOL(X227)
      | ~ hBOOL(X228)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X227),X228)) ),
    inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).

fof(i_0_1487,plain,
    ! [X72,X76] :
      ( X72 = X76
     => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X72),X76))
         => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X76),X72)) ) ),
    inference(fof_simplification,[status(thm)],[fact_953_equalityE]) ).

fof(i_0_1488,plain,
    ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) )
    & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba))))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am]) ).

fof(i_0_1489,plain,
    ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba)))) )
    & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba))))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_1490,plain,
    ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) )
    & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))) ) ),
    inference(fof_nnf,[status(thm)],[fact_14_PW]) ).

fof(i_0_1491,plain,
    ! [X4435,X4436,X4437,X4438,X4439,X4440] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_f412050202t_bool(f,X4436)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_f412050202t_bool(f,X4435)))
        | is_Arr43961803e_indi(esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4435),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4436),arrow_1721807329e_Prof))
        | X4440 = X4437
        | X4439 = X4438
        | X4437 = X4438
        | X4439 = X4440
        | ~ is_Arr1861959080le_alt(X4437)
        | ~ is_Arr1861959080le_alt(X4438)
        | ~ is_Arr1861959080le_alt(X4439)
        | ~ is_Arr1861959080le_alt(X4440) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_f412050202t_bool(f,X4435)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_f412050202t_bool(f,X4436)))
        | is_Arr43961803e_indi(esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4435),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4436),arrow_1721807329e_Prof))
        | X4440 = X4437
        | X4439 = X4438
        | X4437 = X4438
        | X4439 = X4440
        | ~ is_Arr1861959080le_alt(X4437)
        | ~ is_Arr1861959080le_alt(X4438)
        | ~ is_Arr1861959080le_alt(X4439)
        | ~ is_Arr1861959080le_alt(X4440) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_f412050202t_bool(f,X4436)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_f412050202t_bool(f,X4435)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_A1677245848t_bool(X4436,esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_A1677245848t_bool(X4435,esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4435),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4436),arrow_1721807329e_Prof))
        | X4440 = X4437
        | X4439 = X4438
        | X4437 = X4438
        | X4439 = X4440
        | ~ is_Arr1861959080le_alt(X4437)
        | ~ is_Arr1861959080le_alt(X4438)
        | ~ is_Arr1861959080le_alt(X4439)
        | ~ is_Arr1861959080le_alt(X4440) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_f412050202t_bool(f,X4435)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_f412050202t_bool(f,X4436)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_A1677245848t_bool(X4436,esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_A1677245848t_bool(X4435,esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4435),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4436),arrow_1721807329e_Prof))
        | X4440 = X4437
        | X4439 = X4438
        | X4437 = X4438
        | X4439 = X4440
        | ~ is_Arr1861959080le_alt(X4437)
        | ~ is_Arr1861959080le_alt(X4438)
        | ~ is_Arr1861959080le_alt(X4439)
        | ~ is_Arr1861959080le_alt(X4440) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_f412050202t_bool(f,X4436)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_f412050202t_bool(f,X4435)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_A1677245848t_bool(X4436,esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_A1677245848t_bool(X4435,esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4435),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4436),arrow_1721807329e_Prof))
        | X4440 = X4437
        | X4439 = X4438
        | X4437 = X4438
        | X4439 = X4440
        | ~ is_Arr1861959080le_alt(X4437)
        | ~ is_Arr1861959080le_alt(X4438)
        | ~ is_Arr1861959080le_alt(X4439)
        | ~ is_Arr1861959080le_alt(X4440) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_f412050202t_bool(f,X4435)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_f412050202t_bool(f,X4436)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4439),X4440)),hAPP_A1677245848t_bool(X4436,esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4437),X4438)),hAPP_A1677245848t_bool(X4435,esk1_6(X4435,X4436,X4437,X4438,X4439,X4440))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4435),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4436),arrow_1721807329e_Prof))
        | X4440 = X4437
        | X4439 = X4438
        | X4437 = X4438
        | X4439 = X4440
        | ~ is_Arr1861959080le_alt(X4437)
        | ~ is_Arr1861959080le_alt(X4438)
        | ~ is_Arr1861959080le_alt(X4439)
        | ~ is_Arr1861959080le_alt(X4440) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6__C2_C])])])]) ).

fof(i_0_1492,plain,
    ! [X4442,X4443,X4444,X4445,X4446,X4447] :
      ( ( is_Arr43961803e_indi(esk2_6(X4442,X4443,X4444,X4445,X4446,X4447))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4446),X4447)),hAPP_f412050202t_bool(f,X4443)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4444),X4445)),hAPP_f412050202t_bool(f,X4442)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4442),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4443),arrow_1721807329e_Prof))
        | X4447 = X4444
        | X4446 = X4445
        | X4444 = X4445
        | X4446 = X4447
        | ~ is_Arr1861959080le_alt(X4444)
        | ~ is_Arr1861959080le_alt(X4445)
        | ~ is_Arr1861959080le_alt(X4446)
        | ~ is_Arr1861959080le_alt(X4447) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4446),X4447)),hAPP_A1677245848t_bool(X4443,esk2_6(X4442,X4443,X4444,X4445,X4446,X4447))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4444),X4445)),hAPP_A1677245848t_bool(X4442,esk2_6(X4442,X4443,X4444,X4445,X4446,X4447))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4446),X4447)),hAPP_f412050202t_bool(f,X4443)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4444),X4445)),hAPP_f412050202t_bool(f,X4442)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4442),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4443),arrow_1721807329e_Prof))
        | X4447 = X4444
        | X4446 = X4445
        | X4444 = X4445
        | X4446 = X4447
        | ~ is_Arr1861959080le_alt(X4444)
        | ~ is_Arr1861959080le_alt(X4445)
        | ~ is_Arr1861959080le_alt(X4446)
        | ~ is_Arr1861959080le_alt(X4447) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4446),X4447)),hAPP_A1677245848t_bool(X4443,esk2_6(X4442,X4443,X4444,X4445,X4446,X4447))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4444),X4445)),hAPP_A1677245848t_bool(X4442,esk2_6(X4442,X4443,X4444,X4445,X4446,X4447))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4446),X4447)),hAPP_f412050202t_bool(f,X4443)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4444),X4445)),hAPP_f412050202t_bool(f,X4442)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4442),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4443),arrow_1721807329e_Prof))
        | X4447 = X4444
        | X4446 = X4445
        | X4444 = X4445
        | X4446 = X4447
        | ~ is_Arr1861959080le_alt(X4444)
        | ~ is_Arr1861959080le_alt(X4445)
        | ~ is_Arr1861959080le_alt(X4446)
        | ~ is_Arr1861959080le_alt(X4447) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_7__C1_C])])])]) ).

fof(i_0_1493,plain,
    ! [X4455,X4456,X4457,X4458,X4459,X4460] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_f412050202t_bool(f,X4456)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_f412050202t_bool(f,X4455)))
        | is_Arr43961803e_indi(esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4455),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4456),arrow_1721807329e_Prof))
        | X4457 = X4458
        | X4459 = X4460
        | ~ is_Arr1861959080le_alt(X4457)
        | ~ is_Arr1861959080le_alt(X4458)
        | ~ is_Arr1861959080le_alt(X4459)
        | ~ is_Arr1861959080le_alt(X4460) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_f412050202t_bool(f,X4455)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_f412050202t_bool(f,X4456)))
        | is_Arr43961803e_indi(esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4455),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4456),arrow_1721807329e_Prof))
        | X4457 = X4458
        | X4459 = X4460
        | ~ is_Arr1861959080le_alt(X4457)
        | ~ is_Arr1861959080le_alt(X4458)
        | ~ is_Arr1861959080le_alt(X4459)
        | ~ is_Arr1861959080le_alt(X4460) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_f412050202t_bool(f,X4456)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_f412050202t_bool(f,X4455)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_A1677245848t_bool(X4456,esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_A1677245848t_bool(X4455,esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4455),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4456),arrow_1721807329e_Prof))
        | X4457 = X4458
        | X4459 = X4460
        | ~ is_Arr1861959080le_alt(X4457)
        | ~ is_Arr1861959080le_alt(X4458)
        | ~ is_Arr1861959080le_alt(X4459)
        | ~ is_Arr1861959080le_alt(X4460) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_f412050202t_bool(f,X4455)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_f412050202t_bool(f,X4456)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_A1677245848t_bool(X4456,esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_A1677245848t_bool(X4455,esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4455),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4456),arrow_1721807329e_Prof))
        | X4457 = X4458
        | X4459 = X4460
        | ~ is_Arr1861959080le_alt(X4457)
        | ~ is_Arr1861959080le_alt(X4458)
        | ~ is_Arr1861959080le_alt(X4459)
        | ~ is_Arr1861959080le_alt(X4460) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_f412050202t_bool(f,X4456)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_f412050202t_bool(f,X4455)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_A1677245848t_bool(X4456,esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_A1677245848t_bool(X4455,esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4455),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4456),arrow_1721807329e_Prof))
        | X4457 = X4458
        | X4459 = X4460
        | ~ is_Arr1861959080le_alt(X4457)
        | ~ is_Arr1861959080le_alt(X4458)
        | ~ is_Arr1861959080le_alt(X4459)
        | ~ is_Arr1861959080le_alt(X4460) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_f412050202t_bool(f,X4455)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_f412050202t_bool(f,X4456)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4459),X4460)),hAPP_A1677245848t_bool(X4456,esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4457),X4458)),hAPP_A1677245848t_bool(X4455,esk4_6(X4455,X4456,X4457,X4458,X4459,X4460))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4455),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4456),arrow_1721807329e_Prof))
        | X4457 = X4458
        | X4459 = X4460
        | ~ is_Arr1861959080le_alt(X4457)
        | ~ is_Arr1861959080le_alt(X4458)
        | ~ is_Arr1861959080le_alt(X4459)
        | ~ is_Arr1861959080le_alt(X4460) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_9_pairwise__neutrality])])])]) ).

fof(i_0_1494,plain,
    ! [X4935] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk28_0),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)))
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4935),esk28_0))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X4935))),lab)),lba)))) )
      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk28_0),one_one_nat)))),lab)),lba)))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1363])])])]) ).

fof(i_0_1495,plain,
    ! [X4933] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk27_0),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)))
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4933),esk27_0))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X4933))),lab)),lba)))) )
      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk27_0),one_one_nat)))),lab)),lba)))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I])])])]) ).

fof(i_0_1496,plain,
    ! [X4484,X4485,X4486,X4487,X4488,X4490,X4495] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4485)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4486)))
        | is_Arr43961803e_indi(esk9_5(X4484,X4485,X4486,X4487,X4488))
        | ~ is_Arr1861959080le_alt(X4487)
        | ~ is_Arr1861959080le_alt(X4488)
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4486),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4485),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4484)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4486)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4485)))
        | is_Arr43961803e_indi(esk9_5(X4484,X4485,X4486,X4487,X4488))
        | ~ is_Arr1861959080le_alt(X4487)
        | ~ is_Arr1861959080le_alt(X4488)
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4486),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4485),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4484)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4485)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4486)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_A1677245848t_bool(X4485,esk9_5(X4484,X4485,X4486,X4487,X4488))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_A1677245848t_bool(X4486,esk9_5(X4484,X4485,X4486,X4487,X4488))))
        | ~ is_Arr1861959080le_alt(X4487)
        | ~ is_Arr1861959080le_alt(X4488)
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4486),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4485),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4484)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4486)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4485)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_A1677245848t_bool(X4485,esk9_5(X4484,X4485,X4486,X4487,X4488))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_A1677245848t_bool(X4486,esk9_5(X4484,X4485,X4486,X4487,X4488))))
        | ~ is_Arr1861959080le_alt(X4487)
        | ~ is_Arr1861959080le_alt(X4488)
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4486),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4485),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4484)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4485)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4486)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_A1677245848t_bool(X4485,esk9_5(X4484,X4485,X4486,X4487,X4488))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_A1677245848t_bool(X4486,esk9_5(X4484,X4485,X4486,X4487,X4488))))
        | ~ is_Arr1861959080le_alt(X4487)
        | ~ is_Arr1861959080le_alt(X4488)
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4486),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4485),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4484)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4486)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_f412050202t_bool(X4484,X4485)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_A1677245848t_bool(X4485,esk9_5(X4484,X4485,X4486,X4487,X4488))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4487),X4488)),hAPP_A1677245848t_bool(X4486,esk9_5(X4484,X4485,X4486,X4487,X4488))))
        | ~ is_Arr1861959080le_alt(X4487)
        | ~ is_Arr1861959080le_alt(X4488)
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4486),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4485),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4484)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk10_1(X4490)),arrow_1721807329e_Prof))
        | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4490)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk11_1(X4490)),arrow_1721807329e_Prof))
        | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4490)) )
      & ( is_Arr1861959080le_alt(esk12_1(X4490))
        | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4490)) )
      & ( is_Arr1861959080le_alt(esk13_1(X4490))
        | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4490)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X4490)),esk13_1(X4490))),hAPP_A1677245848t_bool(esk10_1(X4490),X4495)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X4490)),esk13_1(X4490))),hAPP_A1677245848t_bool(esk11_1(X4490),X4495)))
        | ~ is_Arr43961803e_indi(X4495)
        | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4490)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X4490)),esk13_1(X4490))),hAPP_A1677245848t_bool(esk11_1(X4490),X4495)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X4490)),esk13_1(X4490))),hAPP_A1677245848t_bool(esk10_1(X4490),X4495)))
        | ~ is_Arr43961803e_indi(X4495)
        | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4490)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X4490)),esk13_1(X4490))),hAPP_f412050202t_bool(X4490,esk10_1(X4490))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X4490)),esk13_1(X4490))),hAPP_f412050202t_bool(X4490,esk11_1(X4490))))
        | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4490)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X4490)),esk13_1(X4490))),hAPP_f412050202t_bool(X4490,esk10_1(X4490))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X4490)),esk13_1(X4490))),hAPP_f412050202t_bool(X4490,esk11_1(X4490))))
        | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X4490)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_23_IIA__def])])])])])]) ).

fof(i_0_1497,plain,
    ! [X4449,X4450,X4451,X4452,X4453] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_f412050202t_bool(f,X4450)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_f412050202t_bool(f,X4449)))
        | is_Arr43961803e_indi(esk3_5(X4449,X4450,X4451,X4452,X4453))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4449),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4450),arrow_1721807329e_Prof))
        | X4452 = X4451
        | X4453 = X4451
        | X4452 = X4453
        | ~ is_Arr1861959080le_alt(X4451)
        | ~ is_Arr1861959080le_alt(X4452)
        | ~ is_Arr1861959080le_alt(X4453) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_f412050202t_bool(f,X4449)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_f412050202t_bool(f,X4450)))
        | is_Arr43961803e_indi(esk3_5(X4449,X4450,X4451,X4452,X4453))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4449),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4450),arrow_1721807329e_Prof))
        | X4452 = X4451
        | X4453 = X4451
        | X4452 = X4453
        | ~ is_Arr1861959080le_alt(X4451)
        | ~ is_Arr1861959080le_alt(X4452)
        | ~ is_Arr1861959080le_alt(X4453) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_f412050202t_bool(f,X4450)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_f412050202t_bool(f,X4449)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_A1677245848t_bool(X4450,esk3_5(X4449,X4450,X4451,X4452,X4453))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_A1677245848t_bool(X4449,esk3_5(X4449,X4450,X4451,X4452,X4453))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4449),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4450),arrow_1721807329e_Prof))
        | X4452 = X4451
        | X4453 = X4451
        | X4452 = X4453
        | ~ is_Arr1861959080le_alt(X4451)
        | ~ is_Arr1861959080le_alt(X4452)
        | ~ is_Arr1861959080le_alt(X4453) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_f412050202t_bool(f,X4449)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_f412050202t_bool(f,X4450)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_A1677245848t_bool(X4450,esk3_5(X4449,X4450,X4451,X4452,X4453))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_A1677245848t_bool(X4449,esk3_5(X4449,X4450,X4451,X4452,X4453))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4449),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4450),arrow_1721807329e_Prof))
        | X4452 = X4451
        | X4453 = X4451
        | X4452 = X4453
        | ~ is_Arr1861959080le_alt(X4451)
        | ~ is_Arr1861959080le_alt(X4452)
        | ~ is_Arr1861959080le_alt(X4453) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_f412050202t_bool(f,X4450)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_f412050202t_bool(f,X4449)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_A1677245848t_bool(X4450,esk3_5(X4449,X4450,X4451,X4452,X4453))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_A1677245848t_bool(X4449,esk3_5(X4449,X4450,X4451,X4452,X4453))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4449),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4450),arrow_1721807329e_Prof))
        | X4452 = X4451
        | X4453 = X4451
        | X4452 = X4453
        | ~ is_Arr1861959080le_alt(X4451)
        | ~ is_Arr1861959080le_alt(X4452)
        | ~ is_Arr1861959080le_alt(X4453) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_f412050202t_bool(f,X4449)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_f412050202t_bool(f,X4450)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4452),X4453)),hAPP_A1677245848t_bool(X4450,esk3_5(X4449,X4450,X4451,X4452,X4453))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4453),X4451)),hAPP_A1677245848t_bool(X4449,esk3_5(X4449,X4450,X4451,X4452,X4453))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4449),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4450),arrow_1721807329e_Prof))
        | X4452 = X4451
        | X4453 = X4451
        | X4452 = X4453
        | ~ is_Arr1861959080le_alt(X4451)
        | ~ is_Arr1861959080le_alt(X4452)
        | ~ is_Arr1861959080le_alt(X4453) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_8__C4_C])])])]) ).

fof(i_0_1498,plain,
    ! [X4562] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4562),n))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X4562))),lab)),lba)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_n_I2_J])]) ).

fof(i_0_1499,plain,
    ! [X4558] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X4558))),lab)),lba)),arrow_1721807329e_Prof)),
    inference(variable_rename,[status(thm)],[fact_81_PiProf]) ).

fof(i_0_1500,plain,
    ! [X6723,X6724,X6725,X6726] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk245_4(X6723,X6724,X6725,X6726)),esk244_4(X6723,X6724,X6725,X6726)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X6724,X6723)),X6726))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6723),X6725))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X6724,X6725)),X6726)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X6724,esk245_4(X6723,X6724,X6725,X6726))),hAPP_f899613158t_bool(X6724,esk244_4(X6723,X6724,X6725,X6726))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X6724,X6723)),X6726))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6723),X6725))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X6724,X6725)),X6726)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_787_xt4])])])]) ).

fof(i_0_1501,plain,
    ! [X7221,X7222,X7223,X7224] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk410_4(X7221,X7222,X7223,X7224)),esk411_4(X7221,X7222,X7223,X7224)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X7221,X7223)),X7222))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X7221,X7224)),X7222))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7223),X7224)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X7221,esk410_4(X7221,X7222,X7223,X7224))),hAPP_f899613158t_bool(X7221,esk411_4(X7221,X7222,X7223,X7224))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X7221,X7223)),X7222))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X7221,X7224)),X7222))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7223),X7224)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_870_order__le__less__subst2])])])]) ).

fof(i_0_1502,plain,
    ! [X6669,X6670,X6671,X6672] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk227_4(X6669,X6670,X6671,X6672)),esk226_4(X6669,X6670,X6671,X6672)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6670,X6669)),X6672))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6669),X6671))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6670,X6671)),X6672)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X6670,esk227_4(X6669,X6670,X6671,X6672))),hAPP_n588788980t_bool(X6670,esk226_4(X6669,X6670,X6671,X6672))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6670,X6669)),X6672))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6669),X6671))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6670,X6671)),X6672)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_778_xt4])])])]) ).

fof(i_0_1503,plain,
    ! [X6597,X6598,X6599,X6600] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk203_4(X6597,X6598,X6599,X6600)),esk202_4(X6597,X6598,X6599,X6600)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6598,X6597)),X6600))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6597),X6599))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X6598,X6599)),X6600)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6598,esk203_4(X6597,X6598,X6599,X6600))),hAPP_n588788980t_bool(X6598,esk202_4(X6597,X6598,X6599,X6600))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6598,X6597)),X6600))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6597),X6599))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X6598,X6599)),X6600)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_766_xt6])])])]) ).

fof(i_0_1504,plain,
    ! [X7167,X7168,X7169,X7170] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk392_4(X7167,X7168,X7169,X7170)),esk393_4(X7167,X7168,X7169,X7170)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X7167,X7169)),X7168))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X7167,X7170)),X7168))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7169),X7170)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X7167,esk392_4(X7167,X7168,X7169,X7170))),hAPP_n588788980t_bool(X7167,esk393_4(X7167,X7168,X7169,X7170))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X7167,X7169)),X7168))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X7167,X7170)),X7168))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7169),X7170)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_861_order__le__less__subst2])])])]) ).

fof(i_0_1505,plain,
    ! [X7389,X7390,X7391,X7392] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk466_4(X7389,X7390,X7391,X7392)),esk467_4(X7389,X7390,X7391,X7392)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X7389,X7391)),X7390))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X7389,X7392)),X7390))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7391),X7392)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X7389,esk466_4(X7389,X7390,X7391,X7392))),hAPP_n588788980t_bool(X7389,esk467_4(X7389,X7390,X7391,X7392))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X7389,X7391)),X7390))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X7389,X7392)),X7390))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7391),X7392)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_898_order__less__le__subst2])])])]) ).

fof(i_0_1506,plain,
    ! [X6705,X6706,X6707,X6708] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk239_4(X6705,X6706,X6707,X6708)),esk238_4(X6705,X6706,X6707,X6708)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X6706,X6705)),X6708))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6705),X6707))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X6706,X6707)),X6708)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X6706,esk239_4(X6705,X6706,X6707,X6708))),hAPP_f769545506l_bool(X6706,esk238_4(X6705,X6706,X6707,X6708))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X6706,X6705)),X6708))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6705),X6707))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X6706,X6707)),X6708)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_784_xt4])])])]) ).

fof(i_0_1507,plain,
    ! [X7203,X7204,X7205,X7206] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk404_4(X7203,X7204,X7205,X7206)),esk405_4(X7203,X7204,X7205,X7206)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X7203,X7205)),X7204))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X7203,X7206)),X7204))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7205),X7206)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X7203,esk404_4(X7203,X7204,X7205,X7206))),hAPP_f769545506l_bool(X7203,esk405_4(X7203,X7204,X7205,X7206))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X7203,X7205)),X7204))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X7203,X7206)),X7204))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7205),X7206)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_867_order__le__less__subst2])])])]) ).

fof(i_0_1508,plain,
    ! [X6651,X6652,X6653,X6654] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk221_4(X6651,X6652,X6653,X6654)),esk220_4(X6651,X6652,X6653,X6654)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6652,X6651)),X6654))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6651),X6653))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6652,X6653)),X6654)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X6652,esk221_4(X6651,X6652,X6653,X6654))),hAPP_n1674354836l_bool(X6652,esk220_4(X6651,X6652,X6653,X6654))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6652,X6651)),X6654))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6651),X6653))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6652,X6653)),X6654)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_775_xt4])])])]) ).

fof(i_0_1509,plain,
    ! [X6579,X6580,X6581,X6582] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk197_4(X6579,X6580,X6581,X6582)),esk196_4(X6579,X6580,X6581,X6582)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6580,X6579)),X6582))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6579),X6581))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X6580,X6581)),X6582)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6580,esk197_4(X6579,X6580,X6581,X6582))),hAPP_n1674354836l_bool(X6580,esk196_4(X6579,X6580,X6581,X6582))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6580,X6579)),X6582))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6579),X6581))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X6580,X6581)),X6582)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_763_xt6])])])]) ).

fof(i_0_1510,plain,
    ! [X7149,X7150,X7151,X7152] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk386_4(X7149,X7150,X7151,X7152)),esk387_4(X7149,X7150,X7151,X7152)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X7149,X7151)),X7150))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X7149,X7152)),X7150))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7151),X7152)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X7149,esk386_4(X7149,X7150,X7151,X7152))),hAPP_n1674354836l_bool(X7149,esk387_4(X7149,X7150,X7151,X7152))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X7149,X7151)),X7150))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X7149,X7152)),X7150))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7151),X7152)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_858_order__le__less__subst2])])])]) ).

fof(i_0_1511,plain,
    ! [X7371,X7372,X7373,X7374] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk460_4(X7371,X7372,X7373,X7374)),esk461_4(X7371,X7372,X7373,X7374)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X7371,X7373)),X7372))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X7371,X7374)),X7372))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7373),X7374)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X7371,esk460_4(X7371,X7372,X7373,X7374))),hAPP_n1674354836l_bool(X7371,esk461_4(X7371,X7372,X7373,X7374))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X7371,X7373)),X7372))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X7371,X7374)),X7372))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7373),X7374)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_895_order__less__le__subst2])])])]) ).

fof(i_0_1512,plain,
    ! [X6711,X6712,X6713,X6714] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk241_4(X6711,X6712,X6713,X6714)),esk240_4(X6711,X6712,X6713,X6714)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X6712,X6711)),X6714))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6711),X6713))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X6712,X6713)),X6714)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X6712,esk241_4(X6711,X6712,X6713,X6714))),hAPP_f1449238989l_bool(X6712,esk240_4(X6711,X6712,X6713,X6714))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X6712,X6711)),X6714))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6711),X6713))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X6712,X6713)),X6714)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_785_xt4])])])]) ).

fof(i_0_1513,plain,
    ! [X7209,X7210,X7211,X7212] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk406_4(X7209,X7210,X7211,X7212)),esk407_4(X7209,X7210,X7211,X7212)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X7209,X7211)),X7210))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X7209,X7212)),X7210))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7211),X7212)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X7209,esk406_4(X7209,X7210,X7211,X7212))),hAPP_f1449238989l_bool(X7209,esk407_4(X7209,X7210,X7211,X7212))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X7209,X7211)),X7210))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X7209,X7212)),X7210))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7211),X7212)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_868_order__le__less__subst2])])])]) ).

fof(i_0_1514,plain,
    ! [X6657,X6658,X6659,X6660] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk223_4(X6657,X6658,X6659,X6660)),esk222_4(X6657,X6658,X6659,X6660)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6658,X6657)),X6660))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6657),X6659))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6658,X6659)),X6660)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X6658,esk223_4(X6657,X6658,X6659,X6660))),hAPP_n295497947l_bool(X6658,esk222_4(X6657,X6658,X6659,X6660))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6658,X6657)),X6660))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6657),X6659))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6658,X6659)),X6660)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_776_xt4])])])]) ).

fof(i_0_1515,plain,
    ! [X6585,X6586,X6587,X6588] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk199_4(X6585,X6586,X6587,X6588)),esk198_4(X6585,X6586,X6587,X6588)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6586,X6585)),X6588))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6585),X6587))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X6586,X6587)),X6588)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6586,esk199_4(X6585,X6586,X6587,X6588))),hAPP_n295497947l_bool(X6586,esk198_4(X6585,X6586,X6587,X6588))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6586,X6585)),X6588))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6585),X6587))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X6586,X6587)),X6588)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_764_xt6])])])]) ).

fof(i_0_1516,plain,
    ! [X7155,X7156,X7157,X7158] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk388_4(X7155,X7156,X7157,X7158)),esk389_4(X7155,X7156,X7157,X7158)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X7155,X7157)),X7156))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X7155,X7158)),X7156))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7157),X7158)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X7155,esk388_4(X7155,X7156,X7157,X7158))),hAPP_n295497947l_bool(X7155,esk389_4(X7155,X7156,X7157,X7158))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X7155,X7157)),X7156))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X7155,X7158)),X7156))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7157),X7158)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_859_order__le__less__subst2])])])]) ).

fof(i_0_1517,plain,
    ! [X7377,X7378,X7379,X7380] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk462_4(X7377,X7378,X7379,X7380)),esk463_4(X7377,X7378,X7379,X7380)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X7377,X7379)),X7378))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X7377,X7380)),X7378))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7379),X7380)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X7377,esk462_4(X7377,X7378,X7379,X7380))),hAPP_n295497947l_bool(X7377,esk463_4(X7377,X7378,X7379,X7380))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X7377,X7379)),X7378))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X7377,X7380)),X7378))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7379),X7380)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_896_order__less__le__subst2])])])]) ).

fof(i_0_1518,plain,
    ! [X6717,X6718,X6719,X6720] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk243_4(X6717,X6718,X6719,X6720)),esk242_4(X6717,X6718,X6719,X6720)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X6718,X6717)),X6720))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6717),X6719))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X6718,X6719)),X6720)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X6718,esk243_4(X6717,X6718,X6719,X6720))),hAPP_f226010187l_bool(X6718,esk242_4(X6717,X6718,X6719,X6720))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X6718,X6717)),X6720))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6717),X6719))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X6718,X6719)),X6720)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_786_xt4])])])]) ).

fof(i_0_1519,plain,
    ! [X7215,X7216,X7217,X7218] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk408_4(X7215,X7216,X7217,X7218)),esk409_4(X7215,X7216,X7217,X7218)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X7215,X7217)),X7216))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X7215,X7218)),X7216))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7217),X7218)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X7215,esk408_4(X7215,X7216,X7217,X7218))),hAPP_f226010187l_bool(X7215,esk409_4(X7215,X7216,X7217,X7218))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X7215,X7217)),X7216))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X7215,X7218)),X7216))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7217),X7218)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_869_order__le__less__subst2])])])]) ).

fof(i_0_1520,plain,
    ! [X6663,X6664,X6665,X6666] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk225_4(X6663,X6664,X6665,X6666)),esk224_4(X6663,X6664,X6665,X6666)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6664,X6663)),X6666))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6663),X6665))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6664,X6665)),X6666)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X6664,esk225_4(X6663,X6664,X6665,X6666))),hAPP_n2095207769l_bool(X6664,esk224_4(X6663,X6664,X6665,X6666))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6664,X6663)),X6666))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6663),X6665))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6664,X6665)),X6666)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_777_xt4])])])]) ).

fof(i_0_1521,plain,
    ! [X6591,X6592,X6593,X6594] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk201_4(X6591,X6592,X6593,X6594)),esk200_4(X6591,X6592,X6593,X6594)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6592,X6591)),X6594))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6591),X6593))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X6592,X6593)),X6594)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6592,esk201_4(X6591,X6592,X6593,X6594))),hAPP_n2095207769l_bool(X6592,esk200_4(X6591,X6592,X6593,X6594))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6592,X6591)),X6594))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6591),X6593))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X6592,X6593)),X6594)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_765_xt6])])])]) ).

fof(i_0_1522,plain,
    ! [X7161,X7162,X7163,X7164] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk390_4(X7161,X7162,X7163,X7164)),esk391_4(X7161,X7162,X7163,X7164)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X7161,X7163)),X7162))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X7161,X7164)),X7162))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7163),X7164)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X7161,esk390_4(X7161,X7162,X7163,X7164))),hAPP_n2095207769l_bool(X7161,esk391_4(X7161,X7162,X7163,X7164))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X7161,X7163)),X7162))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X7161,X7164)),X7162))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7163),X7164)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_860_order__le__less__subst2])])])]) ).

fof(i_0_1523,plain,
    ! [X7383,X7384,X7385,X7386] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk464_4(X7383,X7384,X7385,X7386)),esk465_4(X7383,X7384,X7385,X7386)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X7383,X7385)),X7384))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X7383,X7386)),X7384))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7385),X7386)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X7383,esk464_4(X7383,X7384,X7385,X7386))),hAPP_n2095207769l_bool(X7383,esk465_4(X7383,X7384,X7385,X7386))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X7383,X7385)),X7384))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X7383,X7386)),X7384))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7385),X7386)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_897_order__less__le__subst2])])])]) ).

fof(i_0_1524,plain,
    ! [X6693,X6694,X6695,X6696] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk235_4(X6693,X6694,X6695,X6696)),esk234_4(X6693,X6694,X6695,X6696)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X6694,X6693)),X6696))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6693),X6695))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X6694,X6695)),X6696)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X6694,esk235_4(X6693,X6694,X6695,X6696))),hAPP_f1061584978t_bool(X6694,esk234_4(X6693,X6694,X6695,X6696))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X6694,X6693)),X6696))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6693),X6695))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X6694,X6695)),X6696)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_782_xt4])])])]) ).

fof(i_0_1525,plain,
    ! [X7191,X7192,X7193,X7194] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk400_4(X7191,X7192,X7193,X7194)),esk401_4(X7191,X7192,X7193,X7194)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X7191,X7193)),X7192))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X7191,X7194)),X7192))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7193),X7194)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X7191,esk400_4(X7191,X7192,X7193,X7194))),hAPP_f1061584978t_bool(X7191,esk401_4(X7191,X7192,X7193,X7194))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X7191,X7193)),X7192))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X7191,X7194)),X7192))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7193),X7194)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_865_order__le__less__subst2])])])]) ).

fof(i_0_1526,plain,
    ! [X6639,X6640,X6641,X6642] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk217_4(X6639,X6640,X6641,X6642)),esk216_4(X6639,X6640,X6641,X6642)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6640,X6639)),X6642))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6639),X6641))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6640,X6641)),X6642)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X6640,esk217_4(X6639,X6640,X6641,X6642))),hAPP_n454528608t_bool(X6640,esk216_4(X6639,X6640,X6641,X6642))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6640,X6639)),X6642))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6639),X6641))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6640,X6641)),X6642)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_773_xt4])])])]) ).

fof(i_0_1527,plain,
    ! [X6567,X6568,X6569,X6570] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk193_4(X6567,X6568,X6569,X6570)),esk192_4(X6567,X6568,X6569,X6570)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6568,X6567)),X6570))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6567),X6569))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X6568,X6569)),X6570)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6568,esk193_4(X6567,X6568,X6569,X6570))),hAPP_n454528608t_bool(X6568,esk192_4(X6567,X6568,X6569,X6570))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6568,X6567)),X6570))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6567),X6569))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X6568,X6569)),X6570)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_761_xt6])])])]) ).

fof(i_0_1528,plain,
    ! [X7137,X7138,X7139,X7140] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk382_4(X7137,X7138,X7139,X7140)),esk383_4(X7137,X7138,X7139,X7140)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X7137,X7139)),X7138))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X7137,X7140)),X7138))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7139),X7140)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X7137,esk382_4(X7137,X7138,X7139,X7140))),hAPP_n454528608t_bool(X7137,esk383_4(X7137,X7138,X7139,X7140))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X7137,X7139)),X7138))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X7137,X7140)),X7138))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7139),X7140)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_856_order__le__less__subst2])])])]) ).

fof(i_0_1529,plain,
    ! [X7359,X7360,X7361,X7362] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk456_4(X7359,X7360,X7361,X7362)),esk457_4(X7359,X7360,X7361,X7362)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X7359,X7361)),X7360))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X7359,X7362)),X7360))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7361),X7362)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X7359,esk456_4(X7359,X7360,X7361,X7362))),hAPP_n454528608t_bool(X7359,esk457_4(X7359,X7360,X7361,X7362))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X7359,X7361)),X7360))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X7359,X7362)),X7360))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7361),X7362)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_893_order__less__le__subst2])])])]) ).

fof(i_0_1530,plain,
    ! [X6783,X6784,X6785,X6786] :
      ( ( is_fun2093718614t_bool(esk264_4(X6783,X6784,X6785,X6786))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X6784,X6783)),X6786))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6783),X6785))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X6784,X6785)),X6786)) )
      & ( is_fun2093718614t_bool(esk265_4(X6783,X6784,X6785,X6786))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X6784,X6783)),X6786))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6783),X6785))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X6784,X6785)),X6786)) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk265_4(X6783,X6784,X6785,X6786)),esk264_4(X6783,X6784,X6785,X6786)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X6784,X6783)),X6786))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6783),X6785))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X6784,X6785)),X6786)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X6784,esk265_4(X6783,X6784,X6785,X6786))),hAPP_f1363542492t_bool(X6784,esk264_4(X6783,X6784,X6785,X6786))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X6784,X6783)),X6786))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6783),X6785))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X6784,X6785)),X6786)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_797_xt4])])])]) ).

fof(i_0_1531,plain,
    ! [X7281,X7282,X7283,X7284] :
      ( ( is_fun2093718614t_bool(esk430_4(X7281,X7282,X7283,X7284))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X7281,X7283)),X7282))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X7281,X7284)),X7282))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7283),X7284)) )
      & ( is_fun2093718614t_bool(esk431_4(X7281,X7282,X7283,X7284))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X7281,X7283)),X7282))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X7281,X7284)),X7282))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7283),X7284)) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk430_4(X7281,X7282,X7283,X7284)),esk431_4(X7281,X7282,X7283,X7284)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X7281,X7283)),X7282))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X7281,X7284)),X7282))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7283),X7284)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X7281,esk430_4(X7281,X7282,X7283,X7284))),hAPP_f1363542492t_bool(X7281,esk431_4(X7281,X7282,X7283,X7284))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X7281,X7283)),X7282))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X7281,X7284)),X7282))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7283),X7284)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_880_order__le__less__subst2])])])]) ).

fof(i_0_1532,plain,
    ! [X6759,X6760,X6761,X6762] :
      ( ( is_fun961089132t_bool(esk256_4(X6759,X6760,X6761,X6762))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X6760,X6759)),X6762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6759),X6761))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X6760,X6761)),X6762)) )
      & ( is_fun961089132t_bool(esk257_4(X6759,X6760,X6761,X6762))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X6760,X6759)),X6762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6759),X6761))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X6760,X6761)),X6762)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk257_4(X6759,X6760,X6761,X6762)),esk256_4(X6759,X6760,X6761,X6762)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X6760,X6759)),X6762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6759),X6761))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X6760,X6761)),X6762)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X6760,esk257_4(X6759,X6760,X6761,X6762))),hAPP_f856106132t_bool(X6760,esk256_4(X6759,X6760,X6761,X6762))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X6760,X6759)),X6762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6759),X6761))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X6760,X6761)),X6762)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_793_xt4])])])]) ).

fof(i_0_1533,plain,
    ! [X7257,X7258,X7259,X7260] :
      ( ( is_fun961089132t_bool(esk422_4(X7257,X7258,X7259,X7260))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X7257,X7259)),X7258))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X7257,X7260)),X7258))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7259),X7260)) )
      & ( is_fun961089132t_bool(esk423_4(X7257,X7258,X7259,X7260))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X7257,X7259)),X7258))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X7257,X7260)),X7258))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7259),X7260)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk422_4(X7257,X7258,X7259,X7260)),esk423_4(X7257,X7258,X7259,X7260)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X7257,X7259)),X7258))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X7257,X7260)),X7258))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7259),X7260)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X7257,esk422_4(X7257,X7258,X7259,X7260))),hAPP_f856106132t_bool(X7257,esk423_4(X7257,X7258,X7259,X7260))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X7257,X7259)),X7258))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X7257,X7260)),X7258))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7259),X7260)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_876_order__le__less__subst2])])])]) ).

fof(i_0_1534,plain,
    ! [X6753,X6754,X6755,X6756] :
      ( ( is_fun288122577l_bool(esk254_4(X6753,X6754,X6755,X6756))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X6754,X6753)),X6756))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6753),X6755))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X6754,X6755)),X6756)) )
      & ( is_fun288122577l_bool(esk255_4(X6753,X6754,X6755,X6756))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X6754,X6753)),X6756))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6753),X6755))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X6754,X6755)),X6756)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk255_4(X6753,X6754,X6755,X6756)),esk254_4(X6753,X6754,X6755,X6756)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X6754,X6753)),X6756))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6753),X6755))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X6754,X6755)),X6756)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X6754,esk255_4(X6753,X6754,X6755,X6756))),hAPP_f985923321t_bool(X6754,esk254_4(X6753,X6754,X6755,X6756))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X6754,X6753)),X6756))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6753),X6755))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X6754,X6755)),X6756)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_792_xt4])])])]) ).

fof(i_0_1535,plain,
    ! [X7251,X7252,X7253,X7254] :
      ( ( is_fun288122577l_bool(esk420_4(X7251,X7252,X7253,X7254))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X7251,X7253)),X7252))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X7251,X7254)),X7252))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7253),X7254)) )
      & ( is_fun288122577l_bool(esk421_4(X7251,X7252,X7253,X7254))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X7251,X7253)),X7252))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X7251,X7254)),X7252))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7253),X7254)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk420_4(X7251,X7252,X7253,X7254)),esk421_4(X7251,X7252,X7253,X7254)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X7251,X7253)),X7252))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X7251,X7254)),X7252))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7253),X7254)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X7251,esk420_4(X7251,X7252,X7253,X7254))),hAPP_f985923321t_bool(X7251,esk421_4(X7251,X7252,X7253,X7254))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X7251,X7253)),X7252))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X7251,X7254)),X7252))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7253),X7254)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_875_order__le__less__subst2])])])]) ).

fof(i_0_1536,plain,
    ! [X6747,X6748,X6749,X6750] :
      ( ( is_fun158382675l_bool(esk252_4(X6747,X6748,X6749,X6750))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X6748,X6747)),X6750))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6747),X6749))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X6748,X6749)),X6750)) )
      & ( is_fun158382675l_bool(esk253_4(X6747,X6748,X6749,X6750))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X6748,X6747)),X6750))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6747),X6749))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X6748,X6749)),X6750)) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk253_4(X6747,X6748,X6749,X6750)),esk252_4(X6747,X6748,X6749,X6750)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X6748,X6747)),X6750))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6747),X6749))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X6748,X6749)),X6750)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X6748,esk253_4(X6747,X6748,X6749,X6750))),hAPP_f839525755t_bool(X6748,esk252_4(X6747,X6748,X6749,X6750))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X6748,X6747)),X6750))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6747),X6749))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X6748,X6749)),X6750)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_791_xt4])])])]) ).

fof(i_0_1537,plain,
    ! [X7245,X7246,X7247,X7248] :
      ( ( is_fun158382675l_bool(esk418_4(X7245,X7246,X7247,X7248))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X7245,X7247)),X7246))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X7245,X7248)),X7246))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7247),X7248)) )
      & ( is_fun158382675l_bool(esk419_4(X7245,X7246,X7247,X7248))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X7245,X7247)),X7246))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X7245,X7248)),X7246))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7247),X7248)) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk418_4(X7245,X7246,X7247,X7248)),esk419_4(X7245,X7246,X7247,X7248)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X7245,X7247)),X7246))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X7245,X7248)),X7246))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7247),X7248)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X7245,esk418_4(X7245,X7246,X7247,X7248))),hAPP_f839525755t_bool(X7245,esk419_4(X7245,X7246,X7247,X7248))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X7245,X7247)),X7246))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X7245,X7248)),X7246))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7247),X7248)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_874_order__le__less__subst2])])])]) ).

fof(i_0_1538,plain,
    ! [X6741,X6742,X6743,X6744] :
      ( ( is_fun279392540l_bool(esk250_4(X6741,X6742,X6743,X6744))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X6742,X6741)),X6744))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6741),X6743))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X6742,X6743)),X6744)) )
      & ( is_fun279392540l_bool(esk251_4(X6741,X6742,X6743,X6744))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X6742,X6741)),X6744))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6741),X6743))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X6742,X6743)),X6744)) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk251_4(X6741,X6742,X6743,X6744)),esk250_4(X6741,X6742,X6743,X6744)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X6742,X6741)),X6744))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6741),X6743))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X6742,X6743)),X6744)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X6742,esk251_4(X6741,X6742,X6743,X6744))),hAPP_f464145314t_bool(X6742,esk250_4(X6741,X6742,X6743,X6744))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X6742,X6741)),X6744))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6741),X6743))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X6742,X6743)),X6744)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_790_xt4])])])]) ).

fof(i_0_1539,plain,
    ! [X7239,X7240,X7241,X7242] :
      ( ( is_fun279392540l_bool(esk416_4(X7239,X7240,X7241,X7242))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X7239,X7241)),X7240))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X7239,X7242)),X7240))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7241),X7242)) )
      & ( is_fun279392540l_bool(esk417_4(X7239,X7240,X7241,X7242))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X7239,X7241)),X7240))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X7239,X7242)),X7240))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7241),X7242)) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk416_4(X7239,X7240,X7241,X7242)),esk417_4(X7239,X7240,X7241,X7242)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X7239,X7241)),X7240))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X7239,X7242)),X7240))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7241),X7242)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X7239,esk416_4(X7239,X7240,X7241,X7242))),hAPP_f464145314t_bool(X7239,esk417_4(X7239,X7240,X7241,X7242))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X7239,X7241)),X7240))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X7239,X7242)),X7240))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7241),X7242)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_873_order__le__less__subst2])])])]) ).

fof(i_0_1540,plain,
    ! [X6771,X6772,X6773,X6774] :
      ( ( is_fun1236654035i_bool(esk260_4(X6771,X6772,X6773,X6774))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6772,X6771)),X6774))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6771),X6773))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6772,X6773)),X6774)) )
      & ( is_fun1236654035i_bool(esk261_4(X6771,X6772,X6773,X6774))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6772,X6771)),X6774))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6771),X6773))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6772,X6773)),X6774)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk261_4(X6771,X6772,X6773,X6774)),esk260_4(X6771,X6772,X6773,X6774)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6772,X6771)),X6774))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6771),X6773))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6772,X6773)),X6774)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X6772,esk261_4(X6771,X6772,X6773,X6774))),hAPP_f2026336507t_bool(X6772,esk260_4(X6771,X6772,X6773,X6774))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6772,X6771)),X6774))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6771),X6773))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6772,X6773)),X6774)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_795_xt4])])])]) ).

fof(i_0_1541,plain,
    ! [X6555,X6556,X6557,X6558] :
      ( ( is_fun1236654035i_bool(esk188_4(X6555,X6556,X6557,X6558))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6556,X6555)),X6558))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6555),X6557))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X6556,X6557)),X6558)) )
      & ( is_fun1236654035i_bool(esk189_4(X6555,X6556,X6557,X6558))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6556,X6555)),X6558))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6555),X6557))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X6556,X6557)),X6558)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk189_4(X6555,X6556,X6557,X6558)),esk188_4(X6555,X6556,X6557,X6558)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6556,X6555)),X6558))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6555),X6557))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X6556,X6557)),X6558)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6556,esk189_4(X6555,X6556,X6557,X6558))),hAPP_f2026336507t_bool(X6556,esk188_4(X6555,X6556,X6557,X6558))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6556,X6555)),X6558))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6555),X6557))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X6556,X6557)),X6558)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_759_xt6])])])]) ).

fof(i_0_1542,plain,
    ! [X7269,X7270,X7271,X7272] :
      ( ( is_fun1236654035i_bool(esk426_4(X7269,X7270,X7271,X7272))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7269,X7271)),X7270))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7269,X7272)),X7270))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7271),X7272)) )
      & ( is_fun1236654035i_bool(esk427_4(X7269,X7270,X7271,X7272))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7269,X7271)),X7270))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7269,X7272)),X7270))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7271),X7272)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk426_4(X7269,X7270,X7271,X7272)),esk427_4(X7269,X7270,X7271,X7272)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7269,X7271)),X7270))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7269,X7272)),X7270))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7271),X7272)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X7269,esk426_4(X7269,X7270,X7271,X7272))),hAPP_f2026336507t_bool(X7269,esk427_4(X7269,X7270,X7271,X7272))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7269,X7271)),X7270))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7269,X7272)),X7270))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7271),X7272)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_878_order__le__less__subst2])])])]) ).

fof(i_0_1543,plain,
    ! [X7347,X7348,X7349,X7350] :
      ( ( is_fun1236654035i_bool(esk452_4(X7347,X7348,X7349,X7350))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7347,X7349)),X7348))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X7347,X7350)),X7348))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7349),X7350)) )
      & ( is_fun1236654035i_bool(esk453_4(X7347,X7348,X7349,X7350))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7347,X7349)),X7348))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X7347,X7350)),X7348))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7349),X7350)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk452_4(X7347,X7348,X7349,X7350)),esk453_4(X7347,X7348,X7349,X7350)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7347,X7349)),X7348))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X7347,X7350)),X7348))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7349),X7350)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7347,esk452_4(X7347,X7348,X7349,X7350))),hAPP_f2026336507t_bool(X7347,esk453_4(X7347,X7348,X7349,X7350))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X7347,X7349)),X7348))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X7347,X7350)),X7348))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7349),X7350)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_891_order__less__le__subst2])])])]) ).

fof(i_0_1544,plain,
    ! [X6777,X6778,X6779,X6780] :
      ( ( is_fun1568535512t_bool(esk262_4(X6777,X6778,X6779,X6780))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6778,X6777)),X6780))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6777),X6779))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6778,X6779)),X6780)) )
      & ( is_fun1568535512t_bool(esk263_4(X6777,X6778,X6779,X6780))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6778,X6777)),X6780))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6777),X6779))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6778,X6779)),X6780)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk263_4(X6777,X6778,X6779,X6780)),esk262_4(X6777,X6778,X6779,X6780)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6778,X6777)),X6780))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6777),X6779))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6778,X6779)),X6780)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X6778,esk263_4(X6777,X6778,X6779,X6780))),hAPP_f543204480t_bool(X6778,esk262_4(X6777,X6778,X6779,X6780))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6778,X6777)),X6780))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6777),X6779))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6778,X6779)),X6780)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_796_xt4])])])]) ).

fof(i_0_1545,plain,
    ! [X6549,X6550,X6551,X6552] :
      ( ( is_fun1568535512t_bool(esk186_4(X6549,X6550,X6551,X6552))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6550,X6549)),X6552))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6549),X6551))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X6550,X6551)),X6552)) )
      & ( is_fun1568535512t_bool(esk187_4(X6549,X6550,X6551,X6552))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6550,X6549)),X6552))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6549),X6551))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X6550,X6551)),X6552)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk187_4(X6549,X6550,X6551,X6552)),esk186_4(X6549,X6550,X6551,X6552)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6550,X6549)),X6552))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6549),X6551))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X6550,X6551)),X6552)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6550,esk187_4(X6549,X6550,X6551,X6552))),hAPP_f543204480t_bool(X6550,esk186_4(X6549,X6550,X6551,X6552))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6550,X6549)),X6552))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6549),X6551))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X6550,X6551)),X6552)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_758_xt6])])])]) ).

fof(i_0_1546,plain,
    ! [X7275,X7276,X7277,X7278] :
      ( ( is_fun1568535512t_bool(esk428_4(X7275,X7276,X7277,X7278))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7275,X7277)),X7276))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7275,X7278)),X7276))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7277),X7278)) )
      & ( is_fun1568535512t_bool(esk429_4(X7275,X7276,X7277,X7278))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7275,X7277)),X7276))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7275,X7278)),X7276))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7277),X7278)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk428_4(X7275,X7276,X7277,X7278)),esk429_4(X7275,X7276,X7277,X7278)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7275,X7277)),X7276))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7275,X7278)),X7276))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7277),X7278)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X7275,esk428_4(X7275,X7276,X7277,X7278))),hAPP_f543204480t_bool(X7275,esk429_4(X7275,X7276,X7277,X7278))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7275,X7277)),X7276))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7275,X7278)),X7276))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7277),X7278)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_879_order__le__less__subst2])])])]) ).

fof(i_0_1547,plain,
    ! [X7341,X7342,X7343,X7344] :
      ( ( is_fun1568535512t_bool(esk450_4(X7341,X7342,X7343,X7344))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7341,X7343)),X7342))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X7341,X7344)),X7342))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7343),X7344)) )
      & ( is_fun1568535512t_bool(esk451_4(X7341,X7342,X7343,X7344))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7341,X7343)),X7342))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X7341,X7344)),X7342))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7343),X7344)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk450_4(X7341,X7342,X7343,X7344)),esk451_4(X7341,X7342,X7343,X7344)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7341,X7343)),X7342))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X7341,X7344)),X7342))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7343),X7344)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7341,esk450_4(X7341,X7342,X7343,X7344))),hAPP_f543204480t_bool(X7341,esk451_4(X7341,X7342,X7343,X7344))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X7341,X7343)),X7342))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X7341,X7344)),X7342))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7343),X7344)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_890_order__less__le__subst2])])])]) ).

fof(i_0_1548,plain,
    ! [X6765,X6766,X6767,X6768] :
      ( ( is_bool(esk258_4(X6765,X6766,X6767,X6768))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X6766,X6765)),X6768))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6765),X6767))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X6766,X6767)),X6768)) )
      & ( is_bool(esk259_4(X6765,X6766,X6767,X6768))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X6766,X6765)),X6768))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6765),X6767))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X6766,X6767)),X6768)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk259_4(X6765,X6766,X6767,X6768)),esk258_4(X6765,X6766,X6767,X6768)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X6766,X6765)),X6768))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6765),X6767))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X6766,X6767)),X6768)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X6766,esk259_4(X6765,X6766,X6767,X6768))),hAPP_b1013836512t_bool(X6766,esk258_4(X6765,X6766,X6767,X6768))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X6766,X6765)),X6768))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6765),X6767))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X6766,X6767)),X6768)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_794_xt4])])])]) ).

fof(i_0_1549,plain,
    ! [X7263,X7264,X7265,X7266] :
      ( ( is_bool(esk424_4(X7263,X7264,X7265,X7266))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X7263,X7265)),X7264))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X7263,X7266)),X7264))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7265),X7266)) )
      & ( is_bool(esk425_4(X7263,X7264,X7265,X7266))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X7263,X7265)),X7264))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X7263,X7266)),X7264))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7265),X7266)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk424_4(X7263,X7264,X7265,X7266)),esk425_4(X7263,X7264,X7265,X7266)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X7263,X7265)),X7264))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X7263,X7266)),X7264))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7265),X7266)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X7263,esk424_4(X7263,X7264,X7265,X7266))),hAPP_b1013836512t_bool(X7263,esk425_4(X7263,X7264,X7265,X7266))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X7263,X7265)),X7264))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X7263,X7266)),X7264))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7265),X7266)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_877_order__le__less__subst2])])])]) ).

fof(i_0_1550,plain,
    ! [X6687,X6688,X6689,X6690] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk233_4(X6687,X6688,X6689,X6690)),esk232_4(X6687,X6688,X6689,X6690)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6688,X6687)),X6690))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6687),X6689))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6688,X6689)),X6690)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X6688,esk233_4(X6687,X6688,X6689,X6690))),hAPP_f800510211t_bool(X6688,esk232_4(X6687,X6688,X6689,X6690))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6688,X6687)),X6690))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6687),X6689))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6688,X6689)),X6690)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_781_xt4])])])]) ).

fof(i_0_1551,plain,
    ! [X6543,X6544,X6545,X6546] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk185_4(X6543,X6544,X6545,X6546)),esk184_4(X6543,X6544,X6545,X6546)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6544,X6543)),X6546))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6543),X6545))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X6544,X6545)),X6546)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6544,esk185_4(X6543,X6544,X6545,X6546))),hAPP_f800510211t_bool(X6544,esk184_4(X6543,X6544,X6545,X6546))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6544,X6543)),X6546))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6543),X6545))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X6544,X6545)),X6546)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_757_xt6])])])]) ).

fof(i_0_1552,plain,
    ! [X7185,X7186,X7187,X7188] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk398_4(X7185,X7186,X7187,X7188)),esk399_4(X7185,X7186,X7187,X7188)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X7185,X7187)),X7186))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X7185,X7188)),X7186))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7187),X7188)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X7185,esk398_4(X7185,X7186,X7187,X7188))),hAPP_f800510211t_bool(X7185,esk399_4(X7185,X7186,X7187,X7188))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X7185,X7187)),X7186))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X7185,X7188)),X7186))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7187),X7188)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_864_order__le__less__subst2])])])]) ).

fof(i_0_1553,plain,
    ! [X7335,X7336,X7337,X7338] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk448_4(X7335,X7336,X7337,X7338)),esk449_4(X7335,X7336,X7337,X7338)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X7335,X7337)),X7336))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X7335,X7338)),X7336))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7337),X7338)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X7335,esk448_4(X7335,X7336,X7337,X7338))),hAPP_f800510211t_bool(X7335,esk449_4(X7335,X7336,X7337,X7338))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X7335,X7337)),X7336))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X7335,X7338)),X7336))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7337),X7338)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_889_order__less__le__subst2])])])]) ).

fof(i_0_1554,plain,
    ! [X6633,X6634,X6635,X6636] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk215_4(X6633,X6634,X6635,X6636)),esk214_4(X6633,X6634,X6635,X6636)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6634,X6633)),X6636))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6633),X6635))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6634,X6635)),X6636)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X6634,esk215_4(X6633,X6634,X6635,X6636))),hAPP_n1699378549t_bool(X6634,esk214_4(X6633,X6634,X6635,X6636))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6634,X6633)),X6636))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6633),X6635))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6634,X6635)),X6636)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_772_xt4])])])]) ).

fof(i_0_1555,plain,
    ! [X6561,X6562,X6563,X6564] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk191_4(X6561,X6562,X6563,X6564)),esk190_4(X6561,X6562,X6563,X6564)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6562,X6561)),X6564))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6561),X6563))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X6562,X6563)),X6564)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6562,esk191_4(X6561,X6562,X6563,X6564))),hAPP_n1699378549t_bool(X6562,esk190_4(X6561,X6562,X6563,X6564))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6562,X6561)),X6564))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6561),X6563))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X6562,X6563)),X6564)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_760_xt6])])])]) ).

fof(i_0_1556,plain,
    ! [X7131,X7132,X7133,X7134] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk380_4(X7131,X7132,X7133,X7134)),esk381_4(X7131,X7132,X7133,X7134)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X7131,X7133)),X7132))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X7131,X7134)),X7132))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7133),X7134)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X7131,esk380_4(X7131,X7132,X7133,X7134))),hAPP_n1699378549t_bool(X7131,esk381_4(X7131,X7132,X7133,X7134))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X7131,X7133)),X7132))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X7131,X7134)),X7132))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7133),X7134)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_855_order__le__less__subst2])])])]) ).

fof(i_0_1557,plain,
    ! [X7353,X7354,X7355,X7356] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk454_4(X7353,X7354,X7355,X7356)),esk455_4(X7353,X7354,X7355,X7356)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X7353,X7355)),X7354))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X7353,X7356)),X7354))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7355),X7356)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X7353,esk454_4(X7353,X7354,X7355,X7356))),hAPP_n1699378549t_bool(X7353,esk455_4(X7353,X7354,X7355,X7356))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X7353,X7355)),X7354))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X7353,X7356)),X7354))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7355),X7356)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_892_order__less__le__subst2])])])]) ).

fof(i_0_1558,plain,
    ! [X6699,X6700,X6701,X6702] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk237_4(X6699,X6700,X6701,X6702)),esk236_4(X6699,X6700,X6701,X6702)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X6700,X6699)),X6702))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6699),X6701))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X6700,X6701)),X6702)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X6700,esk237_4(X6699,X6700,X6701,X6702))),hAPP_f632777549i_bool(X6700,esk236_4(X6699,X6700,X6701,X6702))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X6700,X6699)),X6702))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6699),X6701))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X6700,X6701)),X6702)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_783_xt4])])])]) ).

fof(i_0_1559,plain,
    ! [X7197,X7198,X7199,X7200] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk402_4(X7197,X7198,X7199,X7200)),esk403_4(X7197,X7198,X7199,X7200)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X7197,X7199)),X7198))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X7197,X7200)),X7198))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7199),X7200)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X7197,esk402_4(X7197,X7198,X7199,X7200))),hAPP_f632777549i_bool(X7197,esk403_4(X7197,X7198,X7199,X7200))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X7197,X7199)),X7198))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X7197,X7200)),X7198))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7199),X7200)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_866_order__le__less__subst2])])])]) ).

fof(i_0_1560,plain,
    ! [X6645,X6646,X6647,X6648] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk219_4(X6645,X6646,X6647,X6648)),esk218_4(X6645,X6646,X6647,X6648)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6646,X6645)),X6648))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6645),X6647))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6646,X6647)),X6648)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X6646,esk219_4(X6645,X6646,X6647,X6648))),hAPP_n821919323i_bool(X6646,esk218_4(X6645,X6646,X6647,X6648))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6646,X6645)),X6648))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6645),X6647))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6646,X6647)),X6648)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_774_xt4])])])]) ).

fof(i_0_1561,plain,
    ! [X6573,X6574,X6575,X6576] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk195_4(X6573,X6574,X6575,X6576)),esk194_4(X6573,X6574,X6575,X6576)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6574,X6573)),X6576))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6573),X6575))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X6574,X6575)),X6576)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6574,esk195_4(X6573,X6574,X6575,X6576))),hAPP_n821919323i_bool(X6574,esk194_4(X6573,X6574,X6575,X6576))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6574,X6573)),X6576))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6573),X6575))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X6574,X6575)),X6576)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_762_xt6])])])]) ).

fof(i_0_1562,plain,
    ! [X7143,X7144,X7145,X7146] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk384_4(X7143,X7144,X7145,X7146)),esk385_4(X7143,X7144,X7145,X7146)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X7143,X7145)),X7144))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X7143,X7146)),X7144))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7145),X7146)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X7143,esk384_4(X7143,X7144,X7145,X7146))),hAPP_n821919323i_bool(X7143,esk385_4(X7143,X7144,X7145,X7146))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X7143,X7145)),X7144))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X7143,X7146)),X7144))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7145),X7146)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_857_order__le__less__subst2])])])]) ).

fof(i_0_1563,plain,
    ! [X7365,X7366,X7367,X7368] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk458_4(X7365,X7366,X7367,X7368)),esk459_4(X7365,X7366,X7367,X7368)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X7365,X7367)),X7366))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X7365,X7368)),X7366))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7367),X7368)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X7365,esk458_4(X7365,X7366,X7367,X7368))),hAPP_n821919323i_bool(X7365,esk459_4(X7365,X7366,X7367,X7368))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X7365,X7367)),X7366))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X7365,X7368)),X7366))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7367),X7368)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_894_order__less__le__subst2])])])]) ).

fof(i_0_1564,plain,
    ! [X6735,X6736,X6737,X6738] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk249_4(X6735,X6736,X6737,X6738)),esk248_4(X6735,X6736,X6737,X6738)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X6736,X6735)),X6738))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6735),X6737))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X6736,X6737)),X6738)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X6736,esk249_4(X6735,X6736,X6737,X6738))),hAPP_f861874780t_bool(X6736,esk248_4(X6735,X6736,X6737,X6738))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X6736,X6735)),X6738))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6735),X6737))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X6736,X6737)),X6738)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_789_xt4])])])]) ).

fof(i_0_1565,plain,
    ! [X7233,X7234,X7235,X7236] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk414_4(X7233,X7234,X7235,X7236)),esk415_4(X7233,X7234,X7235,X7236)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X7233,X7235)),X7234))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X7233,X7236)),X7234))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7235),X7236)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X7233,esk414_4(X7233,X7234,X7235,X7236))),hAPP_f861874780t_bool(X7233,esk415_4(X7233,X7234,X7235,X7236))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X7233,X7235)),X7234))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X7233,X7236)),X7234))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7235),X7236)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_872_order__le__less__subst2])])])]) ).

fof(i_0_1566,plain,
    ! [X6681,X6682,X6683,X6684] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk231_4(X6681,X6682,X6683,X6684)),esk230_4(X6681,X6682,X6683,X6684)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6682,X6681)),X6684))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6681),X6683))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6682,X6683)),X6684)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X6682,esk231_4(X6681,X6682,X6683,X6684))),hAPP_n539120590t_bool(X6682,esk230_4(X6681,X6682,X6683,X6684))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6682,X6681)),X6684))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6681),X6683))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6682,X6683)),X6684)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_780_xt4])])])]) ).

fof(i_0_1567,plain,
    ! [X6609,X6610,X6611,X6612] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk207_4(X6609,X6610,X6611,X6612)),esk206_4(X6609,X6610,X6611,X6612)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6610,X6609)),X6612))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6609),X6611))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X6610,X6611)),X6612)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6610,esk207_4(X6609,X6610,X6611,X6612))),hAPP_n539120590t_bool(X6610,esk206_4(X6609,X6610,X6611,X6612))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6610,X6609)),X6612))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6609),X6611))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X6610,X6611)),X6612)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_768_xt6])])])]) ).

fof(i_0_1568,plain,
    ! [X7179,X7180,X7181,X7182] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk396_4(X7179,X7180,X7181,X7182)),esk397_4(X7179,X7180,X7181,X7182)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X7179,X7181)),X7180))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X7179,X7182)),X7180))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7181),X7182)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X7179,esk396_4(X7179,X7180,X7181,X7182))),hAPP_n539120590t_bool(X7179,esk397_4(X7179,X7180,X7181,X7182))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X7179,X7181)),X7180))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X7179,X7182)),X7180))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7181),X7182)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_863_order__le__less__subst2])])])]) ).

fof(i_0_1569,plain,
    ! [X7401,X7402,X7403,X7404] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk470_4(X7401,X7402,X7403,X7404)),esk471_4(X7401,X7402,X7403,X7404)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X7401,X7403)),X7402))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X7401,X7404)),X7402))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7403),X7404)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X7401,esk470_4(X7401,X7402,X7403,X7404))),hAPP_n539120590t_bool(X7401,esk471_4(X7401,X7402,X7403,X7404))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X7401,X7403)),X7402))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X7401,X7404)),X7402))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7403),X7404)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_900_order__less__le__subst2])])])]) ).

fof(i_0_1570,plain,
    ! [X6831,X6832,X6833,X6834] :
      ( ( is_fun2093718614t_bool(esk280_4(X6831,X6832,X6833,X6834))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X6832,X6831)),X6834))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6831),X6833))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X6832,X6833)),X6834)) )
      & ( is_fun2093718614t_bool(esk281_4(X6831,X6832,X6833,X6834))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X6832,X6831)),X6834))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6831),X6833))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X6832,X6833)),X6834)) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk281_4(X6831,X6832,X6833,X6834)),esk280_4(X6831,X6832,X6833,X6834)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X6832,X6831)),X6834))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6831),X6833))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X6832,X6833)),X6834)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X6832,esk281_4(X6831,X6832,X6833,X6834))),hAPP_f1358350510ol_nat(X6832,esk280_4(X6831,X6832,X6833,X6834))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X6832,X6831)),X6834))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6831),X6833))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X6832,X6833)),X6834)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_805_xt4])])])]) ).

fof(i_0_1571,plain,
    ! [X7329,X7330,X7331,X7332] :
      ( ( is_fun2093718614t_bool(esk446_4(X7329,X7330,X7331,X7332))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X7329,X7331)),X7330))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X7329,X7332)),X7330))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7331),X7332)) )
      & ( is_fun2093718614t_bool(esk447_4(X7329,X7330,X7331,X7332))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X7329,X7331)),X7330))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X7329,X7332)),X7330))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7331),X7332)) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk446_4(X7329,X7330,X7331,X7332)),esk447_4(X7329,X7330,X7331,X7332)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X7329,X7331)),X7330))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X7329,X7332)),X7330))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7331),X7332)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X7329,esk446_4(X7329,X7330,X7331,X7332))),hAPP_f1358350510ol_nat(X7329,esk447_4(X7329,X7330,X7331,X7332))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X7329,X7331)),X7330))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X7329,X7332)),X7330))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7331),X7332)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_888_order__le__less__subst2])])])]) ).

fof(i_0_1572,plain,
    ! [X6807,X6808,X6809,X6810] :
      ( ( is_fun961089132t_bool(esk272_4(X6807,X6808,X6809,X6810))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X6808,X6807)),X6810))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6807),X6809))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X6808,X6809)),X6810)) )
      & ( is_fun961089132t_bool(esk273_4(X6807,X6808,X6809,X6810))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X6808,X6807)),X6810))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6807),X6809))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X6808,X6809)),X6810)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk273_4(X6807,X6808,X6809,X6810)),esk272_4(X6807,X6808,X6809,X6810)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X6808,X6807)),X6810))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6807),X6809))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X6808,X6809)),X6810)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X6808,esk273_4(X6807,X6808,X6809,X6810))),hAPP_f816335862ol_nat(X6808,esk272_4(X6807,X6808,X6809,X6810))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X6808,X6807)),X6810))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6807),X6809))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X6808,X6809)),X6810)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_801_xt4])])])]) ).

fof(i_0_1573,plain,
    ! [X7305,X7306,X7307,X7308] :
      ( ( is_fun961089132t_bool(esk438_4(X7305,X7306,X7307,X7308))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X7305,X7307)),X7306))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X7305,X7308)),X7306))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7307),X7308)) )
      & ( is_fun961089132t_bool(esk439_4(X7305,X7306,X7307,X7308))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X7305,X7307)),X7306))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X7305,X7308)),X7306))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7307),X7308)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk438_4(X7305,X7306,X7307,X7308)),esk439_4(X7305,X7306,X7307,X7308)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X7305,X7307)),X7306))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X7305,X7308)),X7306))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7307),X7308)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X7305,esk438_4(X7305,X7306,X7307,X7308))),hAPP_f816335862ol_nat(X7305,esk439_4(X7305,X7306,X7307,X7308))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X7305,X7307)),X7306))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X7305,X7308)),X7306))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7307),X7308)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_884_order__le__less__subst2])])])]) ).

fof(i_0_1574,plain,
    ! [X6801,X6802,X6803,X6804] :
      ( ( is_fun288122577l_bool(esk270_4(X6801,X6802,X6803,X6804))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X6802,X6801)),X6804))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6801),X6803))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X6802,X6803)),X6804)) )
      & ( is_fun288122577l_bool(esk271_4(X6801,X6802,X6803,X6804))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X6802,X6801)),X6804))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6801),X6803))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X6802,X6803)),X6804)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk271_4(X6801,X6802,X6803,X6804)),esk270_4(X6801,X6802,X6803,X6804)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X6802,X6801)),X6804))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6801),X6803))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X6802,X6803)),X6804)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X6802,esk271_4(X6801,X6802,X6803,X6804))),hAPP_f897066961ol_nat(X6802,esk270_4(X6801,X6802,X6803,X6804))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X6802,X6801)),X6804))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6801),X6803))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X6802,X6803)),X6804)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_800_xt4])])])]) ).

fof(i_0_1575,plain,
    ! [X7299,X7300,X7301,X7302] :
      ( ( is_fun288122577l_bool(esk436_4(X7299,X7300,X7301,X7302))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X7299,X7301)),X7300))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X7299,X7302)),X7300))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7301),X7302)) )
      & ( is_fun288122577l_bool(esk437_4(X7299,X7300,X7301,X7302))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X7299,X7301)),X7300))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X7299,X7302)),X7300))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7301),X7302)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk436_4(X7299,X7300,X7301,X7302)),esk437_4(X7299,X7300,X7301,X7302)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X7299,X7301)),X7300))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X7299,X7302)),X7300))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7301),X7302)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X7299,esk436_4(X7299,X7300,X7301,X7302))),hAPP_f897066961ol_nat(X7299,esk437_4(X7299,X7300,X7301,X7302))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X7299,X7301)),X7300))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X7299,X7302)),X7300))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7301),X7302)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_883_order__le__less__subst2])])])]) ).

fof(i_0_1576,plain,
    ! [X6795,X6796,X6797,X6798] :
      ( ( is_fun158382675l_bool(esk268_4(X6795,X6796,X6797,X6798))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X6796,X6795)),X6798))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6795),X6797))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X6796,X6797)),X6798)) )
      & ( is_fun158382675l_bool(esk269_4(X6795,X6796,X6797,X6798))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X6796,X6795)),X6798))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6795),X6797))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X6796,X6797)),X6798)) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk269_4(X6795,X6796,X6797,X6798)),esk268_4(X6795,X6796,X6797,X6798)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X6796,X6795)),X6798))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6795),X6797))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X6796,X6797)),X6798)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X6796,esk269_4(X6795,X6796,X6797,X6798))),hAPP_f1695077327ol_nat(X6796,esk268_4(X6795,X6796,X6797,X6798))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X6796,X6795)),X6798))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6795),X6797))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X6796,X6797)),X6798)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_799_xt4])])])]) ).

fof(i_0_1577,plain,
    ! [X7293,X7294,X7295,X7296] :
      ( ( is_fun158382675l_bool(esk434_4(X7293,X7294,X7295,X7296))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X7293,X7295)),X7294))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X7293,X7296)),X7294))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7295),X7296)) )
      & ( is_fun158382675l_bool(esk435_4(X7293,X7294,X7295,X7296))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X7293,X7295)),X7294))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X7293,X7296)),X7294))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7295),X7296)) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk434_4(X7293,X7294,X7295,X7296)),esk435_4(X7293,X7294,X7295,X7296)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X7293,X7295)),X7294))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X7293,X7296)),X7294))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7295),X7296)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X7293,esk434_4(X7293,X7294,X7295,X7296))),hAPP_f1695077327ol_nat(X7293,esk435_4(X7293,X7294,X7295,X7296))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X7293,X7295)),X7294))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X7293,X7296)),X7294))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7295),X7296)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_882_order__le__less__subst2])])])]) ).

fof(i_0_1578,plain,
    ! [X6789,X6790,X6791,X6792] :
      ( ( is_fun279392540l_bool(esk266_4(X6789,X6790,X6791,X6792))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X6790,X6789)),X6792))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6789),X6791))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X6790,X6791)),X6792)) )
      & ( is_fun279392540l_bool(esk267_4(X6789,X6790,X6791,X6792))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X6790,X6789)),X6792))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6789),X6791))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X6790,X6791)),X6792)) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk267_4(X6789,X6790,X6791,X6792)),esk266_4(X6789,X6790,X6791,X6792)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X6790,X6789)),X6792))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6789),X6791))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X6790,X6791)),X6792)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X6790,esk267_4(X6789,X6790,X6791,X6792))),hAPP_f1313392232ol_nat(X6790,esk266_4(X6789,X6790,X6791,X6792))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X6790,X6789)),X6792))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6789),X6791))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X6790,X6791)),X6792)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_798_xt4])])])]) ).

fof(i_0_1579,plain,
    ! [X7287,X7288,X7289,X7290] :
      ( ( is_fun279392540l_bool(esk432_4(X7287,X7288,X7289,X7290))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X7287,X7289)),X7288))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X7287,X7290)),X7288))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7289),X7290)) )
      & ( is_fun279392540l_bool(esk433_4(X7287,X7288,X7289,X7290))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X7287,X7289)),X7288))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X7287,X7290)),X7288))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7289),X7290)) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk432_4(X7287,X7288,X7289,X7290)),esk433_4(X7287,X7288,X7289,X7290)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X7287,X7289)),X7288))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X7287,X7290)),X7288))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7289),X7290)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X7287,esk432_4(X7287,X7288,X7289,X7290))),hAPP_f1313392232ol_nat(X7287,esk433_4(X7287,X7288,X7289,X7290))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X7287,X7289)),X7288))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X7287,X7290)),X7288))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7289),X7290)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_881_order__le__less__subst2])])])]) ).

fof(i_0_1580,plain,
    ! [X6825,X6826,X6827,X6828] :
      ( ( is_fun1568535512t_bool(esk278_4(X6825,X6826,X6827,X6828))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6826,X6825)),X6828))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6825),X6827))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6826,X6827)),X6828)) )
      & ( is_fun1568535512t_bool(esk279_4(X6825,X6826,X6827,X6828))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6826,X6825)),X6828))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6825),X6827))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6826,X6827)),X6828)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk279_4(X6825,X6826,X6827,X6828)),esk278_4(X6825,X6826,X6827,X6828)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6826,X6825)),X6828))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6825),X6827))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6826,X6827)),X6828)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X6826,esk279_4(X6825,X6826,X6827,X6828))),hAPP_f2030293770ol_nat(X6826,esk278_4(X6825,X6826,X6827,X6828))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6826,X6825)),X6828))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6825),X6827))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6826,X6827)),X6828)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_804_xt4])])])]) ).

fof(i_0_1581,plain,
    ! [X6621,X6622,X6623,X6624] :
      ( ( is_fun1568535512t_bool(esk210_4(X6621,X6622,X6623,X6624))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6622,X6621)),X6624))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6621),X6623))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X6622,X6623)),X6624)) )
      & ( is_fun1568535512t_bool(esk211_4(X6621,X6622,X6623,X6624))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6622,X6621)),X6624))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6621),X6623))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X6622,X6623)),X6624)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk211_4(X6621,X6622,X6623,X6624)),esk210_4(X6621,X6622,X6623,X6624)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6622,X6621)),X6624))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6621),X6623))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X6622,X6623)),X6624)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6622,esk211_4(X6621,X6622,X6623,X6624))),hAPP_f2030293770ol_nat(X6622,esk210_4(X6621,X6622,X6623,X6624))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6622,X6621)),X6624))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6621),X6623))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X6622,X6623)),X6624)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_770_xt6])])])]) ).

fof(i_0_1582,plain,
    ! [X7323,X7324,X7325,X7326] :
      ( ( is_fun1568535512t_bool(esk444_4(X7323,X7324,X7325,X7326))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7323,X7325)),X7324))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7323,X7326)),X7324))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7325),X7326)) )
      & ( is_fun1568535512t_bool(esk445_4(X7323,X7324,X7325,X7326))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7323,X7325)),X7324))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7323,X7326)),X7324))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7325),X7326)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk444_4(X7323,X7324,X7325,X7326)),esk445_4(X7323,X7324,X7325,X7326)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7323,X7325)),X7324))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7323,X7326)),X7324))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7325),X7326)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X7323,esk444_4(X7323,X7324,X7325,X7326))),hAPP_f2030293770ol_nat(X7323,esk445_4(X7323,X7324,X7325,X7326))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7323,X7325)),X7324))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7323,X7326)),X7324))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7325),X7326)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_887_order__le__less__subst2])])])]) ).

fof(i_0_1583,plain,
    ! [X7413,X7414,X7415,X7416] :
      ( ( is_fun1568535512t_bool(esk474_4(X7413,X7414,X7415,X7416))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7413,X7415)),X7414))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X7413,X7416)),X7414))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7415),X7416)) )
      & ( is_fun1568535512t_bool(esk475_4(X7413,X7414,X7415,X7416))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7413,X7415)),X7414))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X7413,X7416)),X7414))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7415),X7416)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk474_4(X7413,X7414,X7415,X7416)),esk475_4(X7413,X7414,X7415,X7416)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7413,X7415)),X7414))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X7413,X7416)),X7414))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7415),X7416)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7413,esk474_4(X7413,X7414,X7415,X7416))),hAPP_f2030293770ol_nat(X7413,esk475_4(X7413,X7414,X7415,X7416))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X7413,X7415)),X7414))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X7413,X7416)),X7414))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7415),X7416)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_902_order__less__le__subst2])])])]) ).

fof(i_0_1584,plain,
    ! [X6615,X6616,X6617,X6618] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk209_4(X6615,X6616,X6617,X6618)),esk208_4(X6615,X6616,X6617,X6618)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X6616,X6615)),X6618))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6615),X6617))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X6616,X6617)),X6618)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X6616,esk209_4(X6615,X6616,X6617,X6618))),hAPP_f22106695ol_nat(X6616,esk208_4(X6615,X6616,X6617,X6618))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X6616,X6615)),X6618))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6615),X6617))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X6616,X6617)),X6618)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_769_xt6])])])]) ).

fof(i_0_1585,plain,
    ! [X7407,X7408,X7409,X7410] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk472_4(X7407,X7408,X7409,X7410)),esk473_4(X7407,X7408,X7409,X7410)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X7407,X7409)),X7408))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X7407,X7410)),X7408))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7409),X7410)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X7407,esk472_4(X7407,X7408,X7409,X7410))),hAPP_f22106695ol_nat(X7407,esk473_4(X7407,X7408,X7409,X7410))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X7407,X7409)),X7408))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X7407,X7410)),X7408))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7409),X7410)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_901_order__less__le__subst2])])])]) ).

fof(i_0_1586,plain,
    ! [X6813,X6814,X6815,X6816] :
      ( ( is_bool(esk274_4(X6813,X6814,X6815,X6816))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X6814,X6813)),X6816))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6813),X6815))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X6814,X6815)),X6816)) )
      & ( is_bool(esk275_4(X6813,X6814,X6815,X6816))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X6814,X6813)),X6816))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6813),X6815))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X6814,X6815)),X6816)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk275_4(X6813,X6814,X6815,X6816)),esk274_4(X6813,X6814,X6815,X6816)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X6814,X6813)),X6816))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6813),X6815))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X6814,X6815)),X6816)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X6814,esk275_4(X6813,X6814,X6815,X6816))),hAPP_bool_nat(X6814,esk274_4(X6813,X6814,X6815,X6816))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X6814,X6813)),X6816))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6813),X6815))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X6814,X6815)),X6816)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_802_xt4])])])]) ).

fof(i_0_1587,plain,
    ! [X7311,X7312,X7313,X7314] :
      ( ( is_bool(esk440_4(X7311,X7312,X7313,X7314))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X7311,X7313)),X7312))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X7311,X7314)),X7312))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7313),X7314)) )
      & ( is_bool(esk441_4(X7311,X7312,X7313,X7314))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X7311,X7313)),X7312))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X7311,X7314)),X7312))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7313),X7314)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk440_4(X7311,X7312,X7313,X7314)),esk441_4(X7311,X7312,X7313,X7314)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X7311,X7313)),X7312))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X7311,X7314)),X7312))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7313),X7314)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X7311,esk440_4(X7311,X7312,X7313,X7314))),hAPP_bool_nat(X7311,esk441_4(X7311,X7312,X7313,X7314))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X7311,X7313)),X7312))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X7311,X7314)),X7312))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7313),X7314)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_885_order__le__less__subst2])])])]) ).

fof(i_0_1588,plain,
    ! [X6819,X6820,X6821,X6822] :
      ( ( is_fun1236654035i_bool(esk276_4(X6819,X6820,X6821,X6822))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6820,X6819)),X6822))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6819),X6821))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6820,X6821)),X6822)) )
      & ( is_fun1236654035i_bool(esk277_4(X6819,X6820,X6821,X6822))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6820,X6819)),X6822))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6819),X6821))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6820,X6821)),X6822)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk277_4(X6819,X6820,X6821,X6822)),esk276_4(X6819,X6820,X6821,X6822)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6820,X6819)),X6822))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6819),X6821))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6820,X6821)),X6822)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X6820,esk277_4(X6819,X6820,X6821,X6822))),hAPP_f2120083535ol_nat(X6820,esk276_4(X6819,X6820,X6821,X6822))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6820,X6819)),X6822))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6819),X6821))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6820,X6821)),X6822)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_803_xt4])])])]) ).

fof(i_0_1589,plain,
    ! [X6627,X6628,X6629,X6630] :
      ( ( is_fun1236654035i_bool(esk212_4(X6627,X6628,X6629,X6630))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6628,X6627)),X6630))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6627),X6629))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X6628,X6629)),X6630)) )
      & ( is_fun1236654035i_bool(esk213_4(X6627,X6628,X6629,X6630))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6628,X6627)),X6630))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6627),X6629))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X6628,X6629)),X6630)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk213_4(X6627,X6628,X6629,X6630)),esk212_4(X6627,X6628,X6629,X6630)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6628,X6627)),X6630))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6627),X6629))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X6628,X6629)),X6630)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6628,esk213_4(X6627,X6628,X6629,X6630))),hAPP_f2120083535ol_nat(X6628,esk212_4(X6627,X6628,X6629,X6630))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6628,X6627)),X6630))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6627),X6629))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X6628,X6629)),X6630)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_771_xt6])])])]) ).

fof(i_0_1590,plain,
    ! [X7317,X7318,X7319,X7320] :
      ( ( is_fun1236654035i_bool(esk442_4(X7317,X7318,X7319,X7320))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7317,X7319)),X7318))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7317,X7320)),X7318))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7319),X7320)) )
      & ( is_fun1236654035i_bool(esk443_4(X7317,X7318,X7319,X7320))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7317,X7319)),X7318))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7317,X7320)),X7318))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7319),X7320)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk442_4(X7317,X7318,X7319,X7320)),esk443_4(X7317,X7318,X7319,X7320)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7317,X7319)),X7318))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7317,X7320)),X7318))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7319),X7320)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X7317,esk442_4(X7317,X7318,X7319,X7320))),hAPP_f2120083535ol_nat(X7317,esk443_4(X7317,X7318,X7319,X7320))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7317,X7319)),X7318))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7317,X7320)),X7318))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7319),X7320)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_886_order__le__less__subst2])])])]) ).

fof(i_0_1591,plain,
    ! [X7419,X7420,X7421,X7422] :
      ( ( is_fun1236654035i_bool(esk476_4(X7419,X7420,X7421,X7422))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7419,X7421)),X7420))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X7419,X7422)),X7420))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7421),X7422)) )
      & ( is_fun1236654035i_bool(esk477_4(X7419,X7420,X7421,X7422))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7419,X7421)),X7420))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X7419,X7422)),X7420))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7421),X7422)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk476_4(X7419,X7420,X7421,X7422)),esk477_4(X7419,X7420,X7421,X7422)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7419,X7421)),X7420))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X7419,X7422)),X7420))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7421),X7422)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7419,esk476_4(X7419,X7420,X7421,X7422))),hAPP_f2120083535ol_nat(X7419,esk477_4(X7419,X7420,X7421,X7422))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X7419,X7421)),X7420))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X7419,X7422)),X7420))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7421),X7422)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_903_order__less__le__subst2])])])]) ).

fof(i_0_1592,plain,
    ! [X6729,X6730,X6731,X6732] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk247_4(X6729,X6730,X6731,X6732)),esk246_4(X6729,X6730,X6731,X6732)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X6730,X6729)),X6732))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6729),X6731))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X6730,X6731)),X6732)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X6730,esk247_4(X6729,X6730,X6731,X6732))),hAPP_f54304608l_bool(X6730,esk246_4(X6729,X6730,X6731,X6732))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X6730,X6729)),X6732))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6729),X6731))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X6730,X6731)),X6732)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_788_xt4])])])]) ).

fof(i_0_1593,plain,
    ! [X7227,X7228,X7229,X7230] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk412_4(X7227,X7228,X7229,X7230)),esk413_4(X7227,X7228,X7229,X7230)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X7227,X7229)),X7228))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X7227,X7230)),X7228))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7229),X7230)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X7227,esk412_4(X7227,X7228,X7229,X7230))),hAPP_f54304608l_bool(X7227,esk413_4(X7227,X7228,X7229,X7230))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X7227,X7229)),X7228))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X7227,X7230)),X7228))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7229),X7230)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_871_order__le__less__subst2])])])]) ).

fof(i_0_1594,plain,
    ! [X6675,X6676,X6677,X6678] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk229_4(X6675,X6676,X6677,X6678)),esk228_4(X6675,X6676,X6677,X6678)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6676,X6675)),X6678))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6675),X6677))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6676,X6677)),X6678)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X6676,esk229_4(X6675,X6676,X6677,X6678))),hAPP_nat_bool(X6676,esk228_4(X6675,X6676,X6677,X6678))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6676,X6675)),X6678))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6675),X6677))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6676,X6677)),X6678)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_779_xt4])])])]) ).

fof(i_0_1595,plain,
    ! [X6603,X6604,X6605,X6606] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk205_4(X6603,X6604,X6605,X6606)),esk204_4(X6603,X6604,X6605,X6606)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6604,X6603)),X6606))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6603),X6605))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X6604,X6605)),X6606)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6604,esk205_4(X6603,X6604,X6605,X6606))),hAPP_nat_bool(X6604,esk204_4(X6603,X6604,X6605,X6606))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6604,X6603)),X6606))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6603),X6605))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X6604,X6605)),X6606)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_767_xt6])])])]) ).

fof(i_0_1596,plain,
    ! [X7173,X7174,X7175,X7176] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk394_4(X7173,X7174,X7175,X7176)),esk395_4(X7173,X7174,X7175,X7176)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X7173,X7175)),X7174))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X7173,X7176)),X7174))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7175),X7176)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X7173,esk394_4(X7173,X7174,X7175,X7176))),hAPP_nat_bool(X7173,esk395_4(X7173,X7174,X7175,X7176))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X7173,X7175)),X7174))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X7173,X7176)),X7174))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7175),X7176)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_862_order__le__less__subst2])])])]) ).

fof(i_0_1597,plain,
    ! [X7395,X7396,X7397,X7398] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk468_4(X7395,X7396,X7397,X7398)),esk469_4(X7395,X7396,X7397,X7398)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X7395,X7397)),X7396))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X7395,X7398)),X7396))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7397),X7398)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X7395,esk468_4(X7395,X7396,X7397,X7398))),hAPP_nat_bool(X7395,esk469_4(X7395,X7396,X7397,X7398))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X7395,X7397)),X7396))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X7395,X7398)),X7396))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7397),X7398)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_899_order__less__le__subst2])])])]) ).

fof(i_0_1598,plain,
    ! [X6302,X6303,X6304,X6305] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk139_4(X6302,X6303,X6304,X6305)),esk138_4(X6302,X6303,X6304,X6305)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6302),hAPP_f899613158t_bool(X6303,X6305)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6302),hAPP_f899613158t_bool(X6303,X6304)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6304),X6305)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X6303,esk139_4(X6302,X6303,X6304,X6305))),hAPP_f899613158t_bool(X6303,esk138_4(X6302,X6303,X6304,X6305))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6302),hAPP_f899613158t_bool(X6303,X6305)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6302),hAPP_f899613158t_bool(X6303,X6304)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6304),X6305)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_688_xt7])])])]) ).

fof(i_0_1599,plain,
    ! [X6248,X6249,X6250,X6251] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk121_4(X6248,X6249,X6250,X6251)),esk120_4(X6248,X6249,X6250,X6251)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6248),hAPP_n588788980t_bool(X6249,X6251)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6248),hAPP_n588788980t_bool(X6249,X6250)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6250),X6251)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X6249,esk121_4(X6248,X6249,X6250,X6251))),hAPP_n588788980t_bool(X6249,esk120_4(X6248,X6249,X6250,X6251))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6248),hAPP_n588788980t_bool(X6249,X6251)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6248),hAPP_n588788980t_bool(X6249,X6250)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6250),X6251)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_679_xt7])])])]) ).

fof(i_0_1600,plain,
    ! [X6176,X6177,X6178,X6179] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk97_4(X6176,X6177,X6178,X6179)),esk96_4(X6176,X6177,X6178,X6179)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6176),hAPP_n588788980t_bool(X6177,X6179)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6176),hAPP_n588788980t_bool(X6177,X6178)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6178),X6179)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6177,esk97_4(X6176,X6177,X6178,X6179))),hAPP_n588788980t_bool(X6177,esk96_4(X6176,X6177,X6178,X6179))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6176),hAPP_n588788980t_bool(X6177,X6179)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6176),hAPP_n588788980t_bool(X6177,X6178)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6178),X6179)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_667_xt5])])])]) ).

fof(i_0_1601,plain,
    ! [X7017,X7018,X7019,X7020] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk342_4(X7017,X7018,X7019,X7020)),esk343_4(X7017,X7018,X7019,X7020)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7018),hAPP_f899613158t_bool(X7019,X7017)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7020),X7017))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7018),hAPP_f899613158t_bool(X7019,X7020))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X7019,esk342_4(X7017,X7018,X7019,X7020))),hAPP_f899613158t_bool(X7019,esk343_4(X7017,X7018,X7019,X7020))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7018),hAPP_f899613158t_bool(X7019,X7017)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7020),X7017))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7018),hAPP_f899613158t_bool(X7019,X7020))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_836_order__less__le__subst1])])])]) ).

fof(i_0_1602,plain,
    ! [X6963,X6964,X6965,X6966] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk324_4(X6963,X6964,X6965,X6966)),esk325_4(X6963,X6964,X6965,X6966)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6964),hAPP_n588788980t_bool(X6965,X6963)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6966),X6963))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6964),hAPP_n588788980t_bool(X6965,X6966))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X6965,esk324_4(X6963,X6964,X6965,X6966))),hAPP_n588788980t_bool(X6965,esk325_4(X6963,X6964,X6965,X6966))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6964),hAPP_n588788980t_bool(X6965,X6963)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6966),X6963))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6964),hAPP_n588788980t_bool(X6965,X6966))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_827_order__less__le__subst1])])])]) ).

fof(i_0_1603,plain,
    ! [X6891,X6892,X6893,X6894] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk300_4(X6891,X6892,X6893,X6894)),esk301_4(X6891,X6892,X6893,X6894)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6892),hAPP_n588788980t_bool(X6893,X6891)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6894),X6891))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6892),hAPP_n588788980t_bool(X6893,X6894))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X6893,esk300_4(X6891,X6892,X6893,X6894))),hAPP_n588788980t_bool(X6893,esk301_4(X6891,X6892,X6893,X6894))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6892),hAPP_n588788980t_bool(X6893,X6891)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6894),X6891))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6892),hAPP_n588788980t_bool(X6893,X6894))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_815_order__le__less__subst1])])])]) ).

fof(i_0_1604,plain,
    ! [X6284,X6285,X6286,X6287] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk133_4(X6284,X6285,X6286,X6287)),esk132_4(X6284,X6285,X6286,X6287)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6284),hAPP_f769545506l_bool(X6285,X6287)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6284),hAPP_f769545506l_bool(X6285,X6286)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6286),X6287)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X6285,esk133_4(X6284,X6285,X6286,X6287))),hAPP_f769545506l_bool(X6285,esk132_4(X6284,X6285,X6286,X6287))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6284),hAPP_f769545506l_bool(X6285,X6287)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6284),hAPP_f769545506l_bool(X6285,X6286)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6286),X6287)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_685_xt7])])])]) ).

fof(i_0_1605,plain,
    ! [X6230,X6231,X6232,X6233] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk115_4(X6230,X6231,X6232,X6233)),esk114_4(X6230,X6231,X6232,X6233)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6230),hAPP_n1674354836l_bool(X6231,X6233)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6230),hAPP_n1674354836l_bool(X6231,X6232)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6232),X6233)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X6231,esk115_4(X6230,X6231,X6232,X6233))),hAPP_n1674354836l_bool(X6231,esk114_4(X6230,X6231,X6232,X6233))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6230),hAPP_n1674354836l_bool(X6231,X6233)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6230),hAPP_n1674354836l_bool(X6231,X6232)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6232),X6233)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_676_xt7])])])]) ).

fof(i_0_1606,plain,
    ! [X6158,X6159,X6160,X6161] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk91_4(X6158,X6159,X6160,X6161)),esk90_4(X6158,X6159,X6160,X6161)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6158),hAPP_n1674354836l_bool(X6159,X6161)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6158),hAPP_n1674354836l_bool(X6159,X6160)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6160),X6161)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6159,esk91_4(X6158,X6159,X6160,X6161))),hAPP_n1674354836l_bool(X6159,esk90_4(X6158,X6159,X6160,X6161))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6158),hAPP_n1674354836l_bool(X6159,X6161)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6158),hAPP_n1674354836l_bool(X6159,X6160)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6160),X6161)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_664_xt5])])])]) ).

fof(i_0_1607,plain,
    ! [X6999,X7000,X7001,X7002] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk336_4(X6999,X7000,X7001,X7002)),esk337_4(X6999,X7000,X7001,X7002)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7000),hAPP_f769545506l_bool(X7001,X6999)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7002),X6999))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7000),hAPP_f769545506l_bool(X7001,X7002))) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X7001,esk336_4(X6999,X7000,X7001,X7002))),hAPP_f769545506l_bool(X7001,esk337_4(X6999,X7000,X7001,X7002))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7000),hAPP_f769545506l_bool(X7001,X6999)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7002),X6999))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7000),hAPP_f769545506l_bool(X7001,X7002))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_833_order__less__le__subst1])])])]) ).

fof(i_0_1608,plain,
    ! [X6945,X6946,X6947,X6948] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk318_4(X6945,X6946,X6947,X6948)),esk319_4(X6945,X6946,X6947,X6948)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6946),hAPP_n1674354836l_bool(X6947,X6945)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6948),X6945))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6946),hAPP_n1674354836l_bool(X6947,X6948))) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X6947,esk318_4(X6945,X6946,X6947,X6948))),hAPP_n1674354836l_bool(X6947,esk319_4(X6945,X6946,X6947,X6948))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6946),hAPP_n1674354836l_bool(X6947,X6945)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6948),X6945))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6946),hAPP_n1674354836l_bool(X6947,X6948))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_824_order__less__le__subst1])])])]) ).

fof(i_0_1609,plain,
    ! [X6873,X6874,X6875,X6876] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk294_4(X6873,X6874,X6875,X6876)),esk295_4(X6873,X6874,X6875,X6876)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6874),hAPP_n1674354836l_bool(X6875,X6873)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6876),X6873))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6874),hAPP_n1674354836l_bool(X6875,X6876))) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X6875,esk294_4(X6873,X6874,X6875,X6876))),hAPP_n1674354836l_bool(X6875,esk295_4(X6873,X6874,X6875,X6876))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6874),hAPP_n1674354836l_bool(X6875,X6873)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6876),X6873))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6874),hAPP_n1674354836l_bool(X6875,X6876))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_812_order__le__less__subst1])])])]) ).

fof(i_0_1610,plain,
    ! [X6290,X6291,X6292,X6293] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk135_4(X6290,X6291,X6292,X6293)),esk134_4(X6290,X6291,X6292,X6293)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6290),hAPP_f1449238989l_bool(X6291,X6293)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6290),hAPP_f1449238989l_bool(X6291,X6292)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6292),X6293)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X6291,esk135_4(X6290,X6291,X6292,X6293))),hAPP_f1449238989l_bool(X6291,esk134_4(X6290,X6291,X6292,X6293))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6290),hAPP_f1449238989l_bool(X6291,X6293)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6290),hAPP_f1449238989l_bool(X6291,X6292)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6292),X6293)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_686_xt7])])])]) ).

fof(i_0_1611,plain,
    ! [X6236,X6237,X6238,X6239] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk117_4(X6236,X6237,X6238,X6239)),esk116_4(X6236,X6237,X6238,X6239)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6236),hAPP_n295497947l_bool(X6237,X6239)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6236),hAPP_n295497947l_bool(X6237,X6238)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6238),X6239)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X6237,esk117_4(X6236,X6237,X6238,X6239))),hAPP_n295497947l_bool(X6237,esk116_4(X6236,X6237,X6238,X6239))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6236),hAPP_n295497947l_bool(X6237,X6239)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6236),hAPP_n295497947l_bool(X6237,X6238)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6238),X6239)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_677_xt7])])])]) ).

fof(i_0_1612,plain,
    ! [X6164,X6165,X6166,X6167] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk93_4(X6164,X6165,X6166,X6167)),esk92_4(X6164,X6165,X6166,X6167)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6164),hAPP_n295497947l_bool(X6165,X6167)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6164),hAPP_n295497947l_bool(X6165,X6166)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6166),X6167)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6165,esk93_4(X6164,X6165,X6166,X6167))),hAPP_n295497947l_bool(X6165,esk92_4(X6164,X6165,X6166,X6167))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6164),hAPP_n295497947l_bool(X6165,X6167)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6164),hAPP_n295497947l_bool(X6165,X6166)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6166),X6167)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_665_xt5])])])]) ).

fof(i_0_1613,plain,
    ! [X7005,X7006,X7007,X7008] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk338_4(X7005,X7006,X7007,X7008)),esk339_4(X7005,X7006,X7007,X7008)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7006),hAPP_f1449238989l_bool(X7007,X7005)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7008),X7005))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7006),hAPP_f1449238989l_bool(X7007,X7008))) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X7007,esk338_4(X7005,X7006,X7007,X7008))),hAPP_f1449238989l_bool(X7007,esk339_4(X7005,X7006,X7007,X7008))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7006),hAPP_f1449238989l_bool(X7007,X7005)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7008),X7005))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7006),hAPP_f1449238989l_bool(X7007,X7008))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_834_order__less__le__subst1])])])]) ).

fof(i_0_1614,plain,
    ! [X6951,X6952,X6953,X6954] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk320_4(X6951,X6952,X6953,X6954)),esk321_4(X6951,X6952,X6953,X6954)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6952),hAPP_n295497947l_bool(X6953,X6951)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6954),X6951))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6952),hAPP_n295497947l_bool(X6953,X6954))) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X6953,esk320_4(X6951,X6952,X6953,X6954))),hAPP_n295497947l_bool(X6953,esk321_4(X6951,X6952,X6953,X6954))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6952),hAPP_n295497947l_bool(X6953,X6951)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6954),X6951))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6952),hAPP_n295497947l_bool(X6953,X6954))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_825_order__less__le__subst1])])])]) ).

fof(i_0_1615,plain,
    ! [X6879,X6880,X6881,X6882] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk296_4(X6879,X6880,X6881,X6882)),esk297_4(X6879,X6880,X6881,X6882)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6880),hAPP_n295497947l_bool(X6881,X6879)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6882),X6879))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6880),hAPP_n295497947l_bool(X6881,X6882))) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X6881,esk296_4(X6879,X6880,X6881,X6882))),hAPP_n295497947l_bool(X6881,esk297_4(X6879,X6880,X6881,X6882))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6880),hAPP_n295497947l_bool(X6881,X6879)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6882),X6879))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6880),hAPP_n295497947l_bool(X6881,X6882))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_813_order__le__less__subst1])])])]) ).

fof(i_0_1616,plain,
    ! [X6296,X6297,X6298,X6299] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk137_4(X6296,X6297,X6298,X6299)),esk136_4(X6296,X6297,X6298,X6299)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6296),hAPP_f226010187l_bool(X6297,X6299)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6296),hAPP_f226010187l_bool(X6297,X6298)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6298),X6299)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X6297,esk137_4(X6296,X6297,X6298,X6299))),hAPP_f226010187l_bool(X6297,esk136_4(X6296,X6297,X6298,X6299))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6296),hAPP_f226010187l_bool(X6297,X6299)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6296),hAPP_f226010187l_bool(X6297,X6298)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6298),X6299)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_687_xt7])])])]) ).

fof(i_0_1617,plain,
    ! [X6242,X6243,X6244,X6245] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk119_4(X6242,X6243,X6244,X6245)),esk118_4(X6242,X6243,X6244,X6245)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6242),hAPP_n2095207769l_bool(X6243,X6245)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6242),hAPP_n2095207769l_bool(X6243,X6244)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6244),X6245)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X6243,esk119_4(X6242,X6243,X6244,X6245))),hAPP_n2095207769l_bool(X6243,esk118_4(X6242,X6243,X6244,X6245))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6242),hAPP_n2095207769l_bool(X6243,X6245)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6242),hAPP_n2095207769l_bool(X6243,X6244)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6244),X6245)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_678_xt7])])])]) ).

fof(i_0_1618,plain,
    ! [X6170,X6171,X6172,X6173] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk95_4(X6170,X6171,X6172,X6173)),esk94_4(X6170,X6171,X6172,X6173)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6170),hAPP_n2095207769l_bool(X6171,X6173)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6170),hAPP_n2095207769l_bool(X6171,X6172)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6172),X6173)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6171,esk95_4(X6170,X6171,X6172,X6173))),hAPP_n2095207769l_bool(X6171,esk94_4(X6170,X6171,X6172,X6173))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6170),hAPP_n2095207769l_bool(X6171,X6173)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6170),hAPP_n2095207769l_bool(X6171,X6172)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6172),X6173)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_666_xt5])])])]) ).

fof(i_0_1619,plain,
    ! [X7011,X7012,X7013,X7014] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk340_4(X7011,X7012,X7013,X7014)),esk341_4(X7011,X7012,X7013,X7014)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7012),hAPP_f226010187l_bool(X7013,X7011)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7014),X7011))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7012),hAPP_f226010187l_bool(X7013,X7014))) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X7013,esk340_4(X7011,X7012,X7013,X7014))),hAPP_f226010187l_bool(X7013,esk341_4(X7011,X7012,X7013,X7014))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7012),hAPP_f226010187l_bool(X7013,X7011)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7014),X7011))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7012),hAPP_f226010187l_bool(X7013,X7014))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_835_order__less__le__subst1])])])]) ).

fof(i_0_1620,plain,
    ! [X6957,X6958,X6959,X6960] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk322_4(X6957,X6958,X6959,X6960)),esk323_4(X6957,X6958,X6959,X6960)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6958),hAPP_n2095207769l_bool(X6959,X6957)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6960),X6957))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6958),hAPP_n2095207769l_bool(X6959,X6960))) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X6959,esk322_4(X6957,X6958,X6959,X6960))),hAPP_n2095207769l_bool(X6959,esk323_4(X6957,X6958,X6959,X6960))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6958),hAPP_n2095207769l_bool(X6959,X6957)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6960),X6957))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6958),hAPP_n2095207769l_bool(X6959,X6960))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_826_order__less__le__subst1])])])]) ).

fof(i_0_1621,plain,
    ! [X6885,X6886,X6887,X6888] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk298_4(X6885,X6886,X6887,X6888)),esk299_4(X6885,X6886,X6887,X6888)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6886),hAPP_n2095207769l_bool(X6887,X6885)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6888),X6885))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6886),hAPP_n2095207769l_bool(X6887,X6888))) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X6887,esk298_4(X6885,X6886,X6887,X6888))),hAPP_n2095207769l_bool(X6887,esk299_4(X6885,X6886,X6887,X6888))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6886),hAPP_n2095207769l_bool(X6887,X6885)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6888),X6885))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6886),hAPP_n2095207769l_bool(X6887,X6888))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_814_order__le__less__subst1])])])]) ).

fof(i_0_1622,plain,
    ! [X6272,X6273,X6274,X6275] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk129_4(X6272,X6273,X6274,X6275)),esk128_4(X6272,X6273,X6274,X6275)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6272),hAPP_f1061584978t_bool(X6273,X6275)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6272),hAPP_f1061584978t_bool(X6273,X6274)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6274),X6275)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X6273,esk129_4(X6272,X6273,X6274,X6275))),hAPP_f1061584978t_bool(X6273,esk128_4(X6272,X6273,X6274,X6275))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6272),hAPP_f1061584978t_bool(X6273,X6275)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6272),hAPP_f1061584978t_bool(X6273,X6274)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6274),X6275)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_683_xt7])])])]) ).

fof(i_0_1623,plain,
    ! [X6218,X6219,X6220,X6221] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk111_4(X6218,X6219,X6220,X6221)),esk110_4(X6218,X6219,X6220,X6221)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6218),hAPP_n454528608t_bool(X6219,X6221)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6218),hAPP_n454528608t_bool(X6219,X6220)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6220),X6221)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X6219,esk111_4(X6218,X6219,X6220,X6221))),hAPP_n454528608t_bool(X6219,esk110_4(X6218,X6219,X6220,X6221))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6218),hAPP_n454528608t_bool(X6219,X6221)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6218),hAPP_n454528608t_bool(X6219,X6220)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6220),X6221)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_674_xt7])])])]) ).

fof(i_0_1624,plain,
    ! [X6146,X6147,X6148,X6149] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk87_4(X6146,X6147,X6148,X6149)),esk86_4(X6146,X6147,X6148,X6149)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6146),hAPP_n454528608t_bool(X6147,X6149)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6146),hAPP_n454528608t_bool(X6147,X6148)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6148),X6149)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6147,esk87_4(X6146,X6147,X6148,X6149))),hAPP_n454528608t_bool(X6147,esk86_4(X6146,X6147,X6148,X6149))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6146),hAPP_n454528608t_bool(X6147,X6149)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6146),hAPP_n454528608t_bool(X6147,X6148)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6148),X6149)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_662_xt5])])])]) ).

fof(i_0_1625,plain,
    ! [X6987,X6988,X6989,X6990] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk332_4(X6987,X6988,X6989,X6990)),esk333_4(X6987,X6988,X6989,X6990)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6988),hAPP_f1061584978t_bool(X6989,X6987)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6990),X6987))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6988),hAPP_f1061584978t_bool(X6989,X6990))) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X6989,esk332_4(X6987,X6988,X6989,X6990))),hAPP_f1061584978t_bool(X6989,esk333_4(X6987,X6988,X6989,X6990))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6988),hAPP_f1061584978t_bool(X6989,X6987)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6990),X6987))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6988),hAPP_f1061584978t_bool(X6989,X6990))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_831_order__less__le__subst1])])])]) ).

fof(i_0_1626,plain,
    ! [X6933,X6934,X6935,X6936] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk314_4(X6933,X6934,X6935,X6936)),esk315_4(X6933,X6934,X6935,X6936)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6934),hAPP_n454528608t_bool(X6935,X6933)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6936),X6933))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6934),hAPP_n454528608t_bool(X6935,X6936))) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X6935,esk314_4(X6933,X6934,X6935,X6936))),hAPP_n454528608t_bool(X6935,esk315_4(X6933,X6934,X6935,X6936))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6934),hAPP_n454528608t_bool(X6935,X6933)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6936),X6933))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6934),hAPP_n454528608t_bool(X6935,X6936))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_822_order__less__le__subst1])])])]) ).

fof(i_0_1627,plain,
    ! [X6861,X6862,X6863,X6864] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk290_4(X6861,X6862,X6863,X6864)),esk291_4(X6861,X6862,X6863,X6864)))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6862),hAPP_n454528608t_bool(X6863,X6861)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6864),X6861))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6862),hAPP_n454528608t_bool(X6863,X6864))) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X6863,esk290_4(X6861,X6862,X6863,X6864))),hAPP_n454528608t_bool(X6863,esk291_4(X6861,X6862,X6863,X6864))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6862),hAPP_n454528608t_bool(X6863,X6861)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6864),X6861))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6862),hAPP_n454528608t_bool(X6863,X6864))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_810_order__le__less__subst1])])])]) ).

fof(i_0_1628,plain,
    ! [X6362,X6363,X6364,X6365] :
      ( ( is_fun2093718614t_bool(esk158_4(X6362,X6363,X6364,X6365))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6362),hAPP_f1363542492t_bool(X6363,X6365)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6362),hAPP_f1363542492t_bool(X6363,X6364)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6364),X6365)) )
      & ( is_fun2093718614t_bool(esk159_4(X6362,X6363,X6364,X6365))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6362),hAPP_f1363542492t_bool(X6363,X6365)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6362),hAPP_f1363542492t_bool(X6363,X6364)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6364),X6365)) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk159_4(X6362,X6363,X6364,X6365)),esk158_4(X6362,X6363,X6364,X6365)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6362),hAPP_f1363542492t_bool(X6363,X6365)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6362),hAPP_f1363542492t_bool(X6363,X6364)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6364),X6365)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X6363,esk159_4(X6362,X6363,X6364,X6365))),hAPP_f1363542492t_bool(X6363,esk158_4(X6362,X6363,X6364,X6365))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6362),hAPP_f1363542492t_bool(X6363,X6365)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6362),hAPP_f1363542492t_bool(X6363,X6364)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6364),X6365)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_698_xt7])])])]) ).

fof(i_0_1629,plain,
    ! [X6338,X6339,X6340,X6341] :
      ( ( is_fun961089132t_bool(esk150_4(X6338,X6339,X6340,X6341))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6338),hAPP_f856106132t_bool(X6339,X6341)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6338),hAPP_f856106132t_bool(X6339,X6340)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6340),X6341)) )
      & ( is_fun961089132t_bool(esk151_4(X6338,X6339,X6340,X6341))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6338),hAPP_f856106132t_bool(X6339,X6341)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6338),hAPP_f856106132t_bool(X6339,X6340)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6340),X6341)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk151_4(X6338,X6339,X6340,X6341)),esk150_4(X6338,X6339,X6340,X6341)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6338),hAPP_f856106132t_bool(X6339,X6341)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6338),hAPP_f856106132t_bool(X6339,X6340)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6340),X6341)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X6339,esk151_4(X6338,X6339,X6340,X6341))),hAPP_f856106132t_bool(X6339,esk150_4(X6338,X6339,X6340,X6341))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6338),hAPP_f856106132t_bool(X6339,X6341)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6338),hAPP_f856106132t_bool(X6339,X6340)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6340),X6341)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_694_xt7])])])]) ).

fof(i_0_1630,plain,
    ! [X6332,X6333,X6334,X6335] :
      ( ( is_fun288122577l_bool(esk148_4(X6332,X6333,X6334,X6335))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6332),hAPP_f985923321t_bool(X6333,X6335)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6332),hAPP_f985923321t_bool(X6333,X6334)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6334),X6335)) )
      & ( is_fun288122577l_bool(esk149_4(X6332,X6333,X6334,X6335))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6332),hAPP_f985923321t_bool(X6333,X6335)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6332),hAPP_f985923321t_bool(X6333,X6334)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6334),X6335)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk149_4(X6332,X6333,X6334,X6335)),esk148_4(X6332,X6333,X6334,X6335)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6332),hAPP_f985923321t_bool(X6333,X6335)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6332),hAPP_f985923321t_bool(X6333,X6334)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6334),X6335)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X6333,esk149_4(X6332,X6333,X6334,X6335))),hAPP_f985923321t_bool(X6333,esk148_4(X6332,X6333,X6334,X6335))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6332),hAPP_f985923321t_bool(X6333,X6335)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6332),hAPP_f985923321t_bool(X6333,X6334)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6334),X6335)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_693_xt7])])])]) ).

fof(i_0_1631,plain,
    ! [X6326,X6327,X6328,X6329] :
      ( ( is_fun158382675l_bool(esk146_4(X6326,X6327,X6328,X6329))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6326),hAPP_f839525755t_bool(X6327,X6329)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6326),hAPP_f839525755t_bool(X6327,X6328)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6328),X6329)) )
      & ( is_fun158382675l_bool(esk147_4(X6326,X6327,X6328,X6329))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6326),hAPP_f839525755t_bool(X6327,X6329)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6326),hAPP_f839525755t_bool(X6327,X6328)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6328),X6329)) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk147_4(X6326,X6327,X6328,X6329)),esk146_4(X6326,X6327,X6328,X6329)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6326),hAPP_f839525755t_bool(X6327,X6329)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6326),hAPP_f839525755t_bool(X6327,X6328)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6328),X6329)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X6327,esk147_4(X6326,X6327,X6328,X6329))),hAPP_f839525755t_bool(X6327,esk146_4(X6326,X6327,X6328,X6329))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6326),hAPP_f839525755t_bool(X6327,X6329)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6326),hAPP_f839525755t_bool(X6327,X6328)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6328),X6329)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_692_xt7])])])]) ).

fof(i_0_1632,plain,
    ! [X6320,X6321,X6322,X6323] :
      ( ( is_fun279392540l_bool(esk144_4(X6320,X6321,X6322,X6323))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6320),hAPP_f464145314t_bool(X6321,X6323)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6320),hAPP_f464145314t_bool(X6321,X6322)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6322),X6323)) )
      & ( is_fun279392540l_bool(esk145_4(X6320,X6321,X6322,X6323))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6320),hAPP_f464145314t_bool(X6321,X6323)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6320),hAPP_f464145314t_bool(X6321,X6322)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6322),X6323)) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk145_4(X6320,X6321,X6322,X6323)),esk144_4(X6320,X6321,X6322,X6323)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6320),hAPP_f464145314t_bool(X6321,X6323)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6320),hAPP_f464145314t_bool(X6321,X6322)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6322),X6323)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X6321,esk145_4(X6320,X6321,X6322,X6323))),hAPP_f464145314t_bool(X6321,esk144_4(X6320,X6321,X6322,X6323))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6320),hAPP_f464145314t_bool(X6321,X6323)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6320),hAPP_f464145314t_bool(X6321,X6322)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6322),X6323)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_691_xt7])])])]) ).

fof(i_0_1633,plain,
    ! [X6350,X6351,X6352,X6353] :
      ( ( is_fun1236654035i_bool(esk154_4(X6350,X6351,X6352,X6353))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6350),hAPP_f2026336507t_bool(X6351,X6353)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6350),hAPP_f2026336507t_bool(X6351,X6352)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6352),X6353)) )
      & ( is_fun1236654035i_bool(esk155_4(X6350,X6351,X6352,X6353))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6350),hAPP_f2026336507t_bool(X6351,X6353)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6350),hAPP_f2026336507t_bool(X6351,X6352)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6352),X6353)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk155_4(X6350,X6351,X6352,X6353)),esk154_4(X6350,X6351,X6352,X6353)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6350),hAPP_f2026336507t_bool(X6351,X6353)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6350),hAPP_f2026336507t_bool(X6351,X6352)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6352),X6353)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X6351,esk155_4(X6350,X6351,X6352,X6353))),hAPP_f2026336507t_bool(X6351,esk154_4(X6350,X6351,X6352,X6353))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6350),hAPP_f2026336507t_bool(X6351,X6353)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6350),hAPP_f2026336507t_bool(X6351,X6352)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6352),X6353)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_696_xt7])])])]) ).

fof(i_0_1634,plain,
    ! [X6134,X6135,X6136,X6137] :
      ( ( is_fun1236654035i_bool(esk82_4(X6134,X6135,X6136,X6137))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6134),hAPP_f2026336507t_bool(X6135,X6137)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6134),hAPP_f2026336507t_bool(X6135,X6136)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6136),X6137)) )
      & ( is_fun1236654035i_bool(esk83_4(X6134,X6135,X6136,X6137))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6134),hAPP_f2026336507t_bool(X6135,X6137)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6134),hAPP_f2026336507t_bool(X6135,X6136)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6136),X6137)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk83_4(X6134,X6135,X6136,X6137)),esk82_4(X6134,X6135,X6136,X6137)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6134),hAPP_f2026336507t_bool(X6135,X6137)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6134),hAPP_f2026336507t_bool(X6135,X6136)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6136),X6137)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6135,esk83_4(X6134,X6135,X6136,X6137))),hAPP_f2026336507t_bool(X6135,esk82_4(X6134,X6135,X6136,X6137))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6134),hAPP_f2026336507t_bool(X6135,X6137)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6134),hAPP_f2026336507t_bool(X6135,X6136)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6136),X6137)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_660_xt5])])])]) ).

fof(i_0_1635,plain,
    ! [X6356,X6357,X6358,X6359] :
      ( ( is_fun1568535512t_bool(esk156_4(X6356,X6357,X6358,X6359))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6356),hAPP_f543204480t_bool(X6357,X6359)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6356),hAPP_f543204480t_bool(X6357,X6358)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6358),X6359)) )
      & ( is_fun1568535512t_bool(esk157_4(X6356,X6357,X6358,X6359))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6356),hAPP_f543204480t_bool(X6357,X6359)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6356),hAPP_f543204480t_bool(X6357,X6358)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6358),X6359)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk157_4(X6356,X6357,X6358,X6359)),esk156_4(X6356,X6357,X6358,X6359)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6356),hAPP_f543204480t_bool(X6357,X6359)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6356),hAPP_f543204480t_bool(X6357,X6358)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6358),X6359)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X6357,esk157_4(X6356,X6357,X6358,X6359))),hAPP_f543204480t_bool(X6357,esk156_4(X6356,X6357,X6358,X6359))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6356),hAPP_f543204480t_bool(X6357,X6359)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6356),hAPP_f543204480t_bool(X6357,X6358)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6358),X6359)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_697_xt7])])])]) ).

fof(i_0_1636,plain,
    ! [X6128,X6129,X6130,X6131] :
      ( ( is_fun1568535512t_bool(esk80_4(X6128,X6129,X6130,X6131))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6128),hAPP_f543204480t_bool(X6129,X6131)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6128),hAPP_f543204480t_bool(X6129,X6130)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6130),X6131)) )
      & ( is_fun1568535512t_bool(esk81_4(X6128,X6129,X6130,X6131))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6128),hAPP_f543204480t_bool(X6129,X6131)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6128),hAPP_f543204480t_bool(X6129,X6130)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6130),X6131)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk81_4(X6128,X6129,X6130,X6131)),esk80_4(X6128,X6129,X6130,X6131)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6128),hAPP_f543204480t_bool(X6129,X6131)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6128),hAPP_f543204480t_bool(X6129,X6130)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6130),X6131)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6129,esk81_4(X6128,X6129,X6130,X6131))),hAPP_f543204480t_bool(X6129,esk80_4(X6128,X6129,X6130,X6131))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6128),hAPP_f543204480t_bool(X6129,X6131)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6128),hAPP_f543204480t_bool(X6129,X6130)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6130),X6131)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_659_xt5])])])]) ).

fof(i_0_1637,plain,
    ! [X6344,X6345,X6346,X6347] :
      ( ( is_bool(esk152_4(X6344,X6345,X6346,X6347))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6344),hAPP_b1013836512t_bool(X6345,X6347)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6344),hAPP_b1013836512t_bool(X6345,X6346)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6346),X6347)) )
      & ( is_bool(esk153_4(X6344,X6345,X6346,X6347))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6344),hAPP_b1013836512t_bool(X6345,X6347)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6344),hAPP_b1013836512t_bool(X6345,X6346)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6346),X6347)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk153_4(X6344,X6345,X6346,X6347)),esk152_4(X6344,X6345,X6346,X6347)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6344),hAPP_b1013836512t_bool(X6345,X6347)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6344),hAPP_b1013836512t_bool(X6345,X6346)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6346),X6347)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X6345,esk153_4(X6344,X6345,X6346,X6347))),hAPP_b1013836512t_bool(X6345,esk152_4(X6344,X6345,X6346,X6347))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6344),hAPP_b1013836512t_bool(X6345,X6347)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6344),hAPP_b1013836512t_bool(X6345,X6346)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6346),X6347)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_695_xt7])])])]) ).

fof(i_0_1638,plain,
    ! [X6266,X6267,X6268,X6269] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk127_4(X6266,X6267,X6268,X6269)),esk126_4(X6266,X6267,X6268,X6269)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6266),hAPP_f800510211t_bool(X6267,X6269)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6266),hAPP_f800510211t_bool(X6267,X6268)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6268),X6269)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X6267,esk127_4(X6266,X6267,X6268,X6269))),hAPP_f800510211t_bool(X6267,esk126_4(X6266,X6267,X6268,X6269))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6266),hAPP_f800510211t_bool(X6267,X6269)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6266),hAPP_f800510211t_bool(X6267,X6268)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6268),X6269)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_682_xt7])])])]) ).

fof(i_0_1639,plain,
    ! [X6122,X6123,X6124,X6125] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk79_4(X6122,X6123,X6124,X6125)),esk78_4(X6122,X6123,X6124,X6125)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6122),hAPP_f800510211t_bool(X6123,X6125)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6122),hAPP_f800510211t_bool(X6123,X6124)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6124),X6125)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6123,esk79_4(X6122,X6123,X6124,X6125))),hAPP_f800510211t_bool(X6123,esk78_4(X6122,X6123,X6124,X6125))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6122),hAPP_f800510211t_bool(X6123,X6125)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6122),hAPP_f800510211t_bool(X6123,X6124)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6124),X6125)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_658_xt5])])])]) ).

fof(i_0_1640,plain,
    ! [X6212,X6213,X6214,X6215] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk109_4(X6212,X6213,X6214,X6215)),esk108_4(X6212,X6213,X6214,X6215)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6212),hAPP_n1699378549t_bool(X6213,X6215)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6212),hAPP_n1699378549t_bool(X6213,X6214)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6214),X6215)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X6213,esk109_4(X6212,X6213,X6214,X6215))),hAPP_n1699378549t_bool(X6213,esk108_4(X6212,X6213,X6214,X6215))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6212),hAPP_n1699378549t_bool(X6213,X6215)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6212),hAPP_n1699378549t_bool(X6213,X6214)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6214),X6215)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_673_xt7])])])]) ).

fof(i_0_1641,plain,
    ! [X6140,X6141,X6142,X6143] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk85_4(X6140,X6141,X6142,X6143)),esk84_4(X6140,X6141,X6142,X6143)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6140),hAPP_n1699378549t_bool(X6141,X6143)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6140),hAPP_n1699378549t_bool(X6141,X6142)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6142),X6143)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6141,esk85_4(X6140,X6141,X6142,X6143))),hAPP_n1699378549t_bool(X6141,esk84_4(X6140,X6141,X6142,X6143))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6140),hAPP_n1699378549t_bool(X6141,X6143)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6140),hAPP_n1699378549t_bool(X6141,X6142)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6142),X6143)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_661_xt5])])])]) ).

fof(i_0_1642,plain,
    ! [X7077,X7078,X7079,X7080] :
      ( ( is_fun2093718614t_bool(esk362_4(X7077,X7078,X7079,X7080))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7078),hAPP_f1363542492t_bool(X7079,X7077)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7080),X7077))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7078),hAPP_f1363542492t_bool(X7079,X7080))) )
      & ( is_fun2093718614t_bool(esk363_4(X7077,X7078,X7079,X7080))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7078),hAPP_f1363542492t_bool(X7079,X7077)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7080),X7077))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7078),hAPP_f1363542492t_bool(X7079,X7080))) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk362_4(X7077,X7078,X7079,X7080)),esk363_4(X7077,X7078,X7079,X7080)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7078),hAPP_f1363542492t_bool(X7079,X7077)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7080),X7077))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7078),hAPP_f1363542492t_bool(X7079,X7080))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X7079,esk362_4(X7077,X7078,X7079,X7080))),hAPP_f1363542492t_bool(X7079,esk363_4(X7077,X7078,X7079,X7080))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7078),hAPP_f1363542492t_bool(X7079,X7077)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7080),X7077))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7078),hAPP_f1363542492t_bool(X7079,X7080))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_846_order__less__le__subst1])])])]) ).

fof(i_0_1643,plain,
    ! [X7053,X7054,X7055,X7056] :
      ( ( is_fun961089132t_bool(esk354_4(X7053,X7054,X7055,X7056))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7054),hAPP_f856106132t_bool(X7055,X7053)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7056),X7053))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7054),hAPP_f856106132t_bool(X7055,X7056))) )
      & ( is_fun961089132t_bool(esk355_4(X7053,X7054,X7055,X7056))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7054),hAPP_f856106132t_bool(X7055,X7053)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7056),X7053))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7054),hAPP_f856106132t_bool(X7055,X7056))) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk354_4(X7053,X7054,X7055,X7056)),esk355_4(X7053,X7054,X7055,X7056)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7054),hAPP_f856106132t_bool(X7055,X7053)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7056),X7053))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7054),hAPP_f856106132t_bool(X7055,X7056))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X7055,esk354_4(X7053,X7054,X7055,X7056))),hAPP_f856106132t_bool(X7055,esk355_4(X7053,X7054,X7055,X7056))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7054),hAPP_f856106132t_bool(X7055,X7053)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7056),X7053))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7054),hAPP_f856106132t_bool(X7055,X7056))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_842_order__less__le__subst1])])])]) ).

fof(i_0_1644,plain,
    ! [X7047,X7048,X7049,X7050] :
      ( ( is_fun288122577l_bool(esk352_4(X7047,X7048,X7049,X7050))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7048),hAPP_f985923321t_bool(X7049,X7047)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7050),X7047))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7048),hAPP_f985923321t_bool(X7049,X7050))) )
      & ( is_fun288122577l_bool(esk353_4(X7047,X7048,X7049,X7050))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7048),hAPP_f985923321t_bool(X7049,X7047)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7050),X7047))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7048),hAPP_f985923321t_bool(X7049,X7050))) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk352_4(X7047,X7048,X7049,X7050)),esk353_4(X7047,X7048,X7049,X7050)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7048),hAPP_f985923321t_bool(X7049,X7047)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7050),X7047))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7048),hAPP_f985923321t_bool(X7049,X7050))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X7049,esk352_4(X7047,X7048,X7049,X7050))),hAPP_f985923321t_bool(X7049,esk353_4(X7047,X7048,X7049,X7050))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7048),hAPP_f985923321t_bool(X7049,X7047)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7050),X7047))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7048),hAPP_f985923321t_bool(X7049,X7050))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_841_order__less__le__subst1])])])]) ).

fof(i_0_1645,plain,
    ! [X7041,X7042,X7043,X7044] :
      ( ( is_fun158382675l_bool(esk350_4(X7041,X7042,X7043,X7044))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7042),hAPP_f839525755t_bool(X7043,X7041)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7044),X7041))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7042),hAPP_f839525755t_bool(X7043,X7044))) )
      & ( is_fun158382675l_bool(esk351_4(X7041,X7042,X7043,X7044))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7042),hAPP_f839525755t_bool(X7043,X7041)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7044),X7041))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7042),hAPP_f839525755t_bool(X7043,X7044))) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk350_4(X7041,X7042,X7043,X7044)),esk351_4(X7041,X7042,X7043,X7044)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7042),hAPP_f839525755t_bool(X7043,X7041)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7044),X7041))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7042),hAPP_f839525755t_bool(X7043,X7044))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X7043,esk350_4(X7041,X7042,X7043,X7044))),hAPP_f839525755t_bool(X7043,esk351_4(X7041,X7042,X7043,X7044))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7042),hAPP_f839525755t_bool(X7043,X7041)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7044),X7041))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7042),hAPP_f839525755t_bool(X7043,X7044))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_840_order__less__le__subst1])])])]) ).

fof(i_0_1646,plain,
    ! [X7035,X7036,X7037,X7038] :
      ( ( is_fun279392540l_bool(esk348_4(X7035,X7036,X7037,X7038))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7036),hAPP_f464145314t_bool(X7037,X7035)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7038),X7035))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7036),hAPP_f464145314t_bool(X7037,X7038))) )
      & ( is_fun279392540l_bool(esk349_4(X7035,X7036,X7037,X7038))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7036),hAPP_f464145314t_bool(X7037,X7035)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7038),X7035))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7036),hAPP_f464145314t_bool(X7037,X7038))) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk348_4(X7035,X7036,X7037,X7038)),esk349_4(X7035,X7036,X7037,X7038)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7036),hAPP_f464145314t_bool(X7037,X7035)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7038),X7035))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7036),hAPP_f464145314t_bool(X7037,X7038))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X7037,esk348_4(X7035,X7036,X7037,X7038))),hAPP_f464145314t_bool(X7037,esk349_4(X7035,X7036,X7037,X7038))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7036),hAPP_f464145314t_bool(X7037,X7035)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7038),X7035))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7036),hAPP_f464145314t_bool(X7037,X7038))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_839_order__less__le__subst1])])])]) ).

fof(i_0_1647,plain,
    ! [X7065,X7066,X7067,X7068] :
      ( ( is_fun1236654035i_bool(esk358_4(X7065,X7066,X7067,X7068))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7066),hAPP_f2026336507t_bool(X7067,X7065)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7068),X7065))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7066),hAPP_f2026336507t_bool(X7067,X7068))) )
      & ( is_fun1236654035i_bool(esk359_4(X7065,X7066,X7067,X7068))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7066),hAPP_f2026336507t_bool(X7067,X7065)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7068),X7065))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7066),hAPP_f2026336507t_bool(X7067,X7068))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk358_4(X7065,X7066,X7067,X7068)),esk359_4(X7065,X7066,X7067,X7068)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7066),hAPP_f2026336507t_bool(X7067,X7065)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7068),X7065))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7066),hAPP_f2026336507t_bool(X7067,X7068))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X7067,esk358_4(X7065,X7066,X7067,X7068))),hAPP_f2026336507t_bool(X7067,esk359_4(X7065,X7066,X7067,X7068))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7066),hAPP_f2026336507t_bool(X7067,X7065)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7068),X7065))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7066),hAPP_f2026336507t_bool(X7067,X7068))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_844_order__less__le__subst1])])])]) ).

fof(i_0_1648,plain,
    ! [X6849,X6850,X6851,X6852] :
      ( ( is_fun1236654035i_bool(esk286_4(X6849,X6850,X6851,X6852))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6850),hAPP_f2026336507t_bool(X6851,X6849)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6852),X6849))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6850),hAPP_f2026336507t_bool(X6851,X6852))) )
      & ( is_fun1236654035i_bool(esk287_4(X6849,X6850,X6851,X6852))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6850),hAPP_f2026336507t_bool(X6851,X6849)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6852),X6849))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6850),hAPP_f2026336507t_bool(X6851,X6852))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk286_4(X6849,X6850,X6851,X6852)),esk287_4(X6849,X6850,X6851,X6852)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6850),hAPP_f2026336507t_bool(X6851,X6849)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6852),X6849))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6850),hAPP_f2026336507t_bool(X6851,X6852))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X6851,esk286_4(X6849,X6850,X6851,X6852))),hAPP_f2026336507t_bool(X6851,esk287_4(X6849,X6850,X6851,X6852))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6850),hAPP_f2026336507t_bool(X6851,X6849)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6852),X6849))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6850),hAPP_f2026336507t_bool(X6851,X6852))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_808_order__le__less__subst1])])])]) ).

fof(i_0_1649,plain,
    ! [X7071,X7072,X7073,X7074] :
      ( ( is_fun1568535512t_bool(esk360_4(X7071,X7072,X7073,X7074))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7072),hAPP_f543204480t_bool(X7073,X7071)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7074),X7071))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7072),hAPP_f543204480t_bool(X7073,X7074))) )
      & ( is_fun1568535512t_bool(esk361_4(X7071,X7072,X7073,X7074))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7072),hAPP_f543204480t_bool(X7073,X7071)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7074),X7071))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7072),hAPP_f543204480t_bool(X7073,X7074))) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk360_4(X7071,X7072,X7073,X7074)),esk361_4(X7071,X7072,X7073,X7074)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7072),hAPP_f543204480t_bool(X7073,X7071)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7074),X7071))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7072),hAPP_f543204480t_bool(X7073,X7074))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X7073,esk360_4(X7071,X7072,X7073,X7074))),hAPP_f543204480t_bool(X7073,esk361_4(X7071,X7072,X7073,X7074))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7072),hAPP_f543204480t_bool(X7073,X7071)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7074),X7071))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7072),hAPP_f543204480t_bool(X7073,X7074))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_845_order__less__le__subst1])])])]) ).

fof(i_0_1650,plain,
    ! [X6843,X6844,X6845,X6846] :
      ( ( is_fun1568535512t_bool(esk284_4(X6843,X6844,X6845,X6846))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6844),hAPP_f543204480t_bool(X6845,X6843)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6846),X6843))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6844),hAPP_f543204480t_bool(X6845,X6846))) )
      & ( is_fun1568535512t_bool(esk285_4(X6843,X6844,X6845,X6846))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6844),hAPP_f543204480t_bool(X6845,X6843)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6846),X6843))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6844),hAPP_f543204480t_bool(X6845,X6846))) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk284_4(X6843,X6844,X6845,X6846)),esk285_4(X6843,X6844,X6845,X6846)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6844),hAPP_f543204480t_bool(X6845,X6843)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6846),X6843))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6844),hAPP_f543204480t_bool(X6845,X6846))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X6845,esk284_4(X6843,X6844,X6845,X6846))),hAPP_f543204480t_bool(X6845,esk285_4(X6843,X6844,X6845,X6846))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6844),hAPP_f543204480t_bool(X6845,X6843)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6846),X6843))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6844),hAPP_f543204480t_bool(X6845,X6846))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_807_order__le__less__subst1])])])]) ).

fof(i_0_1651,plain,
    ! [X7059,X7060,X7061,X7062] :
      ( ( is_bool(esk356_4(X7059,X7060,X7061,X7062))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7060),hAPP_b1013836512t_bool(X7061,X7059)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7062),X7059))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7060),hAPP_b1013836512t_bool(X7061,X7062))) )
      & ( is_bool(esk357_4(X7059,X7060,X7061,X7062))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7060),hAPP_b1013836512t_bool(X7061,X7059)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7062),X7059))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7060),hAPP_b1013836512t_bool(X7061,X7062))) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk356_4(X7059,X7060,X7061,X7062)),esk357_4(X7059,X7060,X7061,X7062)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7060),hAPP_b1013836512t_bool(X7061,X7059)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7062),X7059))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7060),hAPP_b1013836512t_bool(X7061,X7062))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X7061,esk356_4(X7059,X7060,X7061,X7062))),hAPP_b1013836512t_bool(X7061,esk357_4(X7059,X7060,X7061,X7062))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7060),hAPP_b1013836512t_bool(X7061,X7059)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7062),X7059))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7060),hAPP_b1013836512t_bool(X7061,X7062))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_843_order__less__le__subst1])])])]) ).

fof(i_0_1652,plain,
    ! [X6981,X6982,X6983,X6984] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk330_4(X6981,X6982,X6983,X6984)),esk331_4(X6981,X6982,X6983,X6984)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6982),hAPP_f800510211t_bool(X6983,X6981)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6984),X6981))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6982),hAPP_f800510211t_bool(X6983,X6984))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X6983,esk330_4(X6981,X6982,X6983,X6984))),hAPP_f800510211t_bool(X6983,esk331_4(X6981,X6982,X6983,X6984))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6982),hAPP_f800510211t_bool(X6983,X6981)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6984),X6981))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6982),hAPP_f800510211t_bool(X6983,X6984))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_830_order__less__le__subst1])])])]) ).

fof(i_0_1653,plain,
    ! [X6837,X6838,X6839,X6840] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk282_4(X6837,X6838,X6839,X6840)),esk283_4(X6837,X6838,X6839,X6840)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6838),hAPP_f800510211t_bool(X6839,X6837)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6840),X6837))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6838),hAPP_f800510211t_bool(X6839,X6840))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X6839,esk282_4(X6837,X6838,X6839,X6840))),hAPP_f800510211t_bool(X6839,esk283_4(X6837,X6838,X6839,X6840))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6838),hAPP_f800510211t_bool(X6839,X6837)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6840),X6837))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6838),hAPP_f800510211t_bool(X6839,X6840))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_806_order__le__less__subst1])])])]) ).

fof(i_0_1654,plain,
    ! [X6927,X6928,X6929,X6930] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk312_4(X6927,X6928,X6929,X6930)),esk313_4(X6927,X6928,X6929,X6930)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6928),hAPP_n1699378549t_bool(X6929,X6927)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6930),X6927))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6928),hAPP_n1699378549t_bool(X6929,X6930))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X6929,esk312_4(X6927,X6928,X6929,X6930))),hAPP_n1699378549t_bool(X6929,esk313_4(X6927,X6928,X6929,X6930))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6928),hAPP_n1699378549t_bool(X6929,X6927)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6930),X6927))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6928),hAPP_n1699378549t_bool(X6929,X6930))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_821_order__less__le__subst1])])])]) ).

fof(i_0_1655,plain,
    ! [X6855,X6856,X6857,X6858] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk288_4(X6855,X6856,X6857,X6858)),esk289_4(X6855,X6856,X6857,X6858)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6856),hAPP_n1699378549t_bool(X6857,X6855)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6858),X6855))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6856),hAPP_n1699378549t_bool(X6857,X6858))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X6857,esk288_4(X6855,X6856,X6857,X6858))),hAPP_n1699378549t_bool(X6857,esk289_4(X6855,X6856,X6857,X6858))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6856),hAPP_n1699378549t_bool(X6857,X6855)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6858),X6855))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6856),hAPP_n1699378549t_bool(X6857,X6858))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_809_order__le__less__subst1])])])]) ).

fof(i_0_1656,plain,
    ! [X6278,X6279,X6280,X6281] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk131_4(X6278,X6279,X6280,X6281)),esk130_4(X6278,X6279,X6280,X6281)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6278),hAPP_f632777549i_bool(X6279,X6281)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6278),hAPP_f632777549i_bool(X6279,X6280)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6280),X6281)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X6279,esk131_4(X6278,X6279,X6280,X6281))),hAPP_f632777549i_bool(X6279,esk130_4(X6278,X6279,X6280,X6281))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6278),hAPP_f632777549i_bool(X6279,X6281)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6278),hAPP_f632777549i_bool(X6279,X6280)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6280),X6281)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_684_xt7])])])]) ).

fof(i_0_1657,plain,
    ! [X6224,X6225,X6226,X6227] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk113_4(X6224,X6225,X6226,X6227)),esk112_4(X6224,X6225,X6226,X6227)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6224),hAPP_n821919323i_bool(X6225,X6227)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6224),hAPP_n821919323i_bool(X6225,X6226)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6226),X6227)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X6225,esk113_4(X6224,X6225,X6226,X6227))),hAPP_n821919323i_bool(X6225,esk112_4(X6224,X6225,X6226,X6227))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6224),hAPP_n821919323i_bool(X6225,X6227)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6224),hAPP_n821919323i_bool(X6225,X6226)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6226),X6227)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_675_xt7])])])]) ).

fof(i_0_1658,plain,
    ! [X6152,X6153,X6154,X6155] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk89_4(X6152,X6153,X6154,X6155)),esk88_4(X6152,X6153,X6154,X6155)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6152),hAPP_n821919323i_bool(X6153,X6155)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6152),hAPP_n821919323i_bool(X6153,X6154)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6154),X6155)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6153,esk89_4(X6152,X6153,X6154,X6155))),hAPP_n821919323i_bool(X6153,esk88_4(X6152,X6153,X6154,X6155))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6152),hAPP_n821919323i_bool(X6153,X6155)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6152),hAPP_n821919323i_bool(X6153,X6154)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6154),X6155)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_663_xt5])])])]) ).

fof(i_0_1659,plain,
    ! [X6993,X6994,X6995,X6996] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk334_4(X6993,X6994,X6995,X6996)),esk335_4(X6993,X6994,X6995,X6996)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6994),hAPP_f632777549i_bool(X6995,X6993)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6996),X6993))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6994),hAPP_f632777549i_bool(X6995,X6996))) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X6995,esk334_4(X6993,X6994,X6995,X6996))),hAPP_f632777549i_bool(X6995,esk335_4(X6993,X6994,X6995,X6996))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6994),hAPP_f632777549i_bool(X6995,X6993)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6996),X6993))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6994),hAPP_f632777549i_bool(X6995,X6996))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_832_order__less__le__subst1])])])]) ).

fof(i_0_1660,plain,
    ! [X6939,X6940,X6941,X6942] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk316_4(X6939,X6940,X6941,X6942)),esk317_4(X6939,X6940,X6941,X6942)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6940),hAPP_n821919323i_bool(X6941,X6939)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6942),X6939))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6940),hAPP_n821919323i_bool(X6941,X6942))) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X6941,esk316_4(X6939,X6940,X6941,X6942))),hAPP_n821919323i_bool(X6941,esk317_4(X6939,X6940,X6941,X6942))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6940),hAPP_n821919323i_bool(X6941,X6939)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6942),X6939))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6940),hAPP_n821919323i_bool(X6941,X6942))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_823_order__less__le__subst1])])])]) ).

fof(i_0_1661,plain,
    ! [X6867,X6868,X6869,X6870] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk292_4(X6867,X6868,X6869,X6870)),esk293_4(X6867,X6868,X6869,X6870)))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6868),hAPP_n821919323i_bool(X6869,X6867)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6870),X6867))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6868),hAPP_n821919323i_bool(X6869,X6870))) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X6869,esk292_4(X6867,X6868,X6869,X6870))),hAPP_n821919323i_bool(X6869,esk293_4(X6867,X6868,X6869,X6870))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6868),hAPP_n821919323i_bool(X6869,X6867)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6870),X6867))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6868),hAPP_n821919323i_bool(X6869,X6870))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_811_order__le__less__subst1])])])]) ).

fof(i_0_1662,plain,
    ! [X6314,X6315,X6316,X6317] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk143_4(X6314,X6315,X6316,X6317)),esk142_4(X6314,X6315,X6316,X6317)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6314),hAPP_f861874780t_bool(X6315,X6317)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6314),hAPP_f861874780t_bool(X6315,X6316)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6316),X6317)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X6315,esk143_4(X6314,X6315,X6316,X6317))),hAPP_f861874780t_bool(X6315,esk142_4(X6314,X6315,X6316,X6317))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6314),hAPP_f861874780t_bool(X6315,X6317)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6314),hAPP_f861874780t_bool(X6315,X6316)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6316),X6317)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_690_xt7])])])]) ).

fof(i_0_1663,plain,
    ! [X6260,X6261,X6262,X6263] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk125_4(X6260,X6261,X6262,X6263)),esk124_4(X6260,X6261,X6262,X6263)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6260),hAPP_n539120590t_bool(X6261,X6263)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6260),hAPP_n539120590t_bool(X6261,X6262)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6262),X6263)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X6261,esk125_4(X6260,X6261,X6262,X6263))),hAPP_n539120590t_bool(X6261,esk124_4(X6260,X6261,X6262,X6263))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6260),hAPP_n539120590t_bool(X6261,X6263)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6260),hAPP_n539120590t_bool(X6261,X6262)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6262),X6263)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_681_xt7])])])]) ).

fof(i_0_1664,plain,
    ! [X6188,X6189,X6190,X6191] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk101_4(X6188,X6189,X6190,X6191)),esk100_4(X6188,X6189,X6190,X6191)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6188),hAPP_n539120590t_bool(X6189,X6191)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6188),hAPP_n539120590t_bool(X6189,X6190)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6190),X6191)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6189,esk101_4(X6188,X6189,X6190,X6191))),hAPP_n539120590t_bool(X6189,esk100_4(X6188,X6189,X6190,X6191))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6188),hAPP_n539120590t_bool(X6189,X6191)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6188),hAPP_n539120590t_bool(X6189,X6190)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6190),X6191)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_669_xt5])])])]) ).

fof(i_0_1665,plain,
    ! [X7029,X7030,X7031,X7032] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk346_4(X7029,X7030,X7031,X7032)),esk347_4(X7029,X7030,X7031,X7032)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X7030),hAPP_f861874780t_bool(X7031,X7029)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7032),X7029))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X7030),hAPP_f861874780t_bool(X7031,X7032))) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X7031,esk346_4(X7029,X7030,X7031,X7032))),hAPP_f861874780t_bool(X7031,esk347_4(X7029,X7030,X7031,X7032))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X7030),hAPP_f861874780t_bool(X7031,X7029)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7032),X7029))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X7030),hAPP_f861874780t_bool(X7031,X7032))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_838_order__less__le__subst1])])])]) ).

fof(i_0_1666,plain,
    ! [X6975,X6976,X6977,X6978] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk328_4(X6975,X6976,X6977,X6978)),esk329_4(X6975,X6976,X6977,X6978)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6976),hAPP_n539120590t_bool(X6977,X6975)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6978),X6975))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6976),hAPP_n539120590t_bool(X6977,X6978))) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X6977,esk328_4(X6975,X6976,X6977,X6978))),hAPP_n539120590t_bool(X6977,esk329_4(X6975,X6976,X6977,X6978))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6976),hAPP_n539120590t_bool(X6977,X6975)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6978),X6975))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6976),hAPP_n539120590t_bool(X6977,X6978))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_829_order__less__le__subst1])])])]) ).

fof(i_0_1667,plain,
    ! [X6903,X6904,X6905,X6906] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk304_4(X6903,X6904,X6905,X6906)),esk305_4(X6903,X6904,X6905,X6906)))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6904),hAPP_n539120590t_bool(X6905,X6903)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6906),X6903))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6904),hAPP_n539120590t_bool(X6905,X6906))) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X6905,esk304_4(X6903,X6904,X6905,X6906))),hAPP_n539120590t_bool(X6905,esk305_4(X6903,X6904,X6905,X6906))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6904),hAPP_n539120590t_bool(X6905,X6903)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6906),X6903))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6904),hAPP_n539120590t_bool(X6905,X6906))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_817_order__le__less__subst1])])])]) ).

fof(i_0_1668,plain,
    ! [X6410,X6411,X6412,X6413] :
      ( ( is_fun2093718614t_bool(esk174_4(X6410,X6411,X6412,X6413))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6410),hAPP_f1358350510ol_nat(X6411,X6413)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6410),hAPP_f1358350510ol_nat(X6411,X6412)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6412),X6413)) )
      & ( is_fun2093718614t_bool(esk175_4(X6410,X6411,X6412,X6413))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6410),hAPP_f1358350510ol_nat(X6411,X6413)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6410),hAPP_f1358350510ol_nat(X6411,X6412)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6412),X6413)) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk175_4(X6410,X6411,X6412,X6413)),esk174_4(X6410,X6411,X6412,X6413)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6410),hAPP_f1358350510ol_nat(X6411,X6413)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6410),hAPP_f1358350510ol_nat(X6411,X6412)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6412),X6413)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X6411,esk175_4(X6410,X6411,X6412,X6413))),hAPP_f1358350510ol_nat(X6411,esk174_4(X6410,X6411,X6412,X6413))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6410),hAPP_f1358350510ol_nat(X6411,X6413)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6410),hAPP_f1358350510ol_nat(X6411,X6412)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6412),X6413)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_706_xt7])])])]) ).

fof(i_0_1669,plain,
    ! [X6386,X6387,X6388,X6389] :
      ( ( is_fun961089132t_bool(esk166_4(X6386,X6387,X6388,X6389))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6386),hAPP_f816335862ol_nat(X6387,X6389)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6386),hAPP_f816335862ol_nat(X6387,X6388)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6388),X6389)) )
      & ( is_fun961089132t_bool(esk167_4(X6386,X6387,X6388,X6389))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6386),hAPP_f816335862ol_nat(X6387,X6389)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6386),hAPP_f816335862ol_nat(X6387,X6388)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6388),X6389)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk167_4(X6386,X6387,X6388,X6389)),esk166_4(X6386,X6387,X6388,X6389)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6386),hAPP_f816335862ol_nat(X6387,X6389)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6386),hAPP_f816335862ol_nat(X6387,X6388)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6388),X6389)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X6387,esk167_4(X6386,X6387,X6388,X6389))),hAPP_f816335862ol_nat(X6387,esk166_4(X6386,X6387,X6388,X6389))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6386),hAPP_f816335862ol_nat(X6387,X6389)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6386),hAPP_f816335862ol_nat(X6387,X6388)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6388),X6389)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_702_xt7])])])]) ).

fof(i_0_1670,plain,
    ! [X6380,X6381,X6382,X6383] :
      ( ( is_fun288122577l_bool(esk164_4(X6380,X6381,X6382,X6383))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6380),hAPP_f897066961ol_nat(X6381,X6383)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6380),hAPP_f897066961ol_nat(X6381,X6382)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6382),X6383)) )
      & ( is_fun288122577l_bool(esk165_4(X6380,X6381,X6382,X6383))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6380),hAPP_f897066961ol_nat(X6381,X6383)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6380),hAPP_f897066961ol_nat(X6381,X6382)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6382),X6383)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk165_4(X6380,X6381,X6382,X6383)),esk164_4(X6380,X6381,X6382,X6383)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6380),hAPP_f897066961ol_nat(X6381,X6383)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6380),hAPP_f897066961ol_nat(X6381,X6382)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6382),X6383)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X6381,esk165_4(X6380,X6381,X6382,X6383))),hAPP_f897066961ol_nat(X6381,esk164_4(X6380,X6381,X6382,X6383))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6380),hAPP_f897066961ol_nat(X6381,X6383)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6380),hAPP_f897066961ol_nat(X6381,X6382)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6382),X6383)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_701_xt7])])])]) ).

fof(i_0_1671,plain,
    ! [X6374,X6375,X6376,X6377] :
      ( ( is_fun158382675l_bool(esk162_4(X6374,X6375,X6376,X6377))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6374),hAPP_f1695077327ol_nat(X6375,X6377)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6374),hAPP_f1695077327ol_nat(X6375,X6376)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6376),X6377)) )
      & ( is_fun158382675l_bool(esk163_4(X6374,X6375,X6376,X6377))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6374),hAPP_f1695077327ol_nat(X6375,X6377)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6374),hAPP_f1695077327ol_nat(X6375,X6376)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6376),X6377)) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk163_4(X6374,X6375,X6376,X6377)),esk162_4(X6374,X6375,X6376,X6377)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6374),hAPP_f1695077327ol_nat(X6375,X6377)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6374),hAPP_f1695077327ol_nat(X6375,X6376)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6376),X6377)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X6375,esk163_4(X6374,X6375,X6376,X6377))),hAPP_f1695077327ol_nat(X6375,esk162_4(X6374,X6375,X6376,X6377))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6374),hAPP_f1695077327ol_nat(X6375,X6377)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6374),hAPP_f1695077327ol_nat(X6375,X6376)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6376),X6377)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_700_xt7])])])]) ).

fof(i_0_1672,plain,
    ! [X6368,X6369,X6370,X6371] :
      ( ( is_fun279392540l_bool(esk160_4(X6368,X6369,X6370,X6371))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6368),hAPP_f1313392232ol_nat(X6369,X6371)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6368),hAPP_f1313392232ol_nat(X6369,X6370)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6370),X6371)) )
      & ( is_fun279392540l_bool(esk161_4(X6368,X6369,X6370,X6371))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6368),hAPP_f1313392232ol_nat(X6369,X6371)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6368),hAPP_f1313392232ol_nat(X6369,X6370)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6370),X6371)) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk161_4(X6368,X6369,X6370,X6371)),esk160_4(X6368,X6369,X6370,X6371)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6368),hAPP_f1313392232ol_nat(X6369,X6371)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6368),hAPP_f1313392232ol_nat(X6369,X6370)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6370),X6371)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X6369,esk161_4(X6368,X6369,X6370,X6371))),hAPP_f1313392232ol_nat(X6369,esk160_4(X6368,X6369,X6370,X6371))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6368),hAPP_f1313392232ol_nat(X6369,X6371)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6368),hAPP_f1313392232ol_nat(X6369,X6370)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6370),X6371)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_699_xt7])])])]) ).

fof(i_0_1673,plain,
    ! [X6404,X6405,X6406,X6407] :
      ( ( is_fun1568535512t_bool(esk172_4(X6404,X6405,X6406,X6407))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6404),hAPP_f2030293770ol_nat(X6405,X6407)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6404),hAPP_f2030293770ol_nat(X6405,X6406)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6406),X6407)) )
      & ( is_fun1568535512t_bool(esk173_4(X6404,X6405,X6406,X6407))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6404),hAPP_f2030293770ol_nat(X6405,X6407)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6404),hAPP_f2030293770ol_nat(X6405,X6406)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6406),X6407)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk173_4(X6404,X6405,X6406,X6407)),esk172_4(X6404,X6405,X6406,X6407)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6404),hAPP_f2030293770ol_nat(X6405,X6407)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6404),hAPP_f2030293770ol_nat(X6405,X6406)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6406),X6407)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X6405,esk173_4(X6404,X6405,X6406,X6407))),hAPP_f2030293770ol_nat(X6405,esk172_4(X6404,X6405,X6406,X6407))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6404),hAPP_f2030293770ol_nat(X6405,X6407)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6404),hAPP_f2030293770ol_nat(X6405,X6406)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6406),X6407)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_705_xt7])])])]) ).

fof(i_0_1674,plain,
    ! [X6200,X6201,X6202,X6203] :
      ( ( is_fun1568535512t_bool(esk104_4(X6200,X6201,X6202,X6203))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6200),hAPP_f2030293770ol_nat(X6201,X6203)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6200),hAPP_f2030293770ol_nat(X6201,X6202)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6202),X6203)) )
      & ( is_fun1568535512t_bool(esk105_4(X6200,X6201,X6202,X6203))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6200),hAPP_f2030293770ol_nat(X6201,X6203)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6200),hAPP_f2030293770ol_nat(X6201,X6202)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6202),X6203)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk105_4(X6200,X6201,X6202,X6203)),esk104_4(X6200,X6201,X6202,X6203)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6200),hAPP_f2030293770ol_nat(X6201,X6203)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6200),hAPP_f2030293770ol_nat(X6201,X6202)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6202),X6203)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6201,esk105_4(X6200,X6201,X6202,X6203))),hAPP_f2030293770ol_nat(X6201,esk104_4(X6200,X6201,X6202,X6203))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6200),hAPP_f2030293770ol_nat(X6201,X6203)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6200),hAPP_f2030293770ol_nat(X6201,X6202)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6202),X6203)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_671_xt5])])])]) ).

fof(i_0_1675,plain,
    ! [X6194,X6195,X6196,X6197] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk103_4(X6194,X6195,X6196,X6197)),esk102_4(X6194,X6195,X6196,X6197)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6194),hAPP_f22106695ol_nat(X6195,X6197)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6194),hAPP_f22106695ol_nat(X6195,X6196)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6196),X6197)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X6195,esk103_4(X6194,X6195,X6196,X6197))),hAPP_f22106695ol_nat(X6195,esk102_4(X6194,X6195,X6196,X6197))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6194),hAPP_f22106695ol_nat(X6195,X6197)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6194),hAPP_f22106695ol_nat(X6195,X6196)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6196),X6197)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_670_xt5])])])]) ).

fof(i_0_1676,plain,
    ! [X6392,X6393,X6394,X6395] :
      ( ( is_bool(esk168_4(X6392,X6393,X6394,X6395))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6392),hAPP_bool_nat(X6393,X6395)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6392),hAPP_bool_nat(X6393,X6394)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6394),X6395)) )
      & ( is_bool(esk169_4(X6392,X6393,X6394,X6395))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6392),hAPP_bool_nat(X6393,X6395)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6392),hAPP_bool_nat(X6393,X6394)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6394),X6395)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk169_4(X6392,X6393,X6394,X6395)),esk168_4(X6392,X6393,X6394,X6395)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6392),hAPP_bool_nat(X6393,X6395)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6392),hAPP_bool_nat(X6393,X6394)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6394),X6395)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X6393,esk169_4(X6392,X6393,X6394,X6395))),hAPP_bool_nat(X6393,esk168_4(X6392,X6393,X6394,X6395))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6392),hAPP_bool_nat(X6393,X6395)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6392),hAPP_bool_nat(X6393,X6394)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6394),X6395)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_703_xt7])])])]) ).

fof(i_0_1677,plain,
    ! [X6398,X6399,X6400,X6401] :
      ( ( is_fun1236654035i_bool(esk170_4(X6398,X6399,X6400,X6401))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6398),hAPP_f2120083535ol_nat(X6399,X6401)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6398),hAPP_f2120083535ol_nat(X6399,X6400)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6400),X6401)) )
      & ( is_fun1236654035i_bool(esk171_4(X6398,X6399,X6400,X6401))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6398),hAPP_f2120083535ol_nat(X6399,X6401)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6398),hAPP_f2120083535ol_nat(X6399,X6400)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6400),X6401)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk171_4(X6398,X6399,X6400,X6401)),esk170_4(X6398,X6399,X6400,X6401)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6398),hAPP_f2120083535ol_nat(X6399,X6401)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6398),hAPP_f2120083535ol_nat(X6399,X6400)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6400),X6401)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X6399,esk171_4(X6398,X6399,X6400,X6401))),hAPP_f2120083535ol_nat(X6399,esk170_4(X6398,X6399,X6400,X6401))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6398),hAPP_f2120083535ol_nat(X6399,X6401)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6398),hAPP_f2120083535ol_nat(X6399,X6400)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6400),X6401)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_704_xt7])])])]) ).

fof(i_0_1678,plain,
    ! [X6206,X6207,X6208,X6209] :
      ( ( is_fun1236654035i_bool(esk106_4(X6206,X6207,X6208,X6209))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6206),hAPP_f2120083535ol_nat(X6207,X6209)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6206),hAPP_f2120083535ol_nat(X6207,X6208)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6208),X6209)) )
      & ( is_fun1236654035i_bool(esk107_4(X6206,X6207,X6208,X6209))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6206),hAPP_f2120083535ol_nat(X6207,X6209)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6206),hAPP_f2120083535ol_nat(X6207,X6208)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6208),X6209)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk107_4(X6206,X6207,X6208,X6209)),esk106_4(X6206,X6207,X6208,X6209)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6206),hAPP_f2120083535ol_nat(X6207,X6209)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6206),hAPP_f2120083535ol_nat(X6207,X6208)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6208),X6209)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6207,esk107_4(X6206,X6207,X6208,X6209))),hAPP_f2120083535ol_nat(X6207,esk106_4(X6206,X6207,X6208,X6209))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6206),hAPP_f2120083535ol_nat(X6207,X6209)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6206),hAPP_f2120083535ol_nat(X6207,X6208)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6208),X6209)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_672_xt5])])])]) ).

fof(i_0_1679,plain,
    ! [X7125,X7126,X7127,X7128] :
      ( ( is_fun2093718614t_bool(esk378_4(X7125,X7126,X7127,X7128))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7126),hAPP_f1358350510ol_nat(X7127,X7125)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7128),X7125))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7126),hAPP_f1358350510ol_nat(X7127,X7128))) )
      & ( is_fun2093718614t_bool(esk379_4(X7125,X7126,X7127,X7128))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7126),hAPP_f1358350510ol_nat(X7127,X7125)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7128),X7125))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7126),hAPP_f1358350510ol_nat(X7127,X7128))) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk378_4(X7125,X7126,X7127,X7128)),esk379_4(X7125,X7126,X7127,X7128)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7126),hAPP_f1358350510ol_nat(X7127,X7125)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7128),X7125))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7126),hAPP_f1358350510ol_nat(X7127,X7128))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X7127,esk378_4(X7125,X7126,X7127,X7128))),hAPP_f1358350510ol_nat(X7127,esk379_4(X7125,X7126,X7127,X7128))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7126),hAPP_f1358350510ol_nat(X7127,X7125)))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X7128),X7125))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7126),hAPP_f1358350510ol_nat(X7127,X7128))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_854_order__less__le__subst1])])])]) ).

fof(i_0_1680,plain,
    ! [X7101,X7102,X7103,X7104] :
      ( ( is_fun961089132t_bool(esk370_4(X7101,X7102,X7103,X7104))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7102),hAPP_f816335862ol_nat(X7103,X7101)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7104),X7101))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7102),hAPP_f816335862ol_nat(X7103,X7104))) )
      & ( is_fun961089132t_bool(esk371_4(X7101,X7102,X7103,X7104))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7102),hAPP_f816335862ol_nat(X7103,X7101)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7104),X7101))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7102),hAPP_f816335862ol_nat(X7103,X7104))) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk370_4(X7101,X7102,X7103,X7104)),esk371_4(X7101,X7102,X7103,X7104)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7102),hAPP_f816335862ol_nat(X7103,X7101)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7104),X7101))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7102),hAPP_f816335862ol_nat(X7103,X7104))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X7103,esk370_4(X7101,X7102,X7103,X7104))),hAPP_f816335862ol_nat(X7103,esk371_4(X7101,X7102,X7103,X7104))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7102),hAPP_f816335862ol_nat(X7103,X7101)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7104),X7101))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7102),hAPP_f816335862ol_nat(X7103,X7104))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_850_order__less__le__subst1])])])]) ).

fof(i_0_1681,plain,
    ! [X7095,X7096,X7097,X7098] :
      ( ( is_fun288122577l_bool(esk368_4(X7095,X7096,X7097,X7098))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7096),hAPP_f897066961ol_nat(X7097,X7095)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7098),X7095))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7096),hAPP_f897066961ol_nat(X7097,X7098))) )
      & ( is_fun288122577l_bool(esk369_4(X7095,X7096,X7097,X7098))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7096),hAPP_f897066961ol_nat(X7097,X7095)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7098),X7095))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7096),hAPP_f897066961ol_nat(X7097,X7098))) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk368_4(X7095,X7096,X7097,X7098)),esk369_4(X7095,X7096,X7097,X7098)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7096),hAPP_f897066961ol_nat(X7097,X7095)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7098),X7095))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7096),hAPP_f897066961ol_nat(X7097,X7098))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X7097,esk368_4(X7095,X7096,X7097,X7098))),hAPP_f897066961ol_nat(X7097,esk369_4(X7095,X7096,X7097,X7098))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7096),hAPP_f897066961ol_nat(X7097,X7095)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7098),X7095))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7096),hAPP_f897066961ol_nat(X7097,X7098))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_849_order__less__le__subst1])])])]) ).

fof(i_0_1682,plain,
    ! [X7089,X7090,X7091,X7092] :
      ( ( is_fun158382675l_bool(esk366_4(X7089,X7090,X7091,X7092))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7090),hAPP_f1695077327ol_nat(X7091,X7089)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7092),X7089))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7090),hAPP_f1695077327ol_nat(X7091,X7092))) )
      & ( is_fun158382675l_bool(esk367_4(X7089,X7090,X7091,X7092))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7090),hAPP_f1695077327ol_nat(X7091,X7089)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7092),X7089))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7090),hAPP_f1695077327ol_nat(X7091,X7092))) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk366_4(X7089,X7090,X7091,X7092)),esk367_4(X7089,X7090,X7091,X7092)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7090),hAPP_f1695077327ol_nat(X7091,X7089)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7092),X7089))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7090),hAPP_f1695077327ol_nat(X7091,X7092))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X7091,esk366_4(X7089,X7090,X7091,X7092))),hAPP_f1695077327ol_nat(X7091,esk367_4(X7089,X7090,X7091,X7092))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7090),hAPP_f1695077327ol_nat(X7091,X7089)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7092),X7089))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7090),hAPP_f1695077327ol_nat(X7091,X7092))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_848_order__less__le__subst1])])])]) ).

fof(i_0_1683,plain,
    ! [X7083,X7084,X7085,X7086] :
      ( ( is_fun279392540l_bool(esk364_4(X7083,X7084,X7085,X7086))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7084),hAPP_f1313392232ol_nat(X7085,X7083)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7086),X7083))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7084),hAPP_f1313392232ol_nat(X7085,X7086))) )
      & ( is_fun279392540l_bool(esk365_4(X7083,X7084,X7085,X7086))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7084),hAPP_f1313392232ol_nat(X7085,X7083)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7086),X7083))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7084),hAPP_f1313392232ol_nat(X7085,X7086))) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk364_4(X7083,X7084,X7085,X7086)),esk365_4(X7083,X7084,X7085,X7086)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7084),hAPP_f1313392232ol_nat(X7085,X7083)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7086),X7083))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7084),hAPP_f1313392232ol_nat(X7085,X7086))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X7085,esk364_4(X7083,X7084,X7085,X7086))),hAPP_f1313392232ol_nat(X7085,esk365_4(X7083,X7084,X7085,X7086))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7084),hAPP_f1313392232ol_nat(X7085,X7083)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7086),X7083))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7084),hAPP_f1313392232ol_nat(X7085,X7086))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_847_order__less__le__subst1])])])]) ).

fof(i_0_1684,plain,
    ! [X7119,X7120,X7121,X7122] :
      ( ( is_fun1568535512t_bool(esk376_4(X7119,X7120,X7121,X7122))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7120),hAPP_f2030293770ol_nat(X7121,X7119)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7122),X7119))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7120),hAPP_f2030293770ol_nat(X7121,X7122))) )
      & ( is_fun1568535512t_bool(esk377_4(X7119,X7120,X7121,X7122))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7120),hAPP_f2030293770ol_nat(X7121,X7119)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7122),X7119))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7120),hAPP_f2030293770ol_nat(X7121,X7122))) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk376_4(X7119,X7120,X7121,X7122)),esk377_4(X7119,X7120,X7121,X7122)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7120),hAPP_f2030293770ol_nat(X7121,X7119)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7122),X7119))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7120),hAPP_f2030293770ol_nat(X7121,X7122))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X7121,esk376_4(X7119,X7120,X7121,X7122))),hAPP_f2030293770ol_nat(X7121,esk377_4(X7119,X7120,X7121,X7122))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7120),hAPP_f2030293770ol_nat(X7121,X7119)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7122),X7119))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7120),hAPP_f2030293770ol_nat(X7121,X7122))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_853_order__less__le__subst1])])])]) ).

fof(i_0_1685,plain,
    ! [X6915,X6916,X6917,X6918] :
      ( ( is_fun1568535512t_bool(esk308_4(X6915,X6916,X6917,X6918))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6916),hAPP_f2030293770ol_nat(X6917,X6915)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6918),X6915))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6916),hAPP_f2030293770ol_nat(X6917,X6918))) )
      & ( is_fun1568535512t_bool(esk309_4(X6915,X6916,X6917,X6918))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6916),hAPP_f2030293770ol_nat(X6917,X6915)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6918),X6915))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6916),hAPP_f2030293770ol_nat(X6917,X6918))) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk308_4(X6915,X6916,X6917,X6918)),esk309_4(X6915,X6916,X6917,X6918)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6916),hAPP_f2030293770ol_nat(X6917,X6915)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6918),X6915))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6916),hAPP_f2030293770ol_nat(X6917,X6918))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X6917,esk308_4(X6915,X6916,X6917,X6918))),hAPP_f2030293770ol_nat(X6917,esk309_4(X6915,X6916,X6917,X6918))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6916),hAPP_f2030293770ol_nat(X6917,X6915)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6918),X6915))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6916),hAPP_f2030293770ol_nat(X6917,X6918))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_819_order__le__less__subst1])])])]) ).

fof(i_0_1686,plain,
    ! [X6909,X6910,X6911,X6912] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk306_4(X6909,X6910,X6911,X6912)),esk307_4(X6909,X6910,X6911,X6912)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6910),hAPP_f22106695ol_nat(X6911,X6909)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6912),X6909))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6910),hAPP_f22106695ol_nat(X6911,X6912))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X6911,esk306_4(X6909,X6910,X6911,X6912))),hAPP_f22106695ol_nat(X6911,esk307_4(X6909,X6910,X6911,X6912))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6910),hAPP_f22106695ol_nat(X6911,X6909)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6912),X6909))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6910),hAPP_f22106695ol_nat(X6911,X6912))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_818_order__le__less__subst1])])])]) ).

fof(i_0_1687,plain,
    ! [X7107,X7108,X7109,X7110] :
      ( ( is_bool(esk372_4(X7107,X7108,X7109,X7110))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7108),hAPP_bool_nat(X7109,X7107)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7110),X7107))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7108),hAPP_bool_nat(X7109,X7110))) )
      & ( is_bool(esk373_4(X7107,X7108,X7109,X7110))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7108),hAPP_bool_nat(X7109,X7107)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7110),X7107))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7108),hAPP_bool_nat(X7109,X7110))) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk372_4(X7107,X7108,X7109,X7110)),esk373_4(X7107,X7108,X7109,X7110)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7108),hAPP_bool_nat(X7109,X7107)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7110),X7107))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7108),hAPP_bool_nat(X7109,X7110))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X7109,esk372_4(X7107,X7108,X7109,X7110))),hAPP_bool_nat(X7109,esk373_4(X7107,X7108,X7109,X7110))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7108),hAPP_bool_nat(X7109,X7107)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X7110),X7107))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7108),hAPP_bool_nat(X7109,X7110))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_851_order__less__le__subst1])])])]) ).

fof(i_0_1688,plain,
    ! [X7113,X7114,X7115,X7116] :
      ( ( is_fun1236654035i_bool(esk374_4(X7113,X7114,X7115,X7116))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7114),hAPP_f2120083535ol_nat(X7115,X7113)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7116),X7113))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7114),hAPP_f2120083535ol_nat(X7115,X7116))) )
      & ( is_fun1236654035i_bool(esk375_4(X7113,X7114,X7115,X7116))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7114),hAPP_f2120083535ol_nat(X7115,X7113)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7116),X7113))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7114),hAPP_f2120083535ol_nat(X7115,X7116))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk374_4(X7113,X7114,X7115,X7116)),esk375_4(X7113,X7114,X7115,X7116)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7114),hAPP_f2120083535ol_nat(X7115,X7113)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7116),X7113))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7114),hAPP_f2120083535ol_nat(X7115,X7116))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X7115,esk374_4(X7113,X7114,X7115,X7116))),hAPP_f2120083535ol_nat(X7115,esk375_4(X7113,X7114,X7115,X7116))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7114),hAPP_f2120083535ol_nat(X7115,X7113)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7116),X7113))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7114),hAPP_f2120083535ol_nat(X7115,X7116))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_852_order__less__le__subst1])])])]) ).

fof(i_0_1689,plain,
    ! [X6921,X6922,X6923,X6924] :
      ( ( is_fun1236654035i_bool(esk310_4(X6921,X6922,X6923,X6924))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6922),hAPP_f2120083535ol_nat(X6923,X6921)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6924),X6921))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6922),hAPP_f2120083535ol_nat(X6923,X6924))) )
      & ( is_fun1236654035i_bool(esk311_4(X6921,X6922,X6923,X6924))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6922),hAPP_f2120083535ol_nat(X6923,X6921)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6924),X6921))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6922),hAPP_f2120083535ol_nat(X6923,X6924))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk310_4(X6921,X6922,X6923,X6924)),esk311_4(X6921,X6922,X6923,X6924)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6922),hAPP_f2120083535ol_nat(X6923,X6921)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6924),X6921))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6922),hAPP_f2120083535ol_nat(X6923,X6924))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X6923,esk310_4(X6921,X6922,X6923,X6924))),hAPP_f2120083535ol_nat(X6923,esk311_4(X6921,X6922,X6923,X6924))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6922),hAPP_f2120083535ol_nat(X6923,X6921)))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6924),X6921))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6922),hAPP_f2120083535ol_nat(X6923,X6924))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_820_order__le__less__subst1])])])]) ).

fof(i_0_1690,plain,
    ! [X6308,X6309,X6310,X6311] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk141_4(X6308,X6309,X6310,X6311)),esk140_4(X6308,X6309,X6310,X6311)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6308),hAPP_f54304608l_bool(X6309,X6311)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6308),hAPP_f54304608l_bool(X6309,X6310)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6310),X6311)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X6309,esk141_4(X6308,X6309,X6310,X6311))),hAPP_f54304608l_bool(X6309,esk140_4(X6308,X6309,X6310,X6311))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6308),hAPP_f54304608l_bool(X6309,X6311)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6308),hAPP_f54304608l_bool(X6309,X6310)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6310),X6311)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_689_xt7])])])]) ).

fof(i_0_1691,plain,
    ! [X6254,X6255,X6256,X6257] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk123_4(X6254,X6255,X6256,X6257)),esk122_4(X6254,X6255,X6256,X6257)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6254),hAPP_nat_bool(X6255,X6257)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6254),hAPP_nat_bool(X6255,X6256)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6256),X6257)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X6255,esk123_4(X6254,X6255,X6256,X6257))),hAPP_nat_bool(X6255,esk122_4(X6254,X6255,X6256,X6257))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6254),hAPP_nat_bool(X6255,X6257)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6254),hAPP_nat_bool(X6255,X6256)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6256),X6257)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_680_xt7])])])]) ).

fof(i_0_1692,plain,
    ! [X6182,X6183,X6184,X6185] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk99_4(X6182,X6183,X6184,X6185)),esk98_4(X6182,X6183,X6184,X6185)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6182),hAPP_nat_bool(X6183,X6185)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6182),hAPP_nat_bool(X6183,X6184)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6184),X6185)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6183,esk99_4(X6182,X6183,X6184,X6185))),hAPP_nat_bool(X6183,esk98_4(X6182,X6183,X6184,X6185))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6182),hAPP_nat_bool(X6183,X6185)))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6182),hAPP_nat_bool(X6183,X6184)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6184),X6185)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_668_xt5])])])]) ).

fof(i_0_1693,plain,
    ! [X7023,X7024,X7025,X7026] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk344_4(X7023,X7024,X7025,X7026)),esk345_4(X7023,X7024,X7025,X7026)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X7024),hAPP_f54304608l_bool(X7025,X7023)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7026),X7023))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X7024),hAPP_f54304608l_bool(X7025,X7026))) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X7025,esk344_4(X7023,X7024,X7025,X7026))),hAPP_f54304608l_bool(X7025,esk345_4(X7023,X7024,X7025,X7026))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X7024),hAPP_f54304608l_bool(X7025,X7023)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7026),X7023))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X7024),hAPP_f54304608l_bool(X7025,X7026))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_837_order__less__le__subst1])])])]) ).

fof(i_0_1694,plain,
    ! [X6969,X6970,X6971,X6972] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk326_4(X6969,X6970,X6971,X6972)),esk327_4(X6969,X6970,X6971,X6972)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6970),hAPP_nat_bool(X6971,X6969)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6972),X6969))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6970),hAPP_nat_bool(X6971,X6972))) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X6971,esk326_4(X6969,X6970,X6971,X6972))),hAPP_nat_bool(X6971,esk327_4(X6969,X6970,X6971,X6972))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6970),hAPP_nat_bool(X6971,X6969)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6972),X6969))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6970),hAPP_nat_bool(X6971,X6972))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_828_order__less__le__subst1])])])]) ).

fof(i_0_1695,plain,
    ! [X6897,X6898,X6899,X6900] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk302_4(X6897,X6898,X6899,X6900)),esk303_4(X6897,X6898,X6899,X6900)))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6898),hAPP_nat_bool(X6899,X6897)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6900),X6897))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6898),hAPP_nat_bool(X6899,X6900))) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X6899,esk302_4(X6897,X6898,X6899,X6900))),hAPP_nat_bool(X6899,esk303_4(X6897,X6898,X6899,X6900))))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X6898),hAPP_nat_bool(X6899,X6897)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6900),X6897))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X6898),hAPP_nat_bool(X6899,X6900))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_816_order__le__less__subst1])])])]) ).

fof(i_0_1696,plain,
    ! [X7902,X7903] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X7903))
      | hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),X7903))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X7902))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X7903))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X7902))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1112_card__less__Suc])]) ).

fof(i_0_1697,plain,
    ! [X4462,X4463,X4464,X4465] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_f412050202t_bool(f,X4463)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_f412050202t_bool(f,X4462)))
        | is_Arr43961803e_indi(esk5_4(X4462,X4463,X4464,X4465))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4462),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4463),arrow_1721807329e_Prof))
        | X4464 = X4465
        | ~ is_Arr1861959080le_alt(X4464)
        | ~ is_Arr1861959080le_alt(X4465) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_f412050202t_bool(f,X4462)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_f412050202t_bool(f,X4463)))
        | is_Arr43961803e_indi(esk5_4(X4462,X4463,X4464,X4465))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4462),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4463),arrow_1721807329e_Prof))
        | X4464 = X4465
        | ~ is_Arr1861959080le_alt(X4464)
        | ~ is_Arr1861959080le_alt(X4465) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_f412050202t_bool(f,X4463)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_f412050202t_bool(f,X4462)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_A1677245848t_bool(X4463,esk5_4(X4462,X4463,X4464,X4465))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_A1677245848t_bool(X4462,esk5_4(X4462,X4463,X4464,X4465))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4462),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4463),arrow_1721807329e_Prof))
        | X4464 = X4465
        | ~ is_Arr1861959080le_alt(X4464)
        | ~ is_Arr1861959080le_alt(X4465) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_f412050202t_bool(f,X4462)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_f412050202t_bool(f,X4463)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_A1677245848t_bool(X4463,esk5_4(X4462,X4463,X4464,X4465))))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_A1677245848t_bool(X4462,esk5_4(X4462,X4463,X4464,X4465))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4462),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4463),arrow_1721807329e_Prof))
        | X4464 = X4465
        | ~ is_Arr1861959080le_alt(X4464)
        | ~ is_Arr1861959080le_alt(X4465) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_f412050202t_bool(f,X4463)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_f412050202t_bool(f,X4462)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_A1677245848t_bool(X4463,esk5_4(X4462,X4463,X4464,X4465))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_A1677245848t_bool(X4462,esk5_4(X4462,X4463,X4464,X4465))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4462),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4463),arrow_1721807329e_Prof))
        | X4464 = X4465
        | ~ is_Arr1861959080le_alt(X4464)
        | ~ is_Arr1861959080le_alt(X4465) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_f412050202t_bool(f,X4462)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_f412050202t_bool(f,X4463)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4464),X4465)),hAPP_A1677245848t_bool(X4463,esk5_4(X4462,X4463,X4464,X4465))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4465),X4464)),hAPP_A1677245848t_bool(X4462,esk5_4(X4462,X4463,X4464,X4465))))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4462),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4463),arrow_1721807329e_Prof))
        | X4464 = X4465
        | ~ is_Arr1861959080le_alt(X4464)
        | ~ is_Arr1861959080le_alt(X4465) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10__C3_C])])])]) ).

fof(i_0_1698,plain,
    ! [X6441,X6442] :
      ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X6441)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X6442)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6441),X6442)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6441),X6442))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X6441)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X6442))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_718_pred__subset__eq2])]) ).

fof(i_0_1699,plain,
    ! [X7906,X7907] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X7907))
      | hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),X7907))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X7906)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X7907))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X7906))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1364])]) ).

fof(i_0_1700,plain,
    ! [X4776] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | hAPP_A1637648121di_nat(h,X4776) != n
        | hAPP_A1637648121di_nat(h,X4776) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | hAPP_A1637648121di_nat(h,X4776) != n
        | hAPP_A1637648121di_nat(h,X4776) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | hAPP_A1637648121di_nat(h,X4776) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | hAPP_A1637648121di_nat(h,X4776) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | hAPP_A1637648121di_nat(h,X4776) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | hAPP_A1637648121di_nat(h,X4776) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | hAPP_A1637648121di_nat(h,X4776) != n
        | hAPP_A1637648121di_nat(h,X4776) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | hAPP_A1637648121di_nat(h,X4776) != n
        | hAPP_A1637648121di_nat(h,X4776) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | hAPP_A1637648121di_nat(h,X4776) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | hAPP_A1637648121di_nat(h,X4776) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | hAPP_A1637648121di_nat(h,X4776) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | hAPP_A1637648121di_nat(h,X4776) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
      & ( hAPP_A1637648121di_nat(h,X4776) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
      & ( hAPP_A1637648121di_nat(h,X4776) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
      & ( hAPP_A1637648121di_nat(h,X4776) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
      & ( hAPP_A1637648121di_nat(h,X4776) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) )
      & ( hAPP_A1637648121di_nat(h,X4776) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) )
      & ( hAPP_A1637648121di_nat(h,X4776) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4776)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) )
      & ( hAPP_A1637648121di_nat(h,X4776) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4776)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) )
      & ( hAPP_A1637648121di_nat(h,X4776) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4776)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4776)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1365])])]) ).

fof(i_0_1701,plain,
    ! [X4496,X4497,X4498,X4499,X4501,X4505] :
      ( ( is_Arr43961803e_indi(esk14_4(X4496,X4497,X4498,X4499))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4498),X4499)),hAPP_f412050202t_bool(X4496,X4497)))
        | ~ is_Arr1861959080le_alt(X4498)
        | ~ is_Arr1861959080le_alt(X4499)
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4497),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X4496)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4498),X4499)),hAPP_A1677245848t_bool(X4497,esk14_4(X4496,X4497,X4498,X4499))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4498),X4499)),hAPP_f412050202t_bool(X4496,X4497)))
        | ~ is_Arr1861959080le_alt(X4498)
        | ~ is_Arr1861959080le_alt(X4499)
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4497),arrow_1721807329e_Prof))
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X4496)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk15_1(X4501)),arrow_1721807329e_Prof))
        | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X4501)) )
      & ( is_Arr1861959080le_alt(esk16_1(X4501))
        | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X4501)) )
      & ( is_Arr1861959080le_alt(esk17_1(X4501))
        | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X4501)) )
      & ( ~ is_Arr43961803e_indi(X4505)
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk16_1(X4501)),esk17_1(X4501))),hAPP_A1677245848t_bool(esk15_1(X4501),X4505)))
        | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X4501)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk16_1(X4501)),esk17_1(X4501))),hAPP_f412050202t_bool(X4501,esk15_1(X4501))))
        | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X4501)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_24_unanimity__def])])])])])]) ).

fof(i_0_1702,plain,
    ! [X4467] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4467)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( hAPP_A1637648121di_nat(h,X4467) != n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4467)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( hAPP_A1637648121di_nat(h,X4467) = n
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4467)),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( hAPP_A1637648121di_nat(h,X4467) != n
        | hAPP_A1637648121di_nat(h,X4467) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4467)),e)))
        | hAPP_A1637648121di_nat(h,X4467) = n
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( hAPP_A1637648121di_nat(h,X4467) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4467)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4467)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4467)),c),e)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X4467)),n))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4467)),e)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( hAPP_A1637648121di_nat(h,X4467) != n
        | hAPP_A1637648121di_nat(h,X4467) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4467)),e)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4467)),e)))
        | hAPP_A1637648121di_nat(h,X4467) = n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4467)),e)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( hAPP_A1637648121di_nat(h,X4467) != n
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4467)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4467)),e)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X4467)),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X4467)),c),e)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X4467)),e)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X4467))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1366])])]) ).

fof(i_0_1703,plain,
    ! [X7725,X7726,X7727] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk479_3(X7725,X7726,X7727)),esk480_3(X7725,X7726,X7727)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X7727,X7725)),X7726)),hAPP_nat_nat(X7727,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7725),X7726)))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X7727,esk479_3(X7725,X7726,X7727))),hAPP_nat_nat(X7727,esk480_3(X7725,X7726,X7727))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X7727,X7725)),X7726)),hAPP_nat_nat(X7727,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7725),X7726)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1023_mono__nat__linear__lb])])])]) ).

fof(i_0_1704,plain,
    ! [X4765,X4766,X4769,X4770] :
      ( ( is_Arr1861959080le_alt(esk21_2(X4765,X4766))
        | X4766 = X4765
        | ~ is_fun961089132t_bool(X4765)
        | ~ is_fun961089132t_bool(X4766) )
      & ( is_Arr1861959080le_alt(esk22_2(X4765,X4766))
        | X4766 = X4765
        | ~ is_fun961089132t_bool(X4765)
        | ~ is_fun961089132t_bool(X4766) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk21_2(X4765,X4766)),esk22_2(X4765,X4766))),X4766))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk21_2(X4765,X4766)),esk22_2(X4765,X4766))),X4765))
        | X4766 = X4765
        | ~ is_fun961089132t_bool(X4765)
        | ~ is_fun961089132t_bool(X4766) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk21_2(X4765,X4766)),esk22_2(X4765,X4766))),X4766))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk21_2(X4765,X4766)),esk22_2(X4765,X4766))),X4765))
        | X4766 = X4765
        | ~ is_fun961089132t_bool(X4765)
        | ~ is_fun961089132t_bool(X4766) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4769),X4770)),X4766))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4769),X4770)),X4765))
        | ~ is_Arr1861959080le_alt(X4769)
        | ~ is_Arr1861959080le_alt(X4770)
        | X4766 != X4765
        | ~ is_fun961089132t_bool(X4765)
        | ~ is_fun961089132t_bool(X4766) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4769),X4770)),X4765))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4769),X4770)),X4766))
        | ~ is_Arr1861959080le_alt(X4769)
        | ~ is_Arr1861959080le_alt(X4770)
        | X4766 != X4765
        | ~ is_fun961089132t_bool(X4765)
        | ~ is_fun961089132t_bool(X4766) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_181_pred__equals__eq2])])])])]) ).

cnf(i_0_1705,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

fof(i_0_1706,plain,
    ! [X7904,X7905] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X7905))
      | hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X7905))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X7904))))) != zero_zero_nat ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1113_card__less])]) ).

fof(i_0_1707,plain,
    ! [X7730,X7731,X7732] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk481_3(X7730,X7731,X7732)),esk482_3(X7730,X7731,X7732)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7730),X7731))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X7732,X7730)),hAPP_nat_nat(X7732,X7731))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X7732,esk481_3(X7730,X7731,X7732))),hAPP_nat_nat(X7732,esk482_3(X7730,X7731,X7732))))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7730),X7731))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X7732,X7730)),hAPP_nat_nat(X7732,X7731))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1024_less__mono__imp__le__mono])])])]) ).

fof(i_0_1708,plain,
    ! [X4760,X4761,X4762,X4763,X4764] :
      ( ( X4760 != X4761
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4760 != X4764
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4763),X4761)),X4762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4761 != X4764
        | X4760 = X4763
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4763)),X4762))
        | X4760 = X4764
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4761 = X4764
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),X4762))
        | X4760 = X4764
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4760 != X4764
        | X4760 = X4764
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4761 != X4764
        | X4761 = X4764
        | X4760 = X4764
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),X4762))
        | X4761 = X4764
        | X4760 = X4764
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4761 != X4764
        | X4760 != X4763
        | X4760 = X4764
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),X4762))
        | X4760 != X4763
        | X4760 = X4764
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4761 != X4764
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4763)),X4762))
        | X4760 = X4764
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),X4762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4763)),X4762))
        | X4760 = X4764
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4760 != X4764
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4763),X4761)),X4762))
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4761 != X4764
        | X4761 = X4764
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4763),X4761)),X4762))
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),X4762))
        | X4761 = X4764
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4763),X4761)),X4762))
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4761 != X4764
        | X4760 != X4763
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4763),X4761)),X4762))
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),X4762))
        | X4760 != X4763
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4763),X4761)),X4762))
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( X4761 != X4764
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4763)),X4762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4763),X4761)),X4762))
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),X4762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4763)),X4762))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4763),X4761)),X4762))
        | X4760 = X4761
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4760),X4761)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4762),X4763),X4764)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4762),arrow_1681063817le_Lin))
        | X4763 = X4764
        | ~ is_Arr1861959080le_alt(X4760)
        | ~ is_Arr1861959080le_alt(X4761)
        | ~ is_Arr1861959080le_alt(X4763)
        | ~ is_Arr1861959080le_alt(X4764) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_180_in__above])])]) ).

fof(i_0_1709,plain,
    ! [X5981,X5982,X5983] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,esk42_3(X5981,X5982,X5983)),X5983))
        | hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X5981),pi_Pro1122146355t_unit(X5983,X5982))) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X5981,esk42_3(X5981,X5982,X5983))),hAPP_P332578347t_bool(X5982,esk42_3(X5981,X5982,X5983))))
        | hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X5981),pi_Pro1122146355t_unit(X5983,X5982))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_621_Pi__I])])])]) ).

fof(i_0_1710,plain,
    ! [X6089,X6090,X6091] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,esk69_3(X6089,X6090,X6091)),X6091))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6089),pi_Pro666468413t_bool(X6091,X6090))) )
      & ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X6089,esk69_3(X6089,X6090,X6091))),hAPP_P324742453l_bool(X6090,esk69_3(X6089,X6090,X6091))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X6089),pi_Pro666468413t_bool(X6091,X6090))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_648_Pi__I])])])]) ).

fof(i_0_1711,plain,
    ! [X5977,X5978,X5979] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,esk41_3(X5977,X5978,X5979)),X5979))
        | hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X5977),pi_Pro1270767662e_indi(X5979,X5978))) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X5977,esk41_3(X5977,X5978,X5979))),hAPP_P1875867302i_bool(X5978,esk41_3(X5977,X5978,X5979))))
        | hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X5977),pi_Pro1270767662e_indi(X5979,X5978))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_620_Pi__I])])])]) ).

fof(i_0_1712,plain,
    ! [X6017,X6018,X6019] :
      ( ( is_fun961089132t_bool(esk51_3(X6017,X6018,X6019))
        | hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X6017),pi_fun308431217t_unit(X6019,X6018))) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk51_3(X6017,X6018,X6019)),X6019))
        | hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X6017),pi_fun308431217t_unit(X6019,X6018))) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X6017,esk51_3(X6017,X6018,X6019))),hAPP_f1710744577t_bool(X6018,esk51_3(X6017,X6018,X6019))))
        | hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X6017),pi_fun308431217t_unit(X6019,X6018))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_630_Pi__I])])])]) ).

fof(i_0_1713,plain,
    ! [X6013,X6014,X6015] :
      ( ( is_fun961089132t_bool(esk50_3(X6013,X6014,X6015))
        | hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X6013),pi_fun1575168891l_bool(X6015,X6014))) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk50_3(X6013,X6014,X6015)),X6015))
        | hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X6013),pi_fun1575168891l_bool(X6015,X6014))) )
      & ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X6013,esk50_3(X6013,X6014,X6015))),hAPP_f210572555l_bool(X6014,esk50_3(X6013,X6014,X6015))))
        | hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X6013),pi_fun1575168891l_bool(X6015,X6014))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_629_Pi__I])])])]) ).

fof(i_0_1714,plain,
    ! [X6009,X6010,X6011] :
      ( ( is_fun961089132t_bool(esk49_3(X6009,X6010,X6011))
        | hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X6009),pi_fun896360044e_indi(X6011,X6010))) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk49_3(X6009,X6010,X6011)),X6011))
        | hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X6009),pi_fun896360044e_indi(X6011,X6010))) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X6009,esk49_3(X6009,X6010,X6011))),hAPP_f244157820i_bool(X6010,esk49_3(X6009,X6010,X6011))))
        | hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X6009),pi_fun896360044e_indi(X6011,X6010))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_628_Pi__I])])])]) ).

fof(i_0_1715,plain,
    ! [X6005,X6006,X6007] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,esk48_3(X6005,X6006,X6007)),X6007))
        | hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X6005),pi_fun321364250t_unit(X6007,X6006))) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X6005,esk48_3(X6005,X6006,X6007))),hAPP_f1866147972t_bool(X6006,esk48_3(X6005,X6006,X6007))))
        | hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X6005),pi_fun321364250t_unit(X6007,X6006))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_627_Pi__I])])])]) ).

fof(i_0_1716,plain,
    ! [X6001,X6002,X6003] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,esk47_3(X6001,X6002,X6003)),X6003))
        | hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X6001),pi_fun52649508l_bool(X6003,X6002))) )
      & ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X6001,esk47_3(X6001,X6002,X6003))),hAPP_f1624277646l_bool(X6002,esk47_3(X6001,X6002,X6003))))
        | hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X6001),pi_fun52649508l_bool(X6003,X6002))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_626_Pi__I])])])]) ).

fof(i_0_1717,plain,
    ! [X5997,X5998,X5999] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,esk46_3(X5997,X5998,X5999)),X5999))
        | hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X5997),pi_fun1002945429e_indi(X5999,X5998))) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X5997,esk46_3(X5997,X5998,X5999))),hAPP_f1552576127i_bool(X5998,esk46_3(X5997,X5998,X5999))))
        | hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X5997),pi_fun1002945429e_indi(X5999,X5998))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_625_Pi__I])])])]) ).

fof(i_0_1718,plain,
    ! [X6093,X6094,X6095] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk70_3(X6093,X6094,X6095)),X6095))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X6093),pi_fun150026276t_bool(X6095,X6094))) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X6093,esk70_3(X6093,X6094,X6095))),hAPP_f1277514478l_bool(X6094,esk70_3(X6093,X6094,X6095))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X6093),pi_fun150026276t_bool(X6095,X6094))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_649_Pi__I])])])]) ).

fof(i_0_1719,plain,
    ! [X5993,X5994,X5995] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk45_3(X5993,X5994,X5995)),X5995))
        | hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X5993),pi_fun1877263000t_unit(X5995,X5994))) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X5993,esk45_3(X5993,X5994,X5995))),hAPP_f1891021702t_bool(X5994,esk45_3(X5993,X5994,X5995))))
        | hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X5993),pi_fun1877263000t_unit(X5995,X5994))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_624_Pi__I])])])]) ).

fof(i_0_1720,plain,
    ! [X5989,X5990,X5991] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk44_3(X5989,X5990,X5991)),X5991))
        | hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X5989),pi_fun823343522l_bool(X5991,X5990))) )
      & ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X5989,esk44_3(X5989,X5990,X5991))),hAPP_f839832464l_bool(X5990,esk44_3(X5989,X5990,X5991))))
        | hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X5989),pi_fun823343522l_bool(X5991,X5990))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_623_Pi__I])])])]) ).

fof(i_0_1721,plain,
    ! [X5985,X5986,X5987] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk43_3(X5985,X5986,X5987)),X5987))
        | hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X5985),pi_fun753830419e_indi(X5987,X5986))) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X5985,esk43_3(X5985,X5986,X5987))),hAPP_f1948454017i_bool(X5986,esk43_3(X5985,X5986,X5987))))
        | hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X5985),pi_fun753830419e_indi(X5987,X5986))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_622_Pi__I])])])]) ).

fof(i_0_1722,plain,
    ! [X6041,X6042,X6043] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk57_3(X6041,X6042,X6043)),X6043))
        | hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X6041),pi_Pro1928973619le_alt(X6043,X6042))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X6041,esk57_3(X6041,X6042,X6043))),hAPP_P1341894483t_bool(X6042,esk57_3(X6041,X6042,X6043))))
        | hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X6041),pi_Pro1928973619le_alt(X6043,X6042))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_636_Pi__I])])])]) ).

fof(i_0_1723,plain,
    ! [X6073,X6074,X6075] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk65_3(X6073,X6074,X6075)),X6075))
        | hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X6073),pi_Pro718203741t_bool(X6075,X6074))) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X6073,esk65_3(X6073,X6074,X6075))),hAPP_P1294997365l_bool(X6074,esk65_3(X6073,X6074,X6075))))
        | hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X6073),pi_Pro718203741t_bool(X6075,X6074))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_644_Pi__I])])])]) ).

fof(i_0_1724,plain,
    ! [X6065,X6066,X6067] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk63_3(X6065,X6066,X6067)),X6067))
        | hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X6065),pi_Pro1880661658t_bool(X6067,X6066))) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X6065,esk63_3(X6065,X6066,X6067))),hAPP_P1171466554l_bool(X6066,esk63_3(X6065,X6066,X6067))))
        | hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X6065),pi_Pro1880661658t_bool(X6067,X6066))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_642_Pi__I])])])]) ).

fof(i_0_1725,plain,
    ! [X6053,X6054,X6055] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk60_3(X6053,X6054,X6055)),X6055))
        | hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X6053),pi_Pro610293528t_bool(X6055,X6054))) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X6053,esk60_3(X6053,X6054,X6055))),hAPP_P254387896l_bool(X6054,esk60_3(X6053,X6054,X6055))))
        | hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X6053),pi_Pro610293528t_bool(X6055,X6054))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_639_Pi__I])])])]) ).

fof(i_0_1726,plain,
    ! [X6085,X6086,X6087] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk68_3(X6085,X6086,X6087)),X6087))
        | hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X6085),pi_Product_unit_nat(X6087,X6086))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X6085,esk68_3(X6085,X6086,X6087))),hAPP_P32877782t_bool(X6086,esk68_3(X6085,X6086,X6087))))
        | hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X6085),pi_Product_unit_nat(X6087,X6086))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_647_Pi__I])])])]) ).

fof(i_0_1727,plain,
    ! [X6029,X6030,X6031] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk54_3(X6029,X6030,X6031)),X6031))
        | hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X6029),pi_nat_Product_unit(X6031,X6030))) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X6029,esk54_3(X6029,X6030,X6031))),hAPP_n454528608t_bool(X6030,esk54_3(X6029,X6030,X6031))))
        | hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X6029),pi_nat_Product_unit(X6031,X6030))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_633_Pi__I])])])]) ).

fof(i_0_1728,plain,
    ! [X6025,X6026,X6027] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk53_3(X6025,X6026,X6027)),X6027))
        | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X6025),pi_nat_bool(X6027,X6026))) )
      & ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X6025,esk53_3(X6025,X6026,X6027))),hAPP_n1006566506l_bool(X6026,esk53_3(X6025,X6026,X6027))))
        | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X6025),pi_nat_bool(X6027,X6026))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_632_Pi__I])])])]) ).

fof(i_0_1729,plain,
    ! [X6021,X6022,X6023] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk52_3(X6021,X6022,X6023)),X6023))
        | hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X6021),pi_nat660525389e_indi(X6023,X6022))) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X6021,esk52_3(X6021,X6022,X6023))),hAPP_n821919323i_bool(X6022,esk52_3(X6021,X6022,X6023))))
        | hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X6021),pi_nat660525389e_indi(X6023,X6022))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_631_Pi__I])])])]) ).

fof(i_0_1730,plain,
    ! [X6037,X6038,X6039] :
      ( ( is_bool(esk56_3(X6037,X6038,X6039))
        | hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X6037),pi_boo115158845le_alt(X6039,X6038))) )
      & ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk56_3(X6037,X6038,X6039)),X6039))
        | hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X6037),pi_boo115158845le_alt(X6039,X6038))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X6037,esk56_3(X6037,X6038,X6039))),hAPP_b1703662281t_bool(X6038,esk56_3(X6037,X6038,X6039))))
        | hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X6037),pi_boo115158845le_alt(X6039,X6038))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_635_Pi__I])])])]) ).

fof(i_0_1731,plain,
    ! [X6069,X6070,X6071] :
      ( ( is_bool(esk64_3(X6069,X6070,X6071))
        | hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X6069),pi_boo538701011t_bool(X6071,X6070))) )
      & ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk64_3(X6069,X6070,X6071)),X6071))
        | hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X6069),pi_boo538701011t_bool(X6071,X6070))) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X6069,esk64_3(X6069,X6070,X6071))),hAPP_b1812770943l_bool(X6070,esk64_3(X6069,X6070,X6071))))
        | hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X6069),pi_boo538701011t_bool(X6071,X6070))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_643_Pi__I])])])]) ).

fof(i_0_1732,plain,
    ! [X6061,X6062,X6063] :
      ( ( is_bool(esk62_3(X6061,X6062,X6063))
        | hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X6061),pi_boo1117000868t_bool(X6063,X6062))) )
      & ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk62_3(X6061,X6062,X6063)),X6063))
        | hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X6061),pi_boo1117000868t_bool(X6063,X6062))) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X6061,esk62_3(X6061,X6062,X6063))),hAPP_b517355696l_bool(X6062,esk62_3(X6061,X6062,X6063))))
        | hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X6061),pi_boo1117000868t_bool(X6063,X6062))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_641_Pi__I])])])]) ).

fof(i_0_1733,plain,
    ! [X6049,X6050,X6051] :
      ( ( is_bool(esk59_3(X6049,X6050,X6051))
        | hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X6049),pi_boo175444770t_bool(X6051,X6050))) )
      & ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk59_3(X6049,X6050,X6051)),X6051))
        | hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X6049),pi_boo175444770t_bool(X6051,X6050))) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X6049,esk59_3(X6049,X6050,X6051))),hAPP_b1048178734l_bool(X6050,esk59_3(X6049,X6050,X6051))))
        | hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X6049),pi_boo175444770t_bool(X6051,X6050))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_638_Pi__I])])])]) ).

fof(i_0_1734,plain,
    ! [X6081,X6082,X6083] :
      ( ( is_bool(esk67_3(X6081,X6082,X6083))
        | hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X6081),pi_bool_nat(X6083,X6082))) )
      & ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk67_3(X6081,X6082,X6083)),X6083))
        | hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X6081),pi_bool_nat(X6083,X6082))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X6081,esk67_3(X6081,X6082,X6083))),hAPP_b1013836512t_bool(X6082,esk67_3(X6081,X6082,X6083))))
        | hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X6081),pi_bool_nat(X6083,X6082))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_646_Pi__I])])])]) ).

fof(i_0_1735,plain,
    ! [X6033,X6034,X6035] :
      ( ( is_Arr43961803e_indi(esk55_3(X6033,X6034,X6035))
        | hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X6033),pi_Arr1199386158le_alt(X6035,X6034))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk55_3(X6033,X6034,X6035)),X6035))
        | hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X6033),pi_Arr1199386158le_alt(X6035,X6034))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X6033,esk55_3(X6033,X6034,X6035))),hAPP_A1677245848t_bool(X6034,esk55_3(X6033,X6034,X6035))))
        | hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X6033),pi_Arr1199386158le_alt(X6035,X6034))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_634_Pi__I])])])]) ).

fof(i_0_1736,plain,
    ! [X6097,X6098,X6099] :
      ( ( is_Arr43961803e_indi(esk71_3(X6097,X6098,X6099))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6097),pi_Arr990697634t_bool(X6099,X6098))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk71_3(X6097,X6098,X6099)),X6099))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6097),pi_Arr990697634t_bool(X6099,X6098))) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X6097,esk71_3(X6097,X6098,X6099))),hAPP_A60074736l_bool(X6098,esk71_3(X6097,X6098,X6099))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6097),pi_Arr990697634t_bool(X6099,X6098))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_650_Pi__I])])])]) ).

fof(i_0_1737,plain,
    ! [X6057,X6058,X6059] :
      ( ( is_Arr43961803e_indi(esk61_3(X6057,X6058,X6059))
        | hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X6057),pi_Arr1936979349t_bool(X6059,X6058))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk61_3(X6057,X6058,X6059)),X6059))
        | hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X6057),pi_Arr1936979349t_bool(X6059,X6058))) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X6057,esk61_3(X6057,X6058,X6059))),hAPP_A1112981887l_bool(X6058,esk61_3(X6057,X6058,X6059))))
        | hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X6057),pi_Arr1936979349t_bool(X6059,X6058))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_640_Pi__I])])])]) ).

fof(i_0_1738,plain,
    ! [X6045,X6046,X6047] :
      ( ( is_Arr43961803e_indi(esk58_3(X6045,X6046,X6047))
        | hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X6045),pi_Arr2020412179t_bool(X6047,X6046))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk58_3(X6045,X6046,X6047)),X6047))
        | hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X6045),pi_Arr2020412179t_bool(X6047,X6046))) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X6045,esk58_3(X6045,X6046,X6047))),hAPP_A1952883197l_bool(X6046,esk58_3(X6045,X6046,X6047))))
        | hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X6045),pi_Arr2020412179t_bool(X6047,X6046))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_637_Pi__I])])])]) ).

fof(i_0_1739,plain,
    ! [X6077,X6078,X6079] :
      ( ( is_Arr43961803e_indi(esk66_3(X6077,X6078,X6079))
        | hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X6077),pi_Arr346900227di_nat(X6079,X6078))) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk66_3(X6077,X6078,X6079)),X6079))
        | hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X6077),pi_Arr346900227di_nat(X6079,X6078))) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X6077,esk66_3(X6077,X6078,X6079))),hAPP_A2046586321t_bool(X6078,esk66_3(X6077,X6078,X6079))))
        | hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X6077),pi_Arr346900227di_nat(X6079,X6078))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_645_Pi__I])])])]) ).

fof(i_0_1740,plain,
    ! [X4917,X4918,X4919,X4920,X4921] :
      ( ( X4917 != X4918
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4918 != X4920
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4921)),X4919))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4917 != X4920
        | X4918 = X4921
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4921),X4918)),X4919))
        | X4918 = X4920
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4917 = X4920
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),X4919))
        | X4918 = X4920
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4918 != X4920
        | X4918 = X4920
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4917 != X4920
        | X4917 = X4920
        | X4918 = X4920
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),X4919))
        | X4917 = X4920
        | X4918 = X4920
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4917 != X4920
        | X4918 != X4921
        | X4918 = X4920
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),X4919))
        | X4918 != X4921
        | X4918 = X4920
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4917 != X4920
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4921),X4918)),X4919))
        | X4918 = X4920
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),X4919))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4921),X4918)),X4919))
        | X4918 = X4920
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4918 != X4920
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4921)),X4919))
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4917 != X4920
        | X4917 = X4920
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4921)),X4919))
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),X4919))
        | X4917 = X4920
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4921)),X4919))
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4917 != X4920
        | X4918 != X4921
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4921)),X4919))
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),X4919))
        | X4918 != X4921
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4921)),X4919))
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( X4917 != X4920
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4921),X4918)),X4919))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4921)),X4919))
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),X4919))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4921),X4918)),X4919))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4921)),X4919))
        | X4917 = X4918
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4917),X4918)),arrow_1539419881_below(X4919,X4920,X4921)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4919),arrow_1681063817le_Lin))
        | X4920 = X4921
        | ~ is_Arr1861959080le_alt(X4917)
        | ~ is_Arr1861959080le_alt(X4918)
        | ~ is_Arr1861959080le_alt(X4920)
        | ~ is_Arr1861959080le_alt(X4921) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_225_in__below])])]) ).

fof(i_0_1741,plain,
    ! [X4771,X4772] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk23_2(X4771,X4772)),arrow_1721807329e_Prof))
        | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4772),X4771))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4772),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) )
      & ( is_Arr1861959080le_alt(esk24_2(X4771,X4772))
        | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4772),X4771))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4772),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) )
      & ( is_Arr1861959080le_alt(esk25_2(X4771,X4772))
        | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4772),X4771))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4772),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) )
      & ( esk24_2(X4771,X4772) != esk25_2(X4771,X4772)
        | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4772),X4771))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4772),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk24_2(X4771,X4772)),esk25_2(X4771,X4772))),hAPP_A1677245848t_bool(esk23_2(X4771,X4772),X4771)))
        | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4772),X4771))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4772),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk24_2(X4771,X4772)),esk25_2(X4771,X4772))),hAPP_f412050202t_bool(X4772,esk23_2(X4771,X4772))))
        | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4772),X4771))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4772),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_182_dictatorI])])])]) ).

cnf(i_0_1742,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

cnf(i_0_1743,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

cnf(i_0_1744,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

cnf(i_0_1745,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

fof(i_0_1746,plain,
    ! [X8032,X8033,X8034] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8032)),X8033)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8032)),X8034)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8033),X8034)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8033),X8034))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8032)),X8033)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8032)),X8034))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1166_Suc__mult__le__cancel1])]) ).

fof(i_0_1747,plain,
    ! [X8025,X8026,X8027] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8025)),X8026)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8025)),X8027)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8026),X8027)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8026),X8027))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8025)),X8026)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8025)),X8027))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1163_Suc__mult__less__cancel1])]) ).

cnf(i_0_1748,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

fof(i_0_1749,plain,
    ! [X7767,X7768] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk488_2(X7767,X7768)),hAPP_nat_nat(X7768,esk488_2(X7767,X7768))))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),X7768)),X7767)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1040_finite__less__ub])])]) ).

cnf(i_0_1750,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

fof(i_0_1751,plain,
    ! [X4563,X4564,X4565] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4563),X4564)),X4565))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4564),X4563)),X4565))
        | X4563 = X4564
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4565),arrow_1681063817le_Lin))
        | ~ is_Arr1861959080le_alt(X4563)
        | ~ is_Arr1861959080le_alt(X4564) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4564),X4563)),X4565))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4563),X4564)),X4565))
        | X4563 = X4564
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4565),arrow_1681063817le_Lin))
        | ~ is_Arr1861959080le_alt(X4563)
        | ~ is_Arr1861959080le_alt(X4564) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1368])])]) ).

fof(i_0_1752,plain,
    ! [X7753,X7754] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),X7753)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X7754))))),
    inference(variable_rename,[status(thm)],[fact_1037_finite__M__bounded__by__nat]) ).

fof(i_0_1753,plain,
    ! [X4566,X4567,X4568] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4568),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4566),X4567)),X4568))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4567),X4566)),X4568)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1369])]) ).

fof(i_0_1754,plain,
    ! [X4427,X4428,X4429,X4430] :
      ( ( X4428 != X4430
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4429),X4430)))
        | ~ is_Arr1861959080le_alt(X4427)
        | ~ is_Arr1861959080le_alt(X4428)
        | ~ is_Arr1861959080le_alt(X4430) )
      & ( X4427 != X4430
        | X4427 != X4428
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4429),X4430)))
        | ~ is_Arr1861959080le_alt(X4427)
        | ~ is_Arr1861959080le_alt(X4428)
        | ~ is_Arr1861959080le_alt(X4430) )
      & ( X4427 = X4430
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),X4429))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4429),X4430)))
        | ~ is_Arr1861959080le_alt(X4427)
        | ~ is_Arr1861959080le_alt(X4428)
        | ~ is_Arr1861959080le_alt(X4430) )
      & ( X4427 != X4430
        | X4427 = X4430
        | X4428 = X4430
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4429),X4430)))
        | ~ is_Arr1861959080le_alt(X4427)
        | ~ is_Arr1861959080le_alt(X4428)
        | ~ is_Arr1861959080le_alt(X4430) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),X4429))
        | X4427 = X4430
        | X4428 = X4430
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4429),X4430)))
        | ~ is_Arr1861959080le_alt(X4427)
        | ~ is_Arr1861959080le_alt(X4428)
        | ~ is_Arr1861959080le_alt(X4430) )
      & ( X4427 != X4430
        | X4427 = X4428
        | X4428 = X4430
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4429),X4430)))
        | ~ is_Arr1861959080le_alt(X4427)
        | ~ is_Arr1861959080le_alt(X4428)
        | ~ is_Arr1861959080le_alt(X4430) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),X4429))
        | X4427 = X4428
        | X4428 = X4430
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4427),X4428)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4429),X4430)))
        | ~ is_Arr1861959080le_alt(X4427)
        | ~ is_Arr1861959080le_alt(X4428)
        | ~ is_Arr1861959080le_alt(X4430) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_in__mkbot])])]) ).

fof(i_0_1755,plain,
    ! [X4431,X4432,X4433,X4434] :
      ( ( X4431 != X4434
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4433),X4434)))
        | ~ is_Arr1861959080le_alt(X4431)
        | ~ is_Arr1861959080le_alt(X4432)
        | ~ is_Arr1861959080le_alt(X4434) )
      & ( X4432 != X4434
        | X4431 != X4432
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4433),X4434)))
        | ~ is_Arr1861959080le_alt(X4431)
        | ~ is_Arr1861959080le_alt(X4432)
        | ~ is_Arr1861959080le_alt(X4434) )
      & ( X4432 = X4434
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),X4433))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4433),X4434)))
        | ~ is_Arr1861959080le_alt(X4431)
        | ~ is_Arr1861959080le_alt(X4432)
        | ~ is_Arr1861959080le_alt(X4434) )
      & ( X4432 != X4434
        | X4432 = X4434
        | X4431 = X4434
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4433),X4434)))
        | ~ is_Arr1861959080le_alt(X4431)
        | ~ is_Arr1861959080le_alt(X4432)
        | ~ is_Arr1861959080le_alt(X4434) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),X4433))
        | X4432 = X4434
        | X4431 = X4434
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4433),X4434)))
        | ~ is_Arr1861959080le_alt(X4431)
        | ~ is_Arr1861959080le_alt(X4432)
        | ~ is_Arr1861959080le_alt(X4434) )
      & ( X4432 != X4434
        | X4431 = X4432
        | X4431 = X4434
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4433),X4434)))
        | ~ is_Arr1861959080le_alt(X4431)
        | ~ is_Arr1861959080le_alt(X4432)
        | ~ is_Arr1861959080le_alt(X4434) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),X4433))
        | X4431 = X4432
        | X4431 = X4434
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4431),X4432)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4433),X4434)))
        | ~ is_Arr1861959080le_alt(X4431)
        | ~ is_Arr1861959080le_alt(X4432)
        | ~ is_Arr1861959080le_alt(X4434) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_in__mktop])])]) ).

fof(i_0_1756,plain,
    ! [X7941,X7942] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7941),hAPP_n1699378549t_bool(ord_at4362885an_nat(X7942),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7942),hAPP_f22106695ol_nat(finite_card_nat,X7941)))))
      | X7941 = hAPP_n1699378549t_bool(ord_at4362885an_nat(X7942),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7942),hAPP_f22106695ol_nat(finite_card_nat,X7941))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1130_subset__card__intvl__is__intvl])]) ).

fof(i_0_1757,plain,
    ! [X8068,X8069,X8070,X8071] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X8068),X8069)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X8070),X8069)),X8071)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8068),X8070)),X8069)),X8071),
    inference(variable_rename,[status(thm)],[fact_1180_left__add__mult__distrib]) ).

fof(i_0_1758,plain,
    ! [X8075,X8078] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X8075,hAPP_nat_nat(suc,esk511_1(X8075)))),hAPP_nat_nat(X8075,esk511_1(X8075))))
      | hAPP_nat_nat(X8075,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk512_1(X8075)),X8078)) = hAPP_nat_nat(X8075,esk512_1(X8075)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1186_weak__decr__stable])])])]) ).

fof(i_0_1759,plain,
    ! [X6528,X6529] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X6528,esk179_2(X6528,X6529))),hAPP_P606313927t_bool(X6529,esk179_2(X6528,X6529))))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6528),X6529)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_752_le__funI])])]) ).

fof(i_0_1760,plain,
    ! [X5286,X5287,X5288,X5289,X5290] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5286),X5287))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X5286,X5288)),hAPP_P606313927t_bool(X5287,X5288))) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X5289,esk32_2(X5289,X5290))),hAPP_P606313927t_bool(X5290,esk32_2(X5289,X5290))))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5289),X5290)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_369_le__fun__def])])])])]) ).

fof(i_0_1761,plain,
    ! [X6519,X6520] :
      ( ( is_fun961089132t_bool(esk176_2(X6519,X6520))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6519),X6520)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X6519,esk176_2(X6519,X6520))),hAPP_f592646513l_bool(X6520,esk176_2(X6519,X6520))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6519),X6520)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_749_le__funI])])])]) ).

fof(i_0_1762,plain,
    ! [X5268,X5269,X5270,X5271,X5272] :
      ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5268),X5269))
        | ~ is_fun961089132t_bool(X5270)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X5268,X5270)),hAPP_f592646513l_bool(X5269,X5270))) )
      & ( is_fun961089132t_bool(esk29_2(X5271,X5272))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5271),X5272)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X5271,esk29_2(X5271,X5272))),hAPP_f592646513l_bool(X5272,esk29_2(X5271,X5272))))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5271),X5272)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_366_le__fun__def])])])])])]) ).

fof(i_0_1763,plain,
    ! [X6522,X6523] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X6522,esk177_2(X6522,X6523))),hAPP_f312250286l_bool(X6523,esk177_2(X6522,X6523))))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6522),X6523)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_750_le__funI])])]) ).

fof(i_0_1764,plain,
    ! [X5274,X5275,X5276,X5277,X5278] :
      ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5274),X5275))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X5274,X5276)),hAPP_f312250286l_bool(X5275,X5276))) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X5277,esk30_2(X5277,X5278))),hAPP_f312250286l_bool(X5278,esk30_2(X5277,X5278))))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5277),X5278)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_367_le__fun__def])])])])]) ).

fof(i_0_1765,plain,
    ! [X6525,X6526] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X6525,esk178_2(X6525,X6526))),hAPP_f965095724l_bool(X6526,esk178_2(X6525,X6526))))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6525),X6526)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_751_le__funI])])]) ).

fof(i_0_1766,plain,
    ! [X5280,X5281,X5282,X5283,X5284] :
      ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5280),X5281))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X5280,X5282)),hAPP_f965095724l_bool(X5281,X5282))) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X5283,esk31_2(X5283,X5284))),hAPP_f965095724l_bool(X5284,esk31_2(X5283,X5284))))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5283),X5284)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_368_le__fun__def])])])])]) ).

fof(i_0_1767,plain,
    ! [X6534,X6535] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X6534,esk181_2(X6534,X6535))),hAPP_P1676879539t_bool(X6535,esk181_2(X6534,X6535))))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6534),X6535)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_754_le__funI])])]) ).

fof(i_0_1768,plain,
    ! [X5298,X5299,X5300,X5301,X5302] :
      ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5298),X5299))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X5298,X5300)),hAPP_P1676879539t_bool(X5299,X5300))) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X5301,esk34_2(X5301,X5302))),hAPP_P1676879539t_bool(X5302,esk34_2(X5301,X5302))))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5301),X5302)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_371_le__fun__def])])])])]) ).

fof(i_0_1769,plain,
    ! [X6540,X6541] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X6540,esk183_2(X6540,X6541))),hAPP_nat_bool(X6541,esk183_2(X6540,X6541))))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6540),X6541)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_756_le__funI])])]) ).

fof(i_0_1770,plain,
    ! [X5310,X5311,X5312,X5313,X5314] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5310),X5311))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X5310,X5312)),hAPP_nat_bool(X5311,X5312))) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X5313,esk36_2(X5313,X5314))),hAPP_nat_bool(X5314,esk36_2(X5313,X5314))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5313),X5314)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_373_le__fun__def])])])])]) ).

fof(i_0_1771,plain,
    ! [X6531,X6532] :
      ( ( is_Arr43961803e_indi(esk180_2(X6531,X6532))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6531),X6532)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X6531,esk180_2(X6531,X6532))),hAPP_A1785763630i_bool(X6532,esk180_2(X6531,X6532))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6531),X6532)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_753_le__funI])])])]) ).

fof(i_0_1772,plain,
    ! [X5292,X5293,X5294,X5295,X5296] :
      ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5292),X5293))
        | ~ is_Arr43961803e_indi(X5294)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X5292,X5294)),hAPP_A1785763630i_bool(X5293,X5294))) )
      & ( is_Arr43961803e_indi(esk33_2(X5295,X5296))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5295),X5296)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X5295,esk33_2(X5295,X5296))),hAPP_A1785763630i_bool(X5296,esk33_2(X5295,X5296))))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5295),X5296)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_370_le__fun__def])])])])])]) ).

fof(i_0_1773,plain,
    ! [X6537,X6538] :
      ( ( is_Arr1861959080le_alt(esk182_2(X6537,X6538))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6537),X6538)) )
      & ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X6537,esk182_2(X6537,X6538))),hAPP_A1664620203t_bool(X6538,esk182_2(X6537,X6538))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6537),X6538)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_755_le__funI])])])]) ).

fof(i_0_1774,plain,
    ! [X5304,X5305,X5306,X5307,X5308] :
      ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5304),X5305))
        | ~ is_Arr1861959080le_alt(X5306)
        | hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X5304,X5306)),hAPP_A1664620203t_bool(X5305,X5306))) )
      & ( is_Arr1861959080le_alt(esk35_2(X5307,X5308))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5307),X5308)) )
      & ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X5307,esk35_2(X5307,X5308))),hAPP_A1664620203t_bool(X5308,esk35_2(X5307,X5308))))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5307),X5308)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_372_le__fun__def])])])])])]) ).

fof(i_0_1775,plain,
    ! [X4573,X4574,X4575] :
      ( ~ is_Arr1861959080le_alt(X4574)
      | ~ is_Arr1861959080le_alt(X4575)
      | X4574 = X4575
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4573),arrow_1681063817le_Lin))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4573),X4574),X4575)),arrow_1681063817le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_90_above__Lin])]) ).

fof(i_0_1776,plain,
    ! [X6494,X6495,X6496] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6494),X6495)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6496),X6495)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6494),X6496)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6494),X6496))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6494),X6495)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6496),X6495))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_741_add__le__cancel__right])]) ).

fof(i_0_1777,plain,
    ! [X6478,X6479,X6480] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6478),X6479)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6480),X6479)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6478),X6480)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_736_add__le__imp__le__right])]) ).

fof(i_0_1778,plain,
    ! [X7703,X7704,X7705] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7703),X7704)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7703),X7705)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7704),X7705)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7704),X7705))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7703),X7704)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7703),X7705))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1016_nat__add__left__cancel__le])]) ).

fof(i_0_1779,plain,
    ! [X6491,X6492,X6493] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6491),X6492)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6491),X6493)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6492),X6493)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6492),X6493))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6491),X6492)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6491),X6493))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_740_add__le__cancel__left])]) ).

fof(i_0_1780,plain,
    ! [X6475,X6476,X6477] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6475),X6476)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6475),X6477)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6476),X6477)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_735_add__le__imp__le__left])]) ).

fof(i_0_1781,plain,
    ! [X6516,X6517,X6518] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6516),X6517)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6518),X6517)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6516),X6518)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6516),X6518))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6516),X6517)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6518),X6517))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_748_add__less__cancel__right])]) ).

fof(i_0_1782,plain,
    ! [X6500,X6501,X6502] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6500),X6501)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6502),X6501)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6500),X6502)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_743_add__less__imp__less__right])]) ).

fof(i_0_1783,plain,
    ! [X7660,X7661,X7662] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7660),X7661)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7660),X7662)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7661),X7662)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7661),X7662))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7660),X7661)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7660),X7662))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1001_nat__add__left__cancel__less])]) ).

fof(i_0_1784,plain,
    ! [X6513,X6514,X6515] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6513),X6514)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6513),X6515)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6514),X6515)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6514),X6515))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6513),X6514)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6513),X6515))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_747_add__less__cancel__left])]) ).

fof(i_0_1785,plain,
    ! [X6497,X6498,X6499] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6497),X6498)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6497),X6499)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6498),X6499)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_742_add__less__imp__less__left])]) ).

fof(i_0_1786,plain,
    ! [X7615,X7616] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X7615)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X7616)))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7615),X7616)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7615),X7616))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X7615)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X7616))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_980_pred__subset__eq])]) ).

fof(i_0_1787,plain,
    ! [X7609,X7610] :
      ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X7609)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X7610)))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7609),X7610)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7609),X7610))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X7609)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X7610))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_977_pred__subset__eq])]) ).

fof(i_0_1788,plain,
    ! [X7611,X7612] :
      ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X7611)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X7612)))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7611),X7612)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7611),X7612))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X7611)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X7612))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_978_pred__subset__eq])]) ).

fof(i_0_1789,plain,
    ! [X7613,X7614] :
      ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X7613)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X7614)))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7613),X7614)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7613),X7614))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X7613)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X7614))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_979_pred__subset__eq])]) ).

fof(i_0_1790,plain,
    ! [X7607,X7608] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X7607)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X7608)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7607),X7608)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7607),X7608))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X7607)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X7608))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_976_pred__subset__eq])]) ).

fof(i_0_1791,plain,
    ! [X7715,X7716,X7717,X7718] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7717),X7718))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7715),X7716))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7717),X7715)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7718),X7716))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1020_add__le__mono])]) ).

fof(i_0_1792,plain,
    ! [X6481,X6482,X6483,X6484] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6483),X6484))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6481),X6482))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6483),X6481)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6484),X6482))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_737_add__mono])]) ).

fof(i_0_1793,plain,
    ! [X6108,X6109,X6110,X6111] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6110),X6111))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6108),X6109))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6110),X6108)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6111),X6109))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_654_add__less__le__mono])]) ).

fof(i_0_1794,plain,
    ! [X6112,X6113,X6114,X6115] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6114),X6115))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6112),X6113))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6114),X6112)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6115),X6113))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_655_add__le__less__mono])]) ).

fof(i_0_1795,plain,
    ! [X7672,X7673,X7674,X7675] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7674),X7675))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7672),X7673))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7674),X7672)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7675),X7673))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1005_add__less__mono])]) ).

fof(i_0_1796,plain,
    ! [X6503,X6504,X6505,X6506] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6505),X6506))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6503),X6504))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6505),X6503)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6506),X6504))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_744_add__strict__mono])]) ).

fof(i_0_1797,plain,
    ! [X8043,X8044] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8043))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X8043),X8044))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8044))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X8043),X8044))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8043))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8044))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X8043),X8044))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1171_one__le__mult__iff])])]) ).

fof(i_0_1798,plain,
    ! [X8041,X8042] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8042))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8041))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X8041),X8042))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1170_one__less__mult])]) ).

fof(i_0_1799,plain,
    ! [X7908,X7909,X7910] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk496_3(X7908,X7909,X7910)),X7910))
        | hBOOL(hAPP_nat_bool(X7908,X7909))
        | ~ hBOOL(hAPP_nat_bool(X7908,X7910))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7909),X7910)) )
      & ( hBOOL(hAPP_nat_bool(X7908,hAPP_nat_nat(suc,esk496_3(X7908,X7909,X7910))))
        | hBOOL(hAPP_nat_bool(X7908,X7909))
        | ~ hBOOL(hAPP_nat_bool(X7908,X7910))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7909),X7910)) )
      & ( ~ hBOOL(hAPP_nat_bool(X7908,esk496_3(X7908,X7909,X7910)))
        | hBOOL(hAPP_nat_bool(X7908,X7909))
        | ~ hBOOL(hAPP_nat_bool(X7908,X7910))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7909),X7910)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1115_inc__induct])])])]) ).

fof(i_0_1800,plain,
    ! [X8045,X8046,X8047] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X8045),X8046)),hAPP_nat_nat(times_times_nat(X8047),X8046)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8046))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8045),X8047)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8046))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X8045),X8046)),hAPP_nat_nat(times_times_nat(X8047),X8046))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8045),X8047))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X8045),X8046)),hAPP_nat_nat(times_times_nat(X8047),X8046))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1172_mult__le__cancel2])])]) ).

fof(i_0_1801,plain,
    ! [X8056,X8057,X8058] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X8058),X8056)),hAPP_nat_nat(times_times_nat(X8058),X8057)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8056),X8057))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8058)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8056),X8057))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X8058),X8056)),hAPP_nat_nat(times_times_nat(X8058),X8057)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8058)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1176_nat__mult__le__cancel1])])]) ).

fof(i_0_1802,plain,
    ! [X8048,X8049,X8050] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X8048),X8049)),hAPP_nat_nat(times_times_nat(X8048),X8050)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8048))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8049),X8050)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8048))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X8048),X8049)),hAPP_nat_nat(times_times_nat(X8048),X8050))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8049),X8050))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X8048),X8049)),hAPP_nat_nat(times_times_nat(X8048),X8050))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1173_mult__le__cancel1])])]) ).

fof(i_0_1803,plain,
    ! [X8059,X8060,X8061] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8061),X8059)),hAPP_nat_nat(times_times_nat(X8061),X8060)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8059),X8060))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8061)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8059),X8060))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8061),X8059)),hAPP_nat_nat(times_times_nat(X8061),X8060)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8061)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1177_nat__mult__less__cancel1])])]) ).

fof(i_0_1804,plain,
    ! [X7425,X7426,X7427] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7425),X7427))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7425),X7426)),X7427)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7426),X7427))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7425),X7426)),X7427)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1370])])]) ).

fof(i_0_1805,plain,
    ! [X7722,X7723,X7724] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7722),X7723)),X7724))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7722),X7724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1022_add__leD1])]) ).

fof(i_0_1806,plain,
    ! [X7719,X7720,X7721] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7719),X7720)),X7721))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7720),X7721)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1021_add__leD2])]) ).

fof(i_0_1807,plain,
    ! [X7680,X7681,X7682] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7680),X7681)),X7682))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7680),X7682)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1007_add__lessD1])]) ).

fof(i_0_1808,plain,
    ! [X5895,X5896,X5897,X5898] :
      ( ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X5896),pi_Pro1928973619le_alt(X5897,hAPP_f1066247963t_bool(cOMBK_812212462t_unit,X5898))))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5895),X5897))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X5896,X5895)),X5898)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_598_funcset__mem])]) ).

fof(i_0_1809,plain,
    ! [X5891,X5892,X5893,X5894] :
      ( ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X5892),pi_boo115158845le_alt(X5893,hAPP_f340261009t_bool(cOMBK_545135096l_bool,X5894))))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5891),X5893))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X5892,X5891)),X5894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_597_funcset__mem])]) ).

fof(i_0_1810,plain,
    ! [X5887,X5888,X5889,X5890] :
      ( ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X5888),pi_Arr1199386158le_alt(X5889,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X5890))))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5887),X5889))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X5888,X5887)),X5890)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_596_funcset__mem])]) ).

fof(i_0_1811,plain,
    ! [X5943,X5944,X5945,X5946] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X5944),pi_fun150026276t_bool(X5945,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,X5946))))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5943),X5945))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X5944,X5943)),X5946)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_610_funcset__mem])]) ).

fof(i_0_1812,plain,
    ! [X5927,X5928,X5929,X5930] :
      ( ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X5928),pi_Pro718203741t_bool(X5929,hAPP_f2028504885l_bool(cOMBK_384545070t_unit,X5930))))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5927),X5929))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X5928,X5927)),X5930)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_606_funcset__mem])]) ).

fof(i_0_1813,plain,
    ! [X5923,X5924,X5925,X5926] :
      ( ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X5924),pi_boo538701011t_bool(X5925,hAPP_f256804927l_bool(cOMBK_69806648l_bool,X5926))))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5923),X5925))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X5924,X5923)),X5926)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_605_funcset__mem])]) ).

fof(i_0_1814,plain,
    ! [X5947,X5948,X5949,X5950] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5948),pi_Arr990697634t_bool(X5949,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,X5950))))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5947),X5949))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X5948,X5947)),X5950)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_611_funcset__mem])]) ).

fof(i_0_1815,plain,
    ! [X5919,X5920,X5921,X5922] :
      ( ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X5920),pi_Pro1880661658t_bool(X5921,hAPP_f1028353513l_bool(cOMBK_731023445t_unit,X5922))))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5919),X5921))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X5920,X5919)),X5922)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_604_funcset__mem])]) ).

fof(i_0_1816,plain,
    ! [X5915,X5916,X5917,X5918] :
      ( ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X5916),pi_boo1117000868t_bool(X5917,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,X5918))))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5915),X5917))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X5916,X5915)),X5918)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_603_funcset__mem])]) ).

fof(i_0_1817,plain,
    ! [X5911,X5912,X5913,X5914] :
      ( ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X5912),pi_Arr1936979349t_bool(X5913,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,X5914))))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5911),X5913))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X5912,X5911)),X5914)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_602_funcset__mem])]) ).

fof(i_0_1818,plain,
    ! [X5907,X5908,X5909,X5910] :
      ( ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X5908),pi_Pro610293528t_bool(X5909,hAPP_f512628453l_bool(cOMBK_295807955t_unit,X5910))))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5907),X5909))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X5908,X5907)),X5910)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_601_funcset__mem])]) ).

fof(i_0_1819,plain,
    ! [X5903,X5904,X5905,X5906] :
      ( ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X5904),pi_boo175444770t_bool(X5905,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,X5906))))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5903),X5905))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X5904,X5903)),X5906)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_600_funcset__mem])]) ).

fof(i_0_1820,plain,
    ! [X5899,X5900,X5901,X5902] :
      ( ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X5900),pi_Arr2020412179t_bool(X5901,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,X5902))))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5899),X5901))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X5900,X5899)),X5902)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_599_funcset__mem])]) ).

fof(i_0_1821,plain,
    ! [X5883,X5884,X5885,X5886] :
      ( ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X5884),pi_nat_Product_unit(X5885,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,X5886))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5883),X5885))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X5884,X5883)),X5886)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_595_funcset__mem])]) ).

fof(i_0_1822,plain,
    ! [X5871,X5872,X5873,X5874] :
      ( ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X5872),pi_fun308431217t_unit(X5873,hAPP_f478658281t_bool(cOMBK_1589894370t_bool,X5874))))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5871),X5873))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X5872,X5871)),X5874)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_592_funcset__mem])]) ).

fof(i_0_1823,plain,
    ! [X5859,X5860,X5861,X5862] :
      ( ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X5860),pi_fun321364250t_unit(X5861,hAPP_f894574520t_bool(cOMBK_1733280085t_bool,X5862))))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X5859),X5861))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X5860,X5859)),X5862)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_589_funcset__mem])]) ).

fof(i_0_1824,plain,
    ! [X5847,X5848,X5849,X5850] :
      ( ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X5848),pi_fun1877263000t_unit(X5849,hAPP_f587035834t_bool(cOMBK_1048254163t_bool,X5850))))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5847),X5849))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X5848,X5847)),X5850)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_586_funcset__mem])]) ).

fof(i_0_1825,plain,
    ! [X5835,X5836,X5837,X5838] :
      ( ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X5836),pi_Pro1122146355t_unit(X5837,hAPP_f1165814111t_bool(cOMBK_859929070le_alt,X5838))))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X5835),X5837))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X5836,X5835)),X5838)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_583_funcset__mem])]) ).

fof(i_0_1826,plain,
    ! [X5939,X5940,X5941,X5942] :
      ( ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X5940),pi_Product_unit_nat(X5941,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,X5942))))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5939),X5941))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X5940,X5939)),X5942)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_609_funcset__mem])]) ).

fof(i_0_1827,plain,
    ! [X5935,X5936,X5937,X5938] :
      ( ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X5936),pi_bool_nat(X5937,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,X5938))))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5935),X5937))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X5936,X5935)),X5938)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_608_funcset__mem])]) ).

fof(i_0_1828,plain,
    ! [X5931,X5932,X5933,X5934] :
      ( ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X5932),pi_Arr346900227di_nat(X5933,hAPP_f1491725936t_bool(cOMBK_847149194e_indi,X5934))))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5931),X5933))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X5932,X5931)),X5934)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_607_funcset__mem])]) ).

fof(i_0_1829,plain,
    ! [X5827,X5828,X5829,X5830] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5828),pi_Pro666468413t_bool(X5829,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,X5830))))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X5827),X5829))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X5828,X5827)),X5830)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_581_funcset__mem])]) ).

fof(i_0_1830,plain,
    ! [X5867,X5868,X5869,X5870] :
      ( ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X5868),pi_fun1575168891l_bool(X5869,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,X5870))))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5867),X5869))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X5868,X5867)),X5870)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_591_funcset__mem])]) ).

fof(i_0_1831,plain,
    ! [X5855,X5856,X5857,X5858] :
      ( ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X5856),pi_fun52649508l_bool(X5857,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,X5858))))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X5855),X5857))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X5856,X5855)),X5858)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_588_funcset__mem])]) ).

fof(i_0_1832,plain,
    ! [X5843,X5844,X5845,X5846] :
      ( ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X5844),pi_fun823343522l_bool(X5845,hAPP_f746617550l_bool(cOMBK_370033373t_bool,X5846))))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5843),X5845))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X5844,X5843)),X5846)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_585_funcset__mem])]) ).

fof(i_0_1833,plain,
    ! [X5879,X5880,X5881,X5882] :
      ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X5880),pi_nat_bool(X5881,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,X5882))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5879),X5881))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X5880,X5879)),X5882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_594_funcset__mem])]) ).

fof(i_0_1834,plain,
    ! [X5831,X5832,X5833,X5834] :
      ( ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X5832),pi_Pro1270767662e_indi(X5833,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,X5834))))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X5831),X5833))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X5832,X5831)),X5834)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_582_funcset__mem])]) ).

fof(i_0_1835,plain,
    ! [X5863,X5864,X5865,X5866] :
      ( ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X5864),pi_fun896360044e_indi(X5865,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,X5866))))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5863),X5865))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X5864,X5863)),X5866)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_590_funcset__mem])]) ).

fof(i_0_1836,plain,
    ! [X5851,X5852,X5853,X5854] :
      ( ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X5852),pi_fun1002945429e_indi(X5853,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,X5854))))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X5851),X5853))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X5852,X5851)),X5854)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_587_funcset__mem])]) ).

fof(i_0_1837,plain,
    ! [X5839,X5840,X5841,X5842] :
      ( ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X5840),pi_fun753830419e_indi(X5841,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,X5842))))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5839),X5841))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X5840,X5839)),X5842)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_584_funcset__mem])]) ).

fof(i_0_1838,plain,
    ! [X5875,X5876,X5877,X5878] :
      ( ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X5876),pi_nat660525389e_indi(X5877,hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,X5878))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5875),X5877))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X5876,X5875)),X5878)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_593_funcset__mem])]) ).

fof(i_0_1839,plain,
    ! [X8039,X8040] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8040))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8039))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8040),hAPP_nat_nat(times_times_nat(X8040),X8039))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1169_n__less__n__mult__m])]) ).

fof(i_0_1840,plain,
    ! [X8037,X8038] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8038))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X8037))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8038),hAPP_nat_nat(times_times_nat(X8037),X8038))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1168_n__less__m__mult__n])]) ).

fof(i_0_1841,plain,
    ! [X5823,X5824,X5825] :
      ( ~ is_Arr1861959080le_alt(X5824)
      | ~ is_Arr1861959080le_alt(X5825)
      | X5824 = X5825
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5823),arrow_1681063817le_Lin))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,arrow_1539419881_below(X5823,X5824,X5825)),arrow_1681063817le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_578_below__Lin])]) ).

fof(i_0_1842,plain,
    ! [X7712,X7713,X7714] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7713),X7714))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7713),X7712)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7714),X7712))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1019_add__le__mono1])]) ).

fof(i_0_1843,plain,
    ! [X6488,X6489,X6490] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6489),X6490))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6489),X6488)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6490),X6488))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_739_add__right__mono])]) ).

fof(i_0_1844,plain,
    ! [X6485,X6486,X6487] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6486),X6487))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6485),X6486)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6485),X6487))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_738_add__left__mono])]) ).

fof(i_0_1845,plain,
    ! [X7669,X7670,X7671] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7670),X7671))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7670),X7669)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7671),X7669))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1004_add__less__mono1])]) ).

fof(i_0_1846,plain,
    ! [X6510,X6511,X6512] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6511),X6512))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6511),X6510)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6512),X6510))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_746_add__strict__right__mono])]) ).

fof(i_0_1847,plain,
    ! [X6507,X6508,X6509] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6508),X6509))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6507),X6508)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6507),X6509))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_745_add__strict__left__mono])]) ).

fof(i_0_1848,negated_conjecture,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(i_0_1849,plain,
    ! [X7656,X7657] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7656),X7657)),X7656)),
    inference(variable_rename,[status(thm)],[i_0_1371]) ).

fof(i_0_1850,plain,
    ! [X7658,X7659] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7658),X7659)),X7659)),
    inference(variable_rename,[status(thm)],[i_0_1372]) ).

fof(i_0_1851,plain,
    ! [X8017,X8018,X8019] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8018))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8017),X8018)),hAPP_nat_nat(times_times_nat(X8019),X8018))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8017),X8019))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8017),X8018)),hAPP_nat_nat(times_times_nat(X8019),X8018))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8018))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8017),X8019))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8017),X8018)),hAPP_nat_nat(times_times_nat(X8019),X8018))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1160_mult__less__cancel2])])]) ).

fof(i_0_1852,plain,
    ! [X8020,X8021,X8022] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8020))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8020),X8021)),hAPP_nat_nat(times_times_nat(X8020),X8022))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8021),X8022))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8020),X8021)),hAPP_nat_nat(times_times_nat(X8020),X8022))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8020))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8021),X8022))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8020),X8021)),hAPP_nat_nat(times_times_nat(X8020),X8022))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1161_mult__less__cancel1])])]) ).

fof(i_0_1853,plain,
    ! [X5767,X5768,X5769,X5770] :
      ( ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X5768),pi_Pro1928973619le_alt(X5769,X5770)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5767),X5769))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X5768,X5767)),hAPP_P1341894483t_bool(X5770,X5767))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_564_Pi__mem])]) ).

fof(i_0_1854,plain,
    ! [X4799,X4800,X4801,X4802] :
      ( ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X4800),pi_Pro1928973619le_alt(X4801,X4802)))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X4800,X4799)),hAPP_P1341894483t_bool(X4802,X4799)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4799),X4801)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1373])]) ).

fof(i_0_1855,plain,
    ! [X5763,X5764,X5765,X5766] :
      ( ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X5764),pi_boo115158845le_alt(X5765,X5766)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5763),X5765))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X5764,X5763)),hAPP_b1703662281t_bool(X5766,X5763))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_563_Pi__mem])]) ).

fof(i_0_1856,plain,
    ! [X4795,X4796,X4797,X4798] :
      ( ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X4796),pi_boo115158845le_alt(X4797,X4798)))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X4796,X4795)),hAPP_b1703662281t_bool(X4798,X4795)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4795),X4797)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1374])]) ).

fof(i_0_1857,plain,
    ! [X5759,X5760,X5761,X5762] :
      ( ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X5760),pi_Arr1199386158le_alt(X5761,X5762)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5759),X5761))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X5760,X5759)),hAPP_A1677245848t_bool(X5762,X5759))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_562_Pi__mem])]) ).

fof(i_0_1858,plain,
    ! [X4791,X4792,X4793,X4794] :
      ( ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X4792),pi_Arr1199386158le_alt(X4793,X4794)))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X4792,X4791)),hAPP_A1677245848t_bool(X4794,X4791)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4791),X4793)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1375])]) ).

fof(i_0_1859,plain,
    ! [X5815,X5816,X5817,X5818] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X5816),pi_fun150026276t_bool(X5817,X5818)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5815),X5817))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X5816,X5815)),hAPP_f1277514478l_bool(X5818,X5815))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_576_Pi__mem])]) ).

fof(i_0_1860,plain,
    ! [X4903,X4904,X4905,X4906] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4904),pi_fun150026276t_bool(X4905,X4906)))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X4904,X4903)),hAPP_f1277514478l_bool(X4906,X4903)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4903),X4905)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1376])]) ).

fof(i_0_1861,plain,
    ! [X5799,X5800,X5801,X5802] :
      ( ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X5800),pi_Pro718203741t_bool(X5801,X5802)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5799),X5801))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X5800,X5799)),hAPP_P1294997365l_bool(X5802,X5799))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_572_Pi__mem])]) ).

fof(i_0_1862,plain,
    ! [X4831,X4832,X4833,X4834] :
      ( ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X4832),pi_Pro718203741t_bool(X4833,X4834)))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X4832,X4831)),hAPP_P1294997365l_bool(X4834,X4831)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4831),X4833)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1377])]) ).

fof(i_0_1863,plain,
    ! [X5795,X5796,X5797,X5798] :
      ( ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X5796),pi_boo538701011t_bool(X5797,X5798)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5795),X5797))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X5796,X5795)),hAPP_b1812770943l_bool(X5798,X5795))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_571_Pi__mem])]) ).

fof(i_0_1864,plain,
    ! [X4827,X4828,X4829,X4830] :
      ( ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X4828),pi_boo538701011t_bool(X4829,X4830)))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X4828,X4827)),hAPP_b1812770943l_bool(X4830,X4827)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4827),X4829)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1378])]) ).

fof(i_0_1865,plain,
    ! [X5819,X5820,X5821,X5822] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5820),pi_Arr990697634t_bool(X5821,X5822)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5819),X5821))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X5820,X5819)),hAPP_A60074736l_bool(X5822,X5819))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_577_Pi__mem])]) ).

fof(i_0_1866,plain,
    ! [X4907,X4908,X4909,X4910] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4908),pi_Arr990697634t_bool(X4909,X4910)))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X4908,X4907)),hAPP_A60074736l_bool(X4910,X4907)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4907),X4909)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1379])]) ).

fof(i_0_1867,plain,
    ! [X5791,X5792,X5793,X5794] :
      ( ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X5792),pi_Pro1880661658t_bool(X5793,X5794)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5791),X5793))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X5792,X5791)),hAPP_P1171466554l_bool(X5794,X5791))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_570_Pi__mem])]) ).

fof(i_0_1868,plain,
    ! [X4823,X4824,X4825,X4826] :
      ( ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X4824),pi_Pro1880661658t_bool(X4825,X4826)))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X4824,X4823)),hAPP_P1171466554l_bool(X4826,X4823)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4823),X4825)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1380])]) ).

fof(i_0_1869,plain,
    ! [X5787,X5788,X5789,X5790] :
      ( ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X5788),pi_boo1117000868t_bool(X5789,X5790)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5787),X5789))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X5788,X5787)),hAPP_b517355696l_bool(X5790,X5787))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_569_Pi__mem])]) ).

fof(i_0_1870,plain,
    ! [X4819,X4820,X4821,X4822] :
      ( ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X4820),pi_boo1117000868t_bool(X4821,X4822)))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X4820,X4819)),hAPP_b517355696l_bool(X4822,X4819)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4819),X4821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1381])]) ).

fof(i_0_1871,plain,
    ! [X5783,X5784,X5785,X5786] :
      ( ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X5784),pi_Arr1936979349t_bool(X5785,X5786)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5783),X5785))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X5784,X5783)),hAPP_A1112981887l_bool(X5786,X5783))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_568_Pi__mem])]) ).

fof(i_0_1872,plain,
    ! [X4815,X4816,X4817,X4818] :
      ( ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X4816),pi_Arr1936979349t_bool(X4817,X4818)))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X4816,X4815)),hAPP_A1112981887l_bool(X4818,X4815)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4815),X4817)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1382])]) ).

fof(i_0_1873,plain,
    ! [X5779,X5780,X5781,X5782] :
      ( ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X5780),pi_Pro610293528t_bool(X5781,X5782)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5779),X5781))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X5780,X5779)),hAPP_P254387896l_bool(X5782,X5779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_567_Pi__mem])]) ).

fof(i_0_1874,plain,
    ! [X4811,X4812,X4813,X4814] :
      ( ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X4812),pi_Pro610293528t_bool(X4813,X4814)))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X4812,X4811)),hAPP_P254387896l_bool(X4814,X4811)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4811),X4813)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1383])]) ).

fof(i_0_1875,plain,
    ! [X5775,X5776,X5777,X5778] :
      ( ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X5776),pi_boo175444770t_bool(X5777,X5778)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5775),X5777))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X5776,X5775)),hAPP_b1048178734l_bool(X5778,X5775))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_566_Pi__mem])]) ).

fof(i_0_1876,plain,
    ! [X4807,X4808,X4809,X4810] :
      ( ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X4808),pi_boo175444770t_bool(X4809,X4810)))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X4808,X4807)),hAPP_b1048178734l_bool(X4810,X4807)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4807),X4809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1384])]) ).

fof(i_0_1877,plain,
    ! [X5771,X5772,X5773,X5774] :
      ( ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X5772),pi_Arr2020412179t_bool(X5773,X5774)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5771),X5773))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X5772,X5771)),hAPP_A1952883197l_bool(X5774,X5771))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_565_Pi__mem])]) ).

fof(i_0_1878,plain,
    ! [X4803,X4804,X4805,X4806] :
      ( ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X4804),pi_Arr2020412179t_bool(X4805,X4806)))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X4804,X4803)),hAPP_A1952883197l_bool(X4806,X4803)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4803),X4805)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1385])]) ).

fof(i_0_1879,plain,
    ! [X5755,X5756,X5757,X5758] :
      ( ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X5756),pi_nat_Product_unit(X5757,X5758)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5755),X5757))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X5756,X5755)),hAPP_n454528608t_bool(X5758,X5755))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_561_Pi__mem])]) ).

fof(i_0_1880,plain,
    ! [X4899,X4900,X4901,X4902] :
      ( ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X4900),pi_nat_Product_unit(X4901,X4902)))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X4900,X4899)),hAPP_n454528608t_bool(X4902,X4899)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4899),X4901)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1386])]) ).

fof(i_0_1881,plain,
    ! [X5743,X5744,X5745,X5746] :
      ( ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X5744),pi_fun308431217t_unit(X5745,X5746)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5743),X5745))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X5744,X5743)),hAPP_f1710744577t_bool(X5746,X5743))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_558_Pi__mem])]) ).

fof(i_0_1882,plain,
    ! [X4887,X4888,X4889,X4890] :
      ( ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X4888),pi_fun308431217t_unit(X4889,X4890)))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X4888,X4887)),hAPP_f1710744577t_bool(X4890,X4887)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4887),X4889)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1387])]) ).

fof(i_0_1883,plain,
    ! [X5731,X5732,X5733,X5734] :
      ( ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X5732),pi_fun321364250t_unit(X5733,X5734)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X5731),X5733))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X5732,X5731)),hAPP_f1866147972t_bool(X5734,X5731))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_555_Pi__mem])]) ).

fof(i_0_1884,plain,
    ! [X4875,X4876,X4877,X4878] :
      ( ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X4876),pi_fun321364250t_unit(X4877,X4878)))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X4876,X4875)),hAPP_f1866147972t_bool(X4878,X4875)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4875),X4877)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1388])]) ).

fof(i_0_1885,plain,
    ! [X5719,X5720,X5721,X5722] :
      ( ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X5720),pi_fun1877263000t_unit(X5721,X5722)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5719),X5721))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X5720,X5719)),hAPP_f1891021702t_bool(X5722,X5719))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_552_Pi__mem])]) ).

fof(i_0_1886,plain,
    ! [X4863,X4864,X4865,X4866] :
      ( ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X4864),pi_fun1877263000t_unit(X4865,X4866)))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X4864,X4863)),hAPP_f1891021702t_bool(X4866,X4863)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4863),X4865)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1389])]) ).

fof(i_0_1887,plain,
    ! [X5707,X5708,X5709,X5710] :
      ( ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X5708),pi_Pro1122146355t_unit(X5709,X5710)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X5707),X5709))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X5708,X5707)),hAPP_P332578347t_bool(X5710,X5707))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_549_Pi__mem])]) ).

fof(i_0_1888,plain,
    ! [X4851,X4852,X4853,X4854] :
      ( ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X4852),pi_Pro1122146355t_unit(X4853,X4854)))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X4852,X4851)),hAPP_P332578347t_bool(X4854,X4851)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4851),X4853)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1390])]) ).

fof(i_0_1889,plain,
    ! [X5811,X5812,X5813,X5814] :
      ( ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X5812),pi_Product_unit_nat(X5813,X5814)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X5811),X5813))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X5812,X5811)),hAPP_P32877782t_bool(X5814,X5811))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_575_Pi__mem])]) ).

fof(i_0_1890,plain,
    ! [X4843,X4844,X4845,X4846] :
      ( ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X4844),pi_Product_unit_nat(X4845,X4846)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X4844,X4843)),hAPP_P32877782t_bool(X4846,X4843)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4843),X4845)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1391])]) ).

fof(i_0_1891,plain,
    ! [X5807,X5808,X5809,X5810] :
      ( ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X5808),pi_bool_nat(X5809,X5810)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X5807),X5809))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X5808,X5807)),hAPP_b1013836512t_bool(X5810,X5807))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_574_Pi__mem])]) ).

fof(i_0_1892,plain,
    ! [X4839,X4840,X4841,X4842] :
      ( ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X4840),pi_bool_nat(X4841,X4842)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X4840,X4839)),hAPP_b1013836512t_bool(X4842,X4839)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4839),X4841)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1392])]) ).

fof(i_0_1893,plain,
    ! [X5803,X5804,X5805,X5806] :
      ( ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X5804),pi_Arr346900227di_nat(X5805,X5806)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5803),X5805))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X5804,X5803)),hAPP_A2046586321t_bool(X5806,X5803))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_573_Pi__mem])]) ).

fof(i_0_1894,plain,
    ! [X4835,X4836,X4837,X4838] :
      ( ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X4836),pi_Arr346900227di_nat(X4837,X4838)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X4836,X4835)),hAPP_A2046586321t_bool(X4838,X4835)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4835),X4837)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1393])]) ).

fof(i_0_1895,plain,
    ! [X5699,X5700,X5701,X5702] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5700),pi_Pro666468413t_bool(X5701,X5702)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X5699),X5701))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X5700,X5699)),hAPP_P324742453l_bool(X5702,X5699))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_547_Pi__mem])]) ).

fof(i_0_1896,plain,
    ! [X4787,X4788,X4789,X4790] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4788),pi_Pro666468413t_bool(X4789,X4790)))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X4788,X4787)),hAPP_P324742453l_bool(X4790,X4787)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4787),X4789)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1394])]) ).

fof(i_0_1897,plain,
    ! [X5739,X5740,X5741,X5742] :
      ( ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X5740),pi_fun1575168891l_bool(X5741,X5742)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5739),X5741))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X5740,X5739)),hAPP_f210572555l_bool(X5742,X5739))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_557_Pi__mem])]) ).

fof(i_0_1898,plain,
    ! [X4883,X4884,X4885,X4886] :
      ( ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X4884),pi_fun1575168891l_bool(X4885,X4886)))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X4884,X4883)),hAPP_f210572555l_bool(X4886,X4883)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4883),X4885)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1395])]) ).

fof(i_0_1899,plain,
    ! [X5727,X5728,X5729,X5730] :
      ( ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X5728),pi_fun52649508l_bool(X5729,X5730)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X5727),X5729))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X5728,X5727)),hAPP_f1624277646l_bool(X5730,X5727))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_554_Pi__mem])]) ).

fof(i_0_1900,plain,
    ! [X4871,X4872,X4873,X4874] :
      ( ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X4872),pi_fun52649508l_bool(X4873,X4874)))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X4872,X4871)),hAPP_f1624277646l_bool(X4874,X4871)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4871),X4873)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1396])]) ).

fof(i_0_1901,plain,
    ! [X5715,X5716,X5717,X5718] :
      ( ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X5716),pi_fun823343522l_bool(X5717,X5718)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5715),X5717))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X5716,X5715)),hAPP_f839832464l_bool(X5718,X5715))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_551_Pi__mem])]) ).

fof(i_0_1902,plain,
    ! [X4859,X4860,X4861,X4862] :
      ( ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X4860),pi_fun823343522l_bool(X4861,X4862)))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X4860,X4859)),hAPP_f839832464l_bool(X4862,X4859)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4859),X4861)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1397])]) ).

fof(i_0_1903,plain,
    ! [X5751,X5752,X5753,X5754] :
      ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X5752),pi_nat_bool(X5753,X5754)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5751),X5753))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X5752,X5751)),hAPP_n1006566506l_bool(X5754,X5751))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_560_Pi__mem])]) ).

fof(i_0_1904,plain,
    ! [X4895,X4896,X4897,X4898] :
      ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X4896),pi_nat_bool(X4897,X4898)))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X4896,X4895)),hAPP_n1006566506l_bool(X4898,X4895)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4895),X4897)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1398])]) ).

fof(i_0_1905,plain,
    ! [X5703,X5704,X5705,X5706] :
      ( ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X5704),pi_Pro1270767662e_indi(X5705,X5706)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X5703),X5705))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X5704,X5703)),hAPP_P1875867302i_bool(X5706,X5703))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_548_Pi__mem])]) ).

fof(i_0_1906,plain,
    ! [X4847,X4848,X4849,X4850] :
      ( ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X4848),pi_Pro1270767662e_indi(X4849,X4850)))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X4848,X4847)),hAPP_P1875867302i_bool(X4850,X4847)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4847),X4849)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1399])]) ).

fof(i_0_1907,plain,
    ! [X5735,X5736,X5737,X5738] :
      ( ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X5736),pi_fun896360044e_indi(X5737,X5738)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5735),X5737))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X5736,X5735)),hAPP_f244157820i_bool(X5738,X5735))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_556_Pi__mem])]) ).

fof(i_0_1908,plain,
    ! [X4879,X4880,X4881,X4882] :
      ( ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X4880),pi_fun896360044e_indi(X4881,X4882)))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X4880,X4879)),hAPP_f244157820i_bool(X4882,X4879)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4879),X4881)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1400])]) ).

fof(i_0_1909,plain,
    ! [X5723,X5724,X5725,X5726] :
      ( ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X5724),pi_fun1002945429e_indi(X5725,X5726)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X5723),X5725))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X5724,X5723)),hAPP_f1552576127i_bool(X5726,X5723))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_553_Pi__mem])]) ).

fof(i_0_1910,plain,
    ! [X4867,X4868,X4869,X4870] :
      ( ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X4868),pi_fun1002945429e_indi(X4869,X4870)))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X4868,X4867)),hAPP_f1552576127i_bool(X4870,X4867)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4867),X4869)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1401])]) ).

fof(i_0_1911,plain,
    ! [X5711,X5712,X5713,X5714] :
      ( ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X5712),pi_fun753830419e_indi(X5713,X5714)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5711),X5713))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X5712,X5711)),hAPP_f1948454017i_bool(X5714,X5711))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_550_Pi__mem])]) ).

fof(i_0_1912,plain,
    ! [X4855,X4856,X4857,X4858] :
      ( ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X4856),pi_fun753830419e_indi(X4857,X4858)))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X4856,X4855)),hAPP_f1948454017i_bool(X4858,X4855)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4855),X4857)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1402])]) ).

fof(i_0_1913,plain,
    ! [X5747,X5748,X5749,X5750] :
      ( ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X5748),pi_nat660525389e_indi(X5749,X5750)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5747),X5749))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X5748,X5747)),hAPP_n821919323i_bool(X5750,X5747))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_559_Pi__mem])]) ).

fof(i_0_1914,plain,
    ! [X4891,X4892,X4893,X4894] :
      ( ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X4892),pi_nat660525389e_indi(X4893,X4894)))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X4892,X4891)),hAPP_n821919323i_bool(X4894,X4891)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4891),X4893)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1403])]) ).

fof(i_0_1915,plain,
    ! [X7980,X7981,X7982,X7983] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7982),X7983))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7980),X7981))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X7982),X7980)),hAPP_nat_nat(times_times_nat(X7983),X7981))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1144_mult__le__mono])]) ).

fof(i_0_1916,plain,
    ! [X8014,X8015,X8016] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8015),X8016))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8014))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8015),X8014)),hAPP_nat_nat(times_times_nat(X8016),X8014))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1159_mult__less__mono1])]) ).

fof(i_0_1917,plain,
    ! [X8011,X8012,X8013] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8012),X8013))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8011))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X8011),X8012)),hAPP_nat_nat(times_times_nat(X8011),X8013))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1158_mult__less__mono2])]) ).

fof(i_0_1918,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)),
    inference(fof_simplification,[status(thm)],[fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).

fof(i_0_1919,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)),
    inference(fof_simplification,[status(thm)],[fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).

fof(i_0_1920,plain,
    ! [X8106,X8107,X8108] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8107),X8108))
      | hAPP_n1699378549t_bool(ord_at4362885an_nat(X8107),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8108),X8106)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(X8107),X8108)),hAPP_n1699378549t_bool(ord_at4362885an_nat(X8108),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8108),X8106))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1196_atLeastLessThan__add__Un])]) ).

fof(i_0_1921,plain,
    ! [X7789,X7790] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7789),X7790)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7789))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7790)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7789))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7789),X7790))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7790))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7789),X7790))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1055_add__gr__0])])]) ).

fof(i_0_1922,plain,
    ! [X4569,X4570] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4570),arrow_1681063817le_Lin))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4570),X4569)),arrow_1681063817le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_88_mktop__Lin])]) ).

fof(i_0_1923,plain,
    ! [X4571,X4572] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4572),arrow_1681063817le_Lin))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4572),X4571)),arrow_1681063817le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_89_mkbot__Lin])]) ).

fof(i_0_1924,plain,
    ! [X7964,X7965] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7964)),X7965))
        | hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,X7964)),X7965)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,X7964)),X7965))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7964)),X7965)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1136_less__eq__nat_Osimps_I2_J])]) ).

fof(i_0_1925,plain,
    ! [X7791,X7792,X7794] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk490_2(X7791,X7792)),X7791))
        | ~ hBOOL(hAPP_nat_bool(X7792,X7791))
        | hBOOL(hAPP_nat_bool(X7792,zero_zero_nat)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7794),esk490_2(X7791,X7792)))
        | ~ hBOOL(hAPP_nat_bool(X7792,X7794))
        | ~ hBOOL(hAPP_nat_bool(X7792,X7791))
        | hBOOL(hAPP_nat_bool(X7792,zero_zero_nat)) )
      & ( hBOOL(hAPP_nat_bool(X7792,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk490_2(X7791,X7792)),one_one_nat)))
        | ~ hBOOL(hAPP_nat_bool(X7792,X7791))
        | hBOOL(hAPP_nat_bool(X7792,zero_zero_nat)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1404])])])])]) ).

fof(i_0_1926,plain,
    ! [X8083,X8084,X8085,X8087,X8088,X8089] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk513_2(X8083,X8084)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X8084)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8085),X8084))
        | ~ hBOOL(hAPP_nat_bool(X8083,X8085)) )
      & ( hBOOL(hAPP_nat_bool(X8083,esk513_2(X8083,X8084)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8085),X8084))
        | ~ hBOOL(hAPP_nat_bool(X8083,X8085)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk514_2(X8087,X8088)),X8088))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8089),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X8088)))
        | ~ hBOOL(hAPP_nat_bool(X8087,X8089)) )
      & ( hBOOL(hAPP_nat_bool(X8087,esk514_2(X8087,X8088)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8089),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X8088)))
        | ~ hBOOL(hAPP_nat_bool(X8087,X8089)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1191_ex__nat__less])])])])])]) ).

fof(i_0_1927,plain,
    ! [X7956,X7957,X7958,X7960,X7961,X7962] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk509_2(X7956,X7957)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X7957)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7958),X7957))
        | ~ hBOOL(hAPP_nat_bool(X7956,X7958)) )
      & ( hBOOL(hAPP_nat_bool(X7956,esk509_2(X7956,X7957)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7958),X7957))
        | ~ hBOOL(hAPP_nat_bool(X7956,X7958)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk510_2(X7960,X7961)),X7961))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7962),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X7961)))
        | ~ hBOOL(hAPP_nat_bool(X7960,X7962)) )
      & ( hBOOL(hAPP_nat_bool(X7960,esk510_2(X7960,X7961)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7962),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X7961)))
        | ~ hBOOL(hAPP_nat_bool(X7960,X7962)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1134_ex__nat__less__eq])])])])])]) ).

fof(i_0_1928,plain,
    ! [X4911,X4912] :
      ( ( is_fun961089132t_bool(esk26_2(X4911,X4912))
        | X4911 = X4912
        | ~ is_Arr1861959080le_alt(X4911)
        | ~ is_Arr1861959080le_alt(X4912) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk26_2(X4911,X4912)),arrow_1681063817le_Lin))
        | X4911 = X4912
        | ~ is_Arr1861959080le_alt(X4911)
        | ~ is_Arr1861959080le_alt(X4912) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4911),X4912)),esk26_2(X4911,X4912)))
        | X4911 = X4912
        | ~ is_Arr1861959080le_alt(X4911)
        | ~ is_Arr1861959080le_alt(X4912) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_221_complete__Lin])])])]) ).

fof(i_0_1929,plain,
    ! [X8091,X8092,X8094,X8095,X8096,X8098] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk515_2(X8091,X8092)),X8092))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8094),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X8092)))
        | hBOOL(hAPP_nat_bool(X8091,X8094)) )
      & ( ~ hBOOL(hAPP_nat_bool(X8091,esk515_2(X8091,X8092)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8094),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X8092)))
        | hBOOL(hAPP_nat_bool(X8091,X8094)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk516_2(X8095,X8096)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X8096)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8098),X8096))
        | hBOOL(hAPP_nat_bool(X8095,X8098)) )
      & ( ~ hBOOL(hAPP_nat_bool(X8095,esk516_2(X8095,X8096)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8098),X8096))
        | hBOOL(hAPP_nat_bool(X8095,X8098)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1192_all__nat__less])])])])])]) ).

fof(i_0_1930,plain,
    ! [X7948,X7949,X7951,X7952,X7953,X7955] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk507_2(X7948,X7949)),X7949))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7951),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X7949)))
        | hBOOL(hAPP_nat_bool(X7948,X7951)) )
      & ( ~ hBOOL(hAPP_nat_bool(X7948,esk507_2(X7948,X7949)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7951),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X7949)))
        | hBOOL(hAPP_nat_bool(X7948,X7951)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk508_2(X7952,X7953)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X7953)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7955),X7953))
        | hBOOL(hAPP_nat_bool(X7952,X7955)) )
      & ( ~ hBOOL(hAPP_nat_bool(X7952,esk508_2(X7952,X7953)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7955),X7953))
        | hBOOL(hAPP_nat_bool(X7952,X7955)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1133_all__nat__less__eq])])])])])]) ).

fof(i_0_1931,plain,
    ! [X7974,X7975,X7976] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7975),X7976))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X7975),X7974)),hAPP_nat_nat(times_times_nat(X7976),X7974))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1142_mult__le__mono1])]) ).

fof(i_0_1932,plain,
    ! [X7977,X7978,X7979] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7978),X7979))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X7977),X7978)),hAPP_nat_nat(times_times_nat(X7977),X7979))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1143_mult__le__mono2])]) ).

fof(i_0_1933,plain,
    ! [X8103,X8104,X8105] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X8103)),hAPP_n1699378549t_bool(ord_at238088361st_nat(X8104),X8105)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8104),X8103)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8105),X8103)),
    inference(variable_rename,[status(thm)],[fact_1195_image__add__atLeastAtMost]) ).

fof(i_0_1934,plain,
    ! [X7945,X7946,X7947] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X7945)),hAPP_n1699378549t_bool(ord_at4362885an_nat(X7946),X7947)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7946),X7945)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7947),X7945)),
    inference(variable_rename,[status(thm)],[fact_1132_image__add__atLeastLessThan]) ).

fof(i_0_1935,plain,
    ! [X4468,X4470,X4471,X4472,X4475] :
      ( ( ~ hBOOL(hAPP_P606313927t_bool(X4468,esk6_1(X4468)))
        | ~ is_Arr1861959080le_alt(X4470)
        | ~ is_Arr1861959080le_alt(X4471)
        | hBOOL(hAPP_P606313927t_bool(X4468,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4470),X4471))) )
      & ( is_Arr1861959080le_alt(esk7_1(X4472))
        | hBOOL(hAPP_P606313927t_bool(X4472,X4475)) )
      & ( is_Arr1861959080le_alt(esk8_1(X4472))
        | hBOOL(hAPP_P606313927t_bool(X4472,X4475)) )
      & ( ~ hBOOL(hAPP_P606313927t_bool(X4472,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk7_1(X4472)),esk8_1(X4472))))
        | hBOOL(hAPP_P606313927t_bool(X4472,X4475)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_split__paired__All])])])])])]) ).

fof(i_0_1936,plain,
    ! [X7853,X7854] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7853)),hAPP_nat_nat(suc,X7854)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7853),X7854)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7853),X7854))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7853)),hAPP_nat_nat(suc,X7854))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1089_Suc__le__mono])]) ).

fof(i_0_1937,plain,
    ! [X7835,X7836] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7835)),hAPP_nat_nat(suc,X7836)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7835),X7836)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7835),X7836))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7835)),hAPP_nat_nat(suc,X7836))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1080_Suc__less__eq])]) ).

fof(i_0_1938,plain,
    ! [X7818,X7819] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7818)),hAPP_nat_nat(suc,X7819)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7818),X7819)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1072_Suc__less__SucD])]) ).

fof(i_0_1939,plain,
    ! [X7876,X7877] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7876),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7876),X7877)))),
    inference(variable_rename,[status(thm)],[fact_1099_less__add__Suc1]) ).

fof(i_0_1940,plain,
    ! [X7878,X7879] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7878),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7879),X7878)))),
    inference(variable_rename,[status(thm)],[fact_1100_less__add__Suc2]) ).

fof(i_0_1941,plain,
    ! [X7824,X7825,X7826] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7825),X7826))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7826),X7824))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7825)),X7824)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1075_less__trans__Suc])]) ).

fof(i_0_1942,plain,
    ! [X7925,X7926] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7925),esk501_2(X7925,X7926)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7925)),X7926)) )
      & ( X7926 = hAPP_nat_nat(suc,esk501_2(X7925,X7926))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7925)),X7926)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1122_Suc__lessE])])])]) ).

fof(i_0_1943,plain,
    ! [X7857,X7858] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7857),X7858))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7858)),X7857)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7858)),X7857))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7857),X7858)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1405])]) ).

fof(i_0_1944,plain,
    ! [X7866,X7867,X7869,X7870,X7871] :
      ( ( X7866 = hAPP_nat_nat(suc,esk494_2(X7866,X7867))
        | X7866 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7866),hAPP_nat_nat(suc,X7867))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk494_2(X7866,X7867)),X7867))
        | X7866 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7866),hAPP_nat_nat(suc,X7867))) )
      & ( X7869 != zero_zero_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7869),hAPP_nat_nat(suc,X7870))) )
      & ( X7869 != hAPP_nat_nat(suc,X7871)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7871),X7870))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7869),hAPP_nat_nat(suc,X7870))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1096_less__Suc__eq__0__disj])])])])])]) ).

fof(i_0_1945,plain,
    ! [X5691,X5692,X5693,X5694] :
      ( ~ is_Arr43961803e_indi(X5691)
      | ~ is_Arr43961803e_indi(X5692)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5693),X5694))
      | hAPP_A1637648121di_nat(X5693,X5691) != hAPP_A1637648121di_nat(X5693,X5692)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5691),X5694))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5692),X5694))
      | X5691 = X5692 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_545_inj__onD])]) ).

fof(i_0_1946,plain,
    ! [X5675,X5676,X5677,X5678] :
      ( ~ is_Arr43961803e_indi(X5675)
      | ~ is_Arr43961803e_indi(X5676)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5677),X5678))
      | X5675 = X5676
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5675),X5678))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5676),X5678))
      | hAPP_A1637648121di_nat(X5677,X5675) != hAPP_A1637648121di_nat(X5677,X5676) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_541_inj__on__contraD])]) ).

fof(i_0_1947,plain,
    ! [X5683,X5684,X5685,X5686] :
      ( ( hAPP_A1637648121di_nat(X5685,X5684) != hAPP_A1637648121di_nat(X5685,X5683)
        | X5684 = X5683
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5683),X5686))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5684),X5686))
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5685),X5686))
        | ~ is_Arr43961803e_indi(X5683)
        | ~ is_Arr43961803e_indi(X5684) )
      & ( X5684 != X5683
        | hAPP_A1637648121di_nat(X5685,X5684) = hAPP_A1637648121di_nat(X5685,X5683)
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5683),X5686))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5684),X5686))
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5685),X5686))
        | ~ is_Arr43961803e_indi(X5683)
        | ~ is_Arr43961803e_indi(X5684) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_543_inj__on__iff])])]) ).

fof(i_0_1948,plain,
    ! [X5659,X5660,X5661,X5662,X5663,X5664] :
      ( ( ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5659),X5660))
        | ~ is_Arr43961803e_indi(X5661)
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5661),X5660))
        | ~ is_Arr43961803e_indi(X5662)
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5662),X5660))
        | hAPP_A1637648121di_nat(X5659,X5661) != hAPP_A1637648121di_nat(X5659,X5662)
        | X5661 = X5662 )
      & ( is_Arr43961803e_indi(esk37_2(X5663,X5664))
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5663),X5664)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk37_2(X5663,X5664)),X5664))
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5663),X5664)) )
      & ( is_Arr43961803e_indi(esk38_2(X5663,X5664))
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5663),X5664)) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk38_2(X5663,X5664)),X5664))
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5663),X5664)) )
      & ( hAPP_A1637648121di_nat(X5663,esk37_2(X5663,X5664)) = hAPP_A1637648121di_nat(X5663,esk38_2(X5663,X5664))
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5663),X5664)) )
      & ( esk37_2(X5663,X5664) != esk38_2(X5663,X5664)
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5663),X5664)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_539_inj__on__def])])])])])]) ).

fof(i_0_1949,plain,
    ! [X8023,X8024] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8023))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X8023),X8024))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8024))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X8023),X8024))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8023))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8024))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X8023),X8024))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1162_nat__0__less__mult__iff])])]) ).

fof(i_0_1950,plain,
    ! [X7935,X7936] :
      ( ( hBOOL(hAPP_nat_bool(X7936,esk505_2(X7935,X7936)))
        | hBOOL(hAPP_nat_bool(X7936,X7935))
        | ~ hBOOL(hAPP_nat_bool(X7936,zero_zero_nat)) )
      & ( ~ hBOOL(hAPP_nat_bool(X7936,hAPP_nat_nat(suc,esk505_2(X7935,X7936))))
        | hBOOL(hAPP_nat_bool(X7936,X7935))
        | ~ hBOOL(hAPP_nat_bool(X7936,zero_zero_nat)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1126_nat__induct])])])]) ).

fof(i_0_1951,plain,
    ! [X5687,X5688,X5689,X5690] :
      ( ( hAPP_nat_nat(X5689,X5688) != hAPP_nat_nat(X5689,X5687)
        | X5688 = X5687
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5687),X5690))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5688),X5690))
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5689),X5690)) )
      & ( X5688 != X5687
        | hAPP_nat_nat(X5689,X5688) = hAPP_nat_nat(X5689,X5687)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5687),X5690))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5688),X5690))
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5689),X5690)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_544_inj__on__iff])])]) ).

fof(i_0_1952,plain,
    ! [X5695,X5696,X5697,X5698] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5697),X5698))
      | hAPP_nat_nat(X5697,X5695) != hAPP_nat_nat(X5697,X5696)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5695),X5698))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5696),X5698))
      | X5695 = X5696 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_546_inj__onD])]) ).

fof(i_0_1953,plain,
    ! [X5679,X5680,X5681,X5682] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5681),X5682))
      | X5679 = X5680
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5679),X5682))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5680),X5682))
      | hAPP_nat_nat(X5681,X5679) != hAPP_nat_nat(X5681,X5680) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_542_inj__on__contraD])]) ).

fof(i_0_1954,plain,
    ! [X5667,X5668,X5669,X5670,X5671,X5672] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5667),X5668))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5669),X5668))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5670),X5668))
        | hAPP_nat_nat(X5667,X5669) != hAPP_nat_nat(X5667,X5670)
        | X5669 = X5670 )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk39_2(X5671,X5672)),X5672))
        | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5671),X5672)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk40_2(X5671,X5672)),X5672))
        | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5671),X5672)) )
      & ( hAPP_nat_nat(X5671,esk39_2(X5671,X5672)) = hAPP_nat_nat(X5671,esk40_2(X5671,X5672))
        | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5671),X5672)) )
      & ( esk39_2(X5671,X5672) != esk40_2(X5671,X5672)
        | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5671),X5672)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_540_inj__on__def])])])])])]) ).

fof(i_0_1955,plain,
    ! [X6432,X6433,X6434] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6433),X6434))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(X6434,X6432)),pi_Pro666468413t_bool(X6433,X6432))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_715_Pi__anti__mono])]) ).

fof(i_0_1956,plain,
    ! [X6435,X6436,X6437] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6436),X6437))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(X6437,X6435)),pi_fun150026276t_bool(X6436,X6435))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_716_Pi__anti__mono])]) ).

fof(i_0_1957,plain,
    ! [X6438,X6439,X6440] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6439),X6440))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(X6440,X6438)),pi_Arr990697634t_bool(X6439,X6438))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_717_Pi__anti__mono])]) ).

fof(i_0_1958,plain,
    ! [X5220,X5221,X5222] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5221),X5222))
      | hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X5221,X5220)),hAPP_A1664620203t_bool(X5222,X5220))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_343_le__funD])]) ).

fof(i_0_1959,plain,
    ! [X4956,X4957,X4958] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4957),X4958))
      | hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X4957,X4956)),hAPP_A1664620203t_bool(X4958,X4956))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_245_le__funE])]) ).

fof(i_0_1960,plain,
    ! [X5211,X5212,X5213] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5212),X5213))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X5212,X5211)),hAPP_P606313927t_bool(X5213,X5211))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_340_le__funD])]) ).

fof(i_0_1961,plain,
    ! [X4947,X4948,X4949] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4948),X4949))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X4948,X4947)),hAPP_P606313927t_bool(X4949,X4947))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_242_le__funE])]) ).

fof(i_0_1962,plain,
    ! [X5202,X5203,X5204] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5203),X5204))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X5203,X5202)),hAPP_f592646513l_bool(X5204,X5202))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_337_le__funD])]) ).

fof(i_0_1963,plain,
    ! [X4938,X4939,X4940] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4939),X4940))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X4939,X4938)),hAPP_f592646513l_bool(X4940,X4938))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_239_le__funE])]) ).

fof(i_0_1964,plain,
    ! [X5205,X5206,X5207] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5206),X5207))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X5206,X5205)),hAPP_f312250286l_bool(X5207,X5205))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_338_le__funD])]) ).

fof(i_0_1965,plain,
    ! [X4941,X4942,X4943] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4942),X4943))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X4942,X4941)),hAPP_f312250286l_bool(X4943,X4941))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_240_le__funE])]) ).

fof(i_0_1966,plain,
    ! [X5208,X5209,X5210] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5209),X5210))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X5209,X5208)),hAPP_f965095724l_bool(X5210,X5208))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_339_le__funD])]) ).

fof(i_0_1967,plain,
    ! [X4944,X4945,X4946] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4945),X4946))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X4945,X4944)),hAPP_f965095724l_bool(X4946,X4944))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_241_le__funE])]) ).

fof(i_0_1968,plain,
    ! [X5217,X5218,X5219] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5218),X5219))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X5218,X5217)),hAPP_P1676879539t_bool(X5219,X5217))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_342_le__funD])]) ).

fof(i_0_1969,plain,
    ! [X4953,X4954,X4955] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4954),X4955))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X4954,X4953)),hAPP_P1676879539t_bool(X4955,X4953))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_244_le__funE])]) ).

fof(i_0_1970,plain,
    ! [X5223,X5224,X5225] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5224),X5225))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X5224,X5223)),hAPP_nat_bool(X5225,X5223))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_344_le__funD])]) ).

fof(i_0_1971,plain,
    ! [X4959,X4960,X4961] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4960),X4961))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X4960,X4959)),hAPP_nat_bool(X4961,X4959))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_246_le__funE])]) ).

fof(i_0_1972,plain,
    ! [X5214,X5215,X5216] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5215),X5216))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X5215,X5214)),hAPP_A1785763630i_bool(X5216,X5214))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_341_le__funD])]) ).

fof(i_0_1973,plain,
    ! [X4950,X4951,X4952] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4951),X4952))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X4951,X4950)),hAPP_A1785763630i_bool(X4952,X4950))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_243_le__funE])]) ).

fof(i_0_1974,plain,
    ! [X7847,X7848] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7847)),X7848))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7847),X7848)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1086_Suc__leD])]) ).

fof(i_0_1975,plain,
    ! [X7898,X7899] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7898)),X7899))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7898),X7899)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1108_Suc__le__lessD])]) ).

fof(i_0_1976,plain,
    ! [X7890,X7891] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7890)),X7891))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7890),X7891)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7890),X7891))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7890)),X7891)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1104_Suc__le__eq])]) ).

fof(i_0_1977,plain,
    ! [X7886,X7887] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7886),X7887))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7886)),X7887)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7886)),X7887))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7886),X7887)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1102_less__eq__Suc__le])]) ).

fof(i_0_1978,plain,
    ! [X7820,X7821] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7820)),X7821))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7820),X7821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1073_Suc__lessD])]) ).

fof(i_0_1979,plain,
    ! [X7735,X7736,X7737] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7736),X7737))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7736),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7737),X7735))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1025_termination__basic__simps_I3_J])]) ).

fof(i_0_1980,plain,
    ! [X7706,X7707,X7708] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7707),X7708))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7707),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7708),X7706))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1017_trans__le__add1])]) ).

fof(i_0_1981,plain,
    ! [X7738,X7739,X7740] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7739),X7740))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7739),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7738),X7740))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1026_termination__basic__simps_I4_J])]) ).

fof(i_0_1982,plain,
    ! [X7709,X7710,X7711] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7710),X7711))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7710),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7709),X7711))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1018_trans__le__add2])]) ).

fof(i_0_1983,plain,
    ! [X7746,X7747,X7748] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7747),X7748))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7747),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7748),X7746))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1029_termination__basic__simps_I1_J])]) ).

fof(i_0_1984,plain,
    ! [X7663,X7664,X7665] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7664),X7665))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7664),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7665),X7663))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1002_trans__less__add1])]) ).

fof(i_0_1985,plain,
    ! [X7743,X7744,X7745] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7744),X7745))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7744),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7743),X7745))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1028_termination__basic__simps_I2_J])]) ).

fof(i_0_1986,plain,
    ! [X7666,X7667,X7668] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7667),X7668))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7667),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7666),X7668))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1003_trans__less__add2])]) ).

fof(i_0_1987,plain,
    ! [X7750] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),X7750)))),
    inference(variable_rename,[status(thm)],[fact_1032_finite__Collect__le__nat]) ).

fof(i_0_1988,plain,
    ! [X7751] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X7751)))),
    inference(variable_rename,[status(thm)],[fact_1033_finite__Collect__less__nat]) ).

fof(i_0_1989,plain,
    ! [X7803,X7804] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7803),X7804))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7803)),hAPP_nat_nat(suc,X7804))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1060_Suc__mono])]) ).

fof(i_0_1990,plain,
    ! [X7795,X7796,X7798] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk491_2(X7795,X7796)),X7795))
        | ~ hBOOL(hAPP_nat_bool(X7796,X7795))
        | hBOOL(hAPP_nat_bool(X7796,zero_zero_nat)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7798),esk491_2(X7795,X7796)))
        | ~ hBOOL(hAPP_nat_bool(X7796,X7798))
        | ~ hBOOL(hAPP_nat_bool(X7796,X7795))
        | hBOOL(hAPP_nat_bool(X7796,zero_zero_nat)) )
      & ( hBOOL(hAPP_nat_bool(X7796,esk491_2(X7795,X7796)))
        | ~ hBOOL(hAPP_nat_bool(X7796,X7795))
        | hBOOL(hAPP_nat_bool(X7796,zero_zero_nat)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1406])])])])]) ).

fof(i_0_1991,plain,
    ( is_fun961089132t_bool(esk20_0)
    & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),esk20_0))
    & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk20_0),arrow_1681063817le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1407])])]) ).

fof(i_0_1992,plain,
    ( is_fun961089132t_bool(esk19_0)
    & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),esk19_0))
    & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk19_0),arrow_1681063817le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1408])])]) ).

fof(i_0_1993,plain,
    ! [X7576,X7577,X7578] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X7577),X7578))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7578),X7576))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X7577),X7576)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_964_set__rev__mp])]) ).

fof(i_0_1994,plain,
    ! [X7594,X7595,X7596] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7595),X7596))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X7594),X7595))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X7594),X7596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_970_in__mono])]) ).

fof(i_0_1995,plain,
    ! [X7561,X7562,X7563] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7562),X7563))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X7561),X7562))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X7561),X7563)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_959_set__mp])]) ).

fof(i_0_1996,plain,
    ! [X7451,X7452,X7453] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7452),X7453))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X7451),X7452))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X7451),X7453)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_915_subsetD])]) ).

fof(i_0_1997,plain,
    ! [X5021,X5022,X5023] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5022),X5023))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5023),X5021))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5022),X5021)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_270_order__trans])]) ).

fof(i_0_1998,plain,
    ! [X4971,X4972,X4973] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4972),X4973))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4971),X4972))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4971),X4973)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_250_xt1_I6_J])]) ).

fof(i_0_1999,plain,
    ! [X7523,X7524,X7525] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7524),X7525))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7525),X7523))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7524),X7523)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_946_psubset__subset__trans])]) ).

fof(i_0_2000,plain,
    ! [X5527,X5528,X5529] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5528),X5529))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5529),X5527))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5528),X5527)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_477_order__less__le__trans])]) ).

fof(i_0_2001,plain,
    ! [X7538,X7539,X7540] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7539),X7540))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7540),X7538))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7539),X7538)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_951_subset__psubset__trans])]) ).

fof(i_0_2002,plain,
    ! [X5587,X5588,X5589] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5588),X5589))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5589),X5587))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5588),X5587)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_497_order__le__less__trans])]) ).

fof(i_0_2003,plain,
    ! [X5557,X5558,X5559] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5558),X5559))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5557),X5558))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5557),X5559)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_487_xt1_I7_J])]) ).

fof(i_0_2004,plain,
    ! [X5617,X5618,X5619] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5618),X5619))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5617),X5618))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5617),X5619)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_507_xt1_I8_J])]) ).

fof(i_0_2005,plain,
    ! [X5012,X5013,X5014] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5013),X5014))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5014),X5012))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5013),X5012)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_267_order__trans])]) ).

fof(i_0_2006,plain,
    ! [X4962,X4963,X4964] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4963),X4964))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4962),X4963))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4962),X4964)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_247_xt1_I6_J])]) ).

fof(i_0_2007,plain,
    ! [X7514,X7515,X7516] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7515),X7516))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7516),X7514))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7515),X7514)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_943_psubset__subset__trans])]) ).

fof(i_0_2008,plain,
    ! [X5518,X5519,X5520] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5519),X5520))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5520),X5518))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5519),X5518)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_474_order__less__le__trans])]) ).

fof(i_0_2009,plain,
    ! [X7529,X7530,X7531] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7530),X7531))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7531),X7529))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7530),X7529)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_948_subset__psubset__trans])]) ).

fof(i_0_2010,plain,
    ! [X5578,X5579,X5580] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5579),X5580))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5580),X5578))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5579),X5578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_494_order__le__less__trans])]) ).

fof(i_0_2011,plain,
    ! [X5548,X5549,X5550] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5549),X5550))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5548),X5549))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5548),X5550)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_484_xt1_I7_J])]) ).

fof(i_0_2012,plain,
    ! [X5608,X5609,X5610] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5609),X5610))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5608),X5609))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5608),X5610)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_504_xt1_I8_J])]) ).

fof(i_0_2013,plain,
    ! [X7567,X7568,X7569] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X7568),X7569))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7569),X7567))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X7568),X7567)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_961_set__rev__mp])]) ).

fof(i_0_2014,plain,
    ! [X7585,X7586,X7587] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7586),X7587))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X7585),X7586))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X7585),X7587)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_967_in__mono])]) ).

fof(i_0_2015,plain,
    ! [X7552,X7553,X7554] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7553),X7554))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X7552),X7553))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X7552),X7554)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_956_set__mp])]) ).

fof(i_0_2016,plain,
    ! [X7460,X7461,X7462] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7461),X7462))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X7460),X7461))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X7460),X7462)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_918_subsetD])]) ).

fof(i_0_2017,plain,
    ! [X5015,X5016,X5017] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5016),X5017))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5017),X5015))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5016),X5015)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_268_order__trans])]) ).

fof(i_0_2018,plain,
    ! [X4965,X4966,X4967] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4966),X4967))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4965),X4966))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4965),X4967)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_248_xt1_I6_J])]) ).

fof(i_0_2019,plain,
    ! [X7517,X7518,X7519] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7518),X7519))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7519),X7517))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7518),X7517)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_944_psubset__subset__trans])]) ).

fof(i_0_2020,plain,
    ! [X5521,X5522,X5523] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5522),X5523))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5523),X5521))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5522),X5521)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_475_order__less__le__trans])]) ).

fof(i_0_2021,plain,
    ! [X7532,X7533,X7534] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7533),X7534))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7534),X7532))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7533),X7532)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_949_subset__psubset__trans])]) ).

fof(i_0_2022,plain,
    ! [X5581,X5582,X5583] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5582),X5583))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5583),X5581))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5582),X5581)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_495_order__le__less__trans])]) ).

fof(i_0_2023,plain,
    ! [X5551,X5552,X5553] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5552),X5553))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5551),X5552))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5551),X5553)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_485_xt1_I7_J])]) ).

fof(i_0_2024,plain,
    ! [X5611,X5612,X5613] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5612),X5613))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5611),X5612))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5611),X5613)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_505_xt1_I8_J])]) ).

fof(i_0_2025,plain,
    ! [X7570,X7571,X7572] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X7571),X7572))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7572),X7570))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X7571),X7570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_962_set__rev__mp])]) ).

fof(i_0_2026,plain,
    ! [X7588,X7589,X7590] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7589),X7590))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X7588),X7589))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X7588),X7590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_968_in__mono])]) ).

fof(i_0_2027,plain,
    ! [X7555,X7556,X7557] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7556),X7557))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X7555),X7556))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X7555),X7557)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_957_set__mp])]) ).

fof(i_0_2028,plain,
    ! [X7457,X7458,X7459] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7458),X7459))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X7457),X7458))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X7457),X7459)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_917_subsetD])]) ).

fof(i_0_2029,plain,
    ! [X5018,X5019,X5020] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5019),X5020))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5020),X5018))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5019),X5018)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_269_order__trans])]) ).

fof(i_0_2030,plain,
    ! [X4968,X4969,X4970] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4969),X4970))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4968),X4969))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4968),X4970)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_249_xt1_I6_J])]) ).

fof(i_0_2031,plain,
    ! [X7520,X7521,X7522] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7521),X7522))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7522),X7520))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7521),X7520)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_945_psubset__subset__trans])]) ).

fof(i_0_2032,plain,
    ! [X5524,X5525,X5526] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5525),X5526))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5526),X5524))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5525),X5524)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_476_order__less__le__trans])]) ).

fof(i_0_2033,plain,
    ! [X7535,X7536,X7537] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7536),X7537))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7537),X7535))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7536),X7535)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_950_subset__psubset__trans])]) ).

fof(i_0_2034,plain,
    ! [X5584,X5585,X5586] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5585),X5586))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5586),X5584))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5585),X5584)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_496_order__le__less__trans])]) ).

fof(i_0_2035,plain,
    ! [X5554,X5555,X5556] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5555),X5556))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5554),X5555))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5554),X5556)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_486_xt1_I7_J])]) ).

fof(i_0_2036,plain,
    ! [X5614,X5615,X5616] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5615),X5616))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5614),X5615))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5614),X5616)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_506_xt1_I8_J])]) ).

fof(i_0_2037,plain,
    ! [X7573,X7574,X7575] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X7574),X7575))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7575),X7573))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X7574),X7573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_963_set__rev__mp])]) ).

fof(i_0_2038,plain,
    ! [X7591,X7592,X7593] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7592),X7593))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X7591),X7592))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X7591),X7593)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_969_in__mono])]) ).

fof(i_0_2039,plain,
    ! [X7558,X7559,X7560] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7559),X7560))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X7558),X7559))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X7558),X7560)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_958_set__mp])]) ).

fof(i_0_2040,plain,
    ! [X7454,X7455,X7456] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7455),X7456))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X7454),X7455))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X7454),X7456)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_916_subsetD])]) ).

fof(i_0_2041,plain,
    ! [X5030,X5031,X5032] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5031),X5032))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5032),X5030))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5031),X5030)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_273_order__trans])]) ).

fof(i_0_2042,plain,
    ! [X4980,X4981,X4982] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4981),X4982))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4980),X4981))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4980),X4982)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_253_xt1_I6_J])]) ).

fof(i_0_2043,plain,
    ! [X7508,X7509,X7510] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7509),X7510))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7510),X7508))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7509),X7508)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_941_psubset__subset__trans])]) ).

fof(i_0_2044,plain,
    ! [X5512,X5513,X5514] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5513),X5514))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5514),X5512))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5513),X5512)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_472_order__less__le__trans])]) ).

fof(i_0_2045,plain,
    ! [X5572,X5573,X5574] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5573),X5574))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5574),X5572))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5573),X5572)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_492_order__le__less__trans])]) ).

fof(i_0_2046,plain,
    ! [X4602,X4603,X4604] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4603),X4604))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4604),X4602))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4603),X4602)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_102_order__less__trans])]) ).

fof(i_0_2047,plain,
    ! [X5542,X5543,X5544] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5543),X5544))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5542),X5543))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5542),X5544)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_482_xt1_I7_J])]) ).

fof(i_0_2048,plain,
    ! [X5602,X5603,X5604] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5603),X5604))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5602),X5603))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5602),X5604)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_502_xt1_I8_J])]) ).

fof(i_0_2049,plain,
    ! [X4590,X4591,X4592] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4591),X4592))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4590),X4591))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4590),X4592)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_xt1_I10_J])]) ).

fof(i_0_2050,plain,
    ! [X7448,X7449,X7450] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7449),X7450))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X7448),X7449))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X7448),X7450)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_914_subsetD])]) ).

fof(i_0_2051,plain,
    ! [X7546,X7547,X7548] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7547),X7548))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7548),X7546))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7547),X7546)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_954_subset__trans])]) ).

fof(i_0_2052,plain,
    ! [X5039,X5040,X5041] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5040),X5041))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5041),X5039))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5040),X5039)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_276_order__trans])]) ).

fof(i_0_2053,plain,
    ! [X4989,X4990,X4991] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4990),X4991))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4989),X4990))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4989),X4991)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_256_xt1_I6_J])]) ).

fof(i_0_2054,plain,
    ! [X7526,X7527,X7528] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7527),X7528))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7528),X7526))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7527),X7526)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_947_psubset__subset__trans])]) ).

fof(i_0_2055,plain,
    ! [X5536,X5537,X5538] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5537),X5538))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5538),X5536))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5537),X5536)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_480_order__less__le__trans])]) ).

fof(i_0_2056,plain,
    ! [X7541,X7542,X7543] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7542),X7543))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7543),X7541))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7542),X7541)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_952_subset__psubset__trans])]) ).

fof(i_0_2057,plain,
    ! [X5596,X5597,X5598] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5597),X5598))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5598),X5596))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5597),X5596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_500_order__le__less__trans])]) ).

fof(i_0_2058,plain,
    ! [X4599,X4600,X4601] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4600),X4601))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4601),X4599))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4600),X4599)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_101_order__less__trans])]) ).

fof(i_0_2059,plain,
    ! [X5566,X5567,X5568] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5567),X5568))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5566),X5567))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5566),X5568)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_490_xt1_I7_J])]) ).

fof(i_0_2060,plain,
    ! [X5626,X5627,X5628] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5627),X5628))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5626),X5627))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5626),X5628)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_510_xt1_I8_J])]) ).

fof(i_0_2061,plain,
    ! [X4587,X4588,X4589] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4588),X4589))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4587),X4588))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4587),X4589)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_97_xt1_I10_J])]) ).

fof(i_0_2062,plain,
    ! [X7564,X7565,X7566] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7565),X7566))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7566),X7564))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7565),X7564)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_960_set__rev__mp])]) ).

fof(i_0_2063,plain,
    ! [X7582,X7583,X7584] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7583),X7584))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7582),X7583))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7582),X7584)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_966_in__mono])]) ).

fof(i_0_2064,plain,
    ! [X7549,X7550,X7551] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7550),X7551))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7549),X7550))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7549),X7551)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_955_set__mp])]) ).

fof(i_0_2065,plain,
    ! [X7463,X7464,X7465] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7464),X7465))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7463),X7464))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7463),X7465)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_919_subsetD])]) ).

fof(i_0_2066,plain,
    ! [X7445,X7446,X7447] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,X7446),X7447))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X7445),X7446))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X7445),X7447)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_913_subsetD])]) ).

fof(i_0_2067,plain,
    ! [X5027,X5028,X5029] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5028),X5029))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5029),X5027))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5028),X5027)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_272_order__trans])]) ).

fof(i_0_2068,plain,
    ! [X4977,X4978,X4979] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4978),X4979))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4977),X4978))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4977),X4979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_252_xt1_I6_J])]) ).

fof(i_0_2069,plain,
    ! [X7511,X7512,X7513] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7512),X7513))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7513),X7511))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7512),X7511)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_942_psubset__subset__trans])]) ).

fof(i_0_2070,plain,
    ! [X5515,X5516,X5517] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5516),X5517))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5517),X5515))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5516),X5515)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_473_order__less__le__trans])]) ).

fof(i_0_2071,plain,
    ! [X5575,X5576,X5577] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5576),X5577))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5577),X5575))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5576),X5575)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_493_order__le__less__trans])]) ).

fof(i_0_2072,plain,
    ! [X4605,X4606,X4607] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4606),X4607))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4607),X4605))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4606),X4605)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_103_order__less__trans])]) ).

fof(i_0_2073,plain,
    ! [X5545,X5546,X5547] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5546),X5547))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5545),X5546))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5545),X5547)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_483_xt1_I7_J])]) ).

fof(i_0_2074,plain,
    ! [X5605,X5606,X5607] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5606),X5607))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5605),X5606))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5605),X5607)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_503_xt1_I8_J])]) ).

fof(i_0_2075,plain,
    ! [X4593,X4594,X4595] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4594),X4595))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4593),X4594))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4593),X4595)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_99_xt1_I10_J])]) ).

fof(i_0_2076,plain,
    ! [X7442,X7443,X7444] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7443),X7444))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X7442),X7443))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X7442),X7444)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_912_subsetD])]) ).

fof(i_0_2077,plain,
    ! [X5593,X5594,X5595] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5594),X5595))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5595),X5593))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5594),X5593)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_499_order__le__less__trans])]) ).

fof(i_0_2078,plain,
    ! [X5533,X5534,X5535] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5534),X5535))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5535),X5533))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5534),X5533)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_479_order__less__le__trans])]) ).

fof(i_0_2079,plain,
    ! [X5623,X5624,X5625] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5624),X5625))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5623),X5624))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5623),X5625)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_509_xt1_I8_J])]) ).

fof(i_0_2080,plain,
    ! [X5563,X5564,X5565] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5564),X5565))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5563),X5564))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5563),X5565)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_489_xt1_I7_J])]) ).

fof(i_0_2081,plain,
    ! [X5033,X5034,X5035] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5034),X5035))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5035),X5033))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5034),X5033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_274_order__trans])]) ).

fof(i_0_2082,plain,
    ! [X4983,X4984,X4985] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4984),X4985))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4983),X4984))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4983),X4985)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_254_xt1_I6_J])]) ).

fof(i_0_2083,plain,
    ! [X7649,X7650,X7651] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7650),X7651))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7651),X7649))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7650),X7649)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_996_le__trans])]) ).

fof(i_0_2084,plain,
    ! [X5036,X5037,X5038] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5037),X5038))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5038),X5036))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5037),X5036)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_275_order__trans])]) ).

fof(i_0_2085,plain,
    ! [X4986,X4987,X4988] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4987),X4988))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4986),X4987))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4986),X4988)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_255_xt1_I6_J])]) ).

fof(i_0_2086,plain,
    ! [X5539,X5540,X5541] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5540),X5541))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5541),X5539))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5540),X5539)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_481_order__less__le__trans])]) ).

fof(i_0_2087,plain,
    ! [X5599,X5600,X5601] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5600),X5601))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5601),X5599))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5600),X5599)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_501_order__le__less__trans])]) ).

fof(i_0_2088,plain,
    ! [X4608,X4609,X4610] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4609),X4610))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4610),X4608))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4609),X4608)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_104_order__less__trans])]) ).

fof(i_0_2089,plain,
    ! [X5569,X5570,X5571] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5570),X5571))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5569),X5570))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5569),X5571)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_491_xt1_I7_J])]) ).

fof(i_0_2090,plain,
    ! [X5629,X5630,X5631] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5630),X5631))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5629),X5630))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5629),X5631)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_511_xt1_I8_J])]) ).

fof(i_0_2091,plain,
    ! [X4596,X4597,X4598] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4597),X4598))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4596),X4597))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4596),X4598)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_100_xt1_I10_J])]) ).

fof(i_0_2092,plain,
    ! [X5024,X5025,X5026] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5025),X5026))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5026),X5024))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5025),X5024)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_271_order__trans])]) ).

fof(i_0_2093,plain,
    ! [X4974,X4975,X4976] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4975),X4976))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4974),X4975))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4974),X4976)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_251_xt1_I6_J])]) ).

fof(i_0_2094,plain,
    ! [X5530,X5531,X5532] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5531),X5532))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5532),X5530))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5531),X5530)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_478_order__less__le__trans])]) ).

fof(i_0_2095,plain,
    ! [X5590,X5591,X5592] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5591),X5592))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5592),X5590))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5591),X5590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_498_order__le__less__trans])]) ).

fof(i_0_2096,plain,
    ! [X5560,X5561,X5562] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5561),X5562))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5560),X5561))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5560),X5562)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_488_xt1_I7_J])]) ).

fof(i_0_2097,plain,
    ! [X5620,X5621,X5622] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5621),X5622))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5620),X5621))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5620),X5622)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_508_xt1_I8_J])]) ).

fof(i_0_2098,plain,
    ! [X7990,X7991,X7992] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7990),X7991)),X7992) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X7990),X7992)),hAPP_nat_nat(times_times_nat(X7991),X7992)),
    inference(variable_rename,[status(thm)],[fact_1149_add__mult__distrib]) ).

fof(i_0_2099,plain,
    ! [X7896,X7897] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7897),hAPP_nat_nat(suc,X7896)))
        | X7897 = X7896
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7896),X7897)) )
      & ( X7897 != X7896
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7897),hAPP_nat_nat(suc,X7896)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7896),X7897)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1107_le__less__Suc__eq])])]) ).

fof(i_0_2100,plain,
    ! [X7676,X7677,X7678,X7679] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7678),X7679))
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7676),X7679) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7678),X7677)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7676),X7677)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1006_less__add__eq__less])]) ).

fof(i_0_2101,plain,
    ! [X7839,X7840] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7839),X7840))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7840),hAPP_nat_nat(suc,X7839))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7840),hAPP_nat_nat(suc,X7839)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7839),X7840)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1409])]) ).

fof(i_0_2102,plain,
    ! [X7755,X7757,X7758,X7759] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7755))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7757),X7755))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7757),esk484_1(X7755))) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk485_2(X7758,X7759)),X7758))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7758)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk485_2(X7758,X7759)),X7759))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7758)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1038_finite__nat__set__iff__bounded__le])])])])])]) ).

fof(i_0_2103,plain,
    ! [X7761,X7763,X7764,X7765] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7761))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7763),X7761))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7763),esk486_1(X7761))) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk487_2(X7764,X7765)),X7764))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7764)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk487_2(X7764,X7765)),X7765))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7764)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1039_finite__nat__set__iff__bounded])])])])])]) ).

fof(i_0_2104,plain,
    ! [X7770,X7771] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk489_2(X7770,X7771)),X7771))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7771)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk489_2(X7770,X7771)),X7770))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7771)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1041_bounded__nat__set__is__finite])])])]) ).

fof(i_0_2105,plain,
    ! [X7973] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7973),hAPP_nat_nat(times_times_nat(X7973),hAPP_nat_nat(times_times_nat(X7973),X7973)))),
    inference(variable_rename,[status(thm)],[fact_1141_le__cube]) ).

fof(i_0_2106,plain,
    ! [X7654,X7655] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X7654)),X7655)),
    inference(variable_rename,[status(thm)],[fact_998_inj__on__add__nat]) ).

fof(i_0_2107,plain,
    ! [X7919,X7920] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7919)),X7920))
      | X7920 = hAPP_nat_nat(suc,esk499_2(X7919,X7920)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1120_Suc__le__D])])]) ).

fof(i_0_2108,plain,
    ! [X7827,X7828] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7827),X7828))
      | hAPP_nat_nat(suc,X7827) = X7828
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X7827)),X7828)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1076_Suc__lessI])]) ).

fof(i_0_2109,plain,
    ! [X7635,X7636,X7637] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7635),X7636)),X7637) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7635),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7636),X7637)),
    inference(variable_rename,[status(thm)],[fact_990_nat__add__assoc]) ).

fof(i_0_2110,plain,
    ! [X6471,X6472,X6473] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6471),X6472)),X6473) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6471),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6472),X6473)),
    inference(variable_rename,[status(thm)],[fact_733_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(i_0_2111,plain,
    ! [X7894,X7895] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7894),X7895))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7894)),X7895)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1106_Suc__leI])]) ).

fof(i_0_2112,plain,
    ! [X7855,X7856] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7855),hAPP_nat_nat(suc,X7856)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7855),X7856))
        | X7855 = hAPP_nat_nat(suc,X7856) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7855),X7856))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7855),hAPP_nat_nat(suc,X7856))) )
      & ( X7855 != hAPP_nat_nat(suc,X7856)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7855),hAPP_nat_nat(suc,X7856))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1090_le__Suc__eq])])]) ).

fof(i_0_2113,plain,
    ! [X7849,X7850] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7849),hAPP_nat_nat(suc,X7850)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7849),X7850))
      | X7849 = hAPP_nat_nat(suc,X7850) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1410])]) ).

fof(i_0_2114,plain,
    ! [X4576] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4576),arrow_1681063817le_Lin))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X4576)),arrow_1721807329e_Prof)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_const__Lin__Prof])]) ).

fof(i_0_2115,plain,
    ! [X6426,X6427] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6426),X6427))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6426),X6427)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6427),X6426))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6426),X6427)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6426),X6427))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6427),X6426))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X6426),X6427)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1411])])]) ).

fof(i_0_2116,plain,
    ! [X5352,X5353] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5352),X5353))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5352),X5353)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5353),X5352))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5352),X5353)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5352),X5353))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5353),X5352))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5352),X5353)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1412])])]) ).

fof(i_0_2117,plain,
    ! [X6420,X6421] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6420),X6421))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6420),X6421)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6421),X6420))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6420),X6421)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6420),X6421))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6421),X6420))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X6420),X6421)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1413])])]) ).

fof(i_0_2118,plain,
    ! [X5346,X5347] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5346),X5347))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5346),X5347)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5347),X5346))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5346),X5347)) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5346),X5347))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5347),X5346))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5346),X5347)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1414])])]) ).

fof(i_0_2119,plain,
    ! [X6422,X6423] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6422),X6423))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6422),X6423)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6423),X6422))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6422),X6423)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6422),X6423))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6423),X6422))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X6422),X6423)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1415])])]) ).

fof(i_0_2120,plain,
    ! [X5348,X5349] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5348),X5349))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5348),X5349)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5349),X5348))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5348),X5349)) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5348),X5349))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5349),X5348))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5348),X5349)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1416])])]) ).

fof(i_0_2121,plain,
    ! [X6424,X6425] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6424),X6425))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6424),X6425)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6425),X6424))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6424),X6425)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6424),X6425))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6425),X6424))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X6424),X6425)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1417])])]) ).

fof(i_0_2122,plain,
    ! [X5350,X5351] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5350),X5351))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5350),X5351)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5351),X5350))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5350),X5351)) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5350),X5351))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5351),X5350))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5350),X5351)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1418])])]) ).

fof(i_0_2123,plain,
    ! [X6416,X6417] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6416),X6417))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6416),X6417)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6417),X6416))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6416),X6417)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6416),X6417))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6417),X6416))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X6416),X6417)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1419])])]) ).

fof(i_0_2124,plain,
    ! [X5342,X5343] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5342),X5343))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5342),X5343)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5343),X5342))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5342),X5343)) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5342),X5343))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5343),X5342))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5342),X5343)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1420])])]) ).

fof(i_0_2125,plain,
    ! [X6430,X6431] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6430),X6431))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6430),X6431)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6431),X6430))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6430),X6431)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6430),X6431))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6431),X6430))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6430),X6431)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1421])])]) ).

fof(i_0_2126,plain,
    ! [X5358,X5359] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5358),X5359))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5358),X5359)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5359),X5358))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5358),X5359)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5358),X5359))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5359),X5358))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5358),X5359)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1422])])]) ).

fof(i_0_2127,plain,
    ! [X6418,X6419] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6418),X6419))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6418),X6419)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6419),X6418))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6418),X6419)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6418),X6419))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6419),X6418))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X6418),X6419)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1423])])]) ).

fof(i_0_2128,plain,
    ! [X5344,X5345] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5344),X5345))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5344),X5345)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5345),X5344))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5344),X5345)) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5344),X5345))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5345),X5344))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5344),X5345)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1424])])]) ).

fof(i_0_2129,plain,
    ! [X6428,X6429] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6428),X6429))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6428),X6429)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6429),X6428))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6428),X6429)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6428),X6429))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X6429),X6428))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X6428),X6429)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1425])])]) ).

fof(i_0_2130,plain,
    ! [X5356,X5357] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5356),X5357))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5356),X5357)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5357),X5356))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5356),X5357)) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5356),X5357))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5357),X5356))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5356),X5357)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1426])])]) ).

fof(i_0_2131,plain,
    ! [X5360,X5361] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5360),X5361))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5360),X5361)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5361),X5360))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5360),X5361)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5360),X5361))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5361),X5360))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5360),X5361)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1427])])]) ).

fof(i_0_2132,plain,
    ! [X5354,X5355] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5354),X5355))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5354),X5355)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5355),X5354))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5354),X5355)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5354),X5355))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5355),X5354))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5354),X5355)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1428])])]) ).

fof(i_0_2133,plain,
    ! [X7837,X7838] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7837),hAPP_nat_nat(suc,X7838)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7837),X7838))
        | X7837 = X7838 )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7837),X7838))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7837),hAPP_nat_nat(suc,X7838))) )
      & ( X7837 != X7838
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7837),hAPP_nat_nat(suc,X7838))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1081_less__Suc__eq])])]) ).

fof(i_0_2134,plain,
    ! [X7833,X7834] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7833),hAPP_nat_nat(suc,X7834)))
        | X7833 = X7834
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7833),X7834)) )
      & ( X7833 != X7834
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7833),hAPP_nat_nat(suc,X7834)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7833),X7834)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1429])])]) ).

fof(i_0_2135,plain,
    ! [X7831,X7832] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7831),X7832))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7831),hAPP_nat_nat(suc,X7832)))
      | X7832 = X7831 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1430])]) ).

fof(i_0_2136,plain,
    ! [X7822,X7823] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7822),hAPP_nat_nat(suc,X7823)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7822),X7823))
      | X7822 = X7823 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1431])]) ).

fof(i_0_2137,plain,
    ! [X7888,X7889] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7888),hAPP_nat_nat(suc,X7889)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7888),X7889)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7888),X7889))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7888),hAPP_nat_nat(suc,X7889))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1103_less__Suc__eq__le])]) ).

fof(i_0_2138,plain,
    ! [X7859] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7859)),X7859)),
    inference(variable_rename,[status(thm)],[i_0_1432]) ).

fof(i_0_2139,plain,
    ! [X4552,X4553,X4554,X4555,X4556] :
      ( ( ~ hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4552),X4553))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4554),arrow_1721807329e_Prof))
        | hAPP_f412050202t_bool(X4552,X4554) = hAPP_A1677245848t_bool(X4554,X4553) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk18_2(X4555,X4556)),arrow_1721807329e_Prof))
        | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4555),X4556)) )
      & ( hAPP_f412050202t_bool(X4555,esk18_2(X4555,X4556)) != hAPP_A1677245848t_bool(esk18_2(X4555,X4556),X4556)
        | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X4555),X4556)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_dictator__def])])])])])]) ).

fof(i_0_2140,plain,
    ! [X7922,X7923] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7922),esk500_2(X7922,X7923)))
        | X7923 = hAPP_nat_nat(suc,X7922)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7922),X7923)) )
      & ( X7923 = hAPP_nat_nat(suc,esk500_2(X7922,X7923))
        | X7923 = hAPP_nat_nat(suc,X7922)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7922),X7923)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1121_lessE])])])]) ).

fof(i_0_2141,plain,
    ! [X5963,X5964,X5965] :
      ( ~ is_Arr43961803e_indi(X5963)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5964),X5965))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5963),X5965))
      | hAPP_n1951273283e_indi(hilber693666498di_nat(X5965,X5964),hAPP_A1637648121di_nat(X5964,X5963)) = X5963 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_616_inv__into__f__f])]) ).

fof(i_0_2142,plain,
    ! [X5969,X5970,X5971,X5972] :
      ( ~ is_Arr43961803e_indi(X5970)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5971),X5972))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X5970),X5972))
      | hAPP_A1637648121di_nat(X5971,X5970) != X5969
      | hAPP_n1951273283e_indi(hilber693666498di_nat(X5972,X5971),X5969) = X5970 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_618_inv__into__f__eq])]) ).

fof(i_0_2143,plain,
    ! [X7912,X7913] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7912),X7913))
      | X7913 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7912),esk497_2(X7912,X7913))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1116_less__imp__Suc__add])])]) ).

fof(i_0_2144,plain,
    ! [X7880,X7881,X7883,X7884,X7885] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7880),X7881))
        | X7881 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7880),esk495_2(X7880,X7881))) )
      & ( X7884 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7883),X7885))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7883),X7884)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1101_less__iff__Suc__add])])])])]) ).

fof(i_0_2145,plain,
    ! [X7438,X7439] :
      ( ~ is_fun1568535512t_bool(X7438)
      | ~ is_fun1568535512t_bool(X7439)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7438),X7439))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7439),X7438))
      | X7438 = X7439 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_910_equalityI])]) ).

fof(i_0_2146,plain,
    ! [X5258,X5259] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5258),X5259))
        | X5258 != X5259
        | ~ is_fun1568535512t_bool(X5258)
        | ~ is_fun1568535512t_bool(X5259) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5259),X5258))
        | X5258 != X5259
        | ~ is_fun1568535512t_bool(X5258)
        | ~ is_fun1568535512t_bool(X5259) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5258),X5259))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5259),X5258))
        | X5258 = X5259
        | ~ is_fun1568535512t_bool(X5258)
        | ~ is_fun1568535512t_bool(X5259) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_361_order__eq__iff])])]) ).

fof(i_0_2147,plain,
    ! [X5194,X5195] :
      ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5195),X5194))
        | X5195 = X5194
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5194),X5195))
        | ~ is_fun1568535512t_bool(X5194)
        | ~ is_fun1568535512t_bool(X5195) )
      & ( X5195 != X5194
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5195),X5194))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5194),X5195))
        | ~ is_fun1568535512t_bool(X5194)
        | ~ is_fun1568535512t_bool(X5195) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_333_order__antisym__conv])])]) ).

fof(i_0_2148,plain,
    ! [X5054,X5055] :
      ( ~ is_fun1568535512t_bool(X5054)
      | ~ is_fun1568535512t_bool(X5055)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5054),X5055))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5055),X5054))
      | X5054 = X5055 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_283_order__antisym])]) ).

fof(i_0_2149,plain,
    ! [X5004,X5005] :
      ( ~ is_fun1568535512t_bool(X5004)
      | ~ is_fun1568535512t_bool(X5005)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5004),X5005))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5005),X5004))
      | X5005 = X5004 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_263_xt1_I5_J])]) ).

fof(i_0_2150,plain,
    ! [X5260,X5261] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5260),X5261))
        | X5260 != X5261
        | ~ is_fun2093718614t_bool(X5260)
        | ~ is_fun2093718614t_bool(X5261) )
      & ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5261),X5260))
        | X5260 != X5261
        | ~ is_fun2093718614t_bool(X5260)
        | ~ is_fun2093718614t_bool(X5261) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5260),X5261))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5261),X5260))
        | X5260 = X5261
        | ~ is_fun2093718614t_bool(X5260)
        | ~ is_fun2093718614t_bool(X5261) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_362_order__eq__iff])])]) ).

fof(i_0_2151,plain,
    ! [X5196,X5197] :
      ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5197),X5196))
        | X5197 = X5196
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5196),X5197))
        | ~ is_fun2093718614t_bool(X5196)
        | ~ is_fun2093718614t_bool(X5197) )
      & ( X5197 != X5196
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5197),X5196))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5196),X5197))
        | ~ is_fun2093718614t_bool(X5196)
        | ~ is_fun2093718614t_bool(X5197) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_334_order__antisym__conv])])]) ).

fof(i_0_2152,plain,
    ! [X5056,X5057] :
      ( ~ is_fun2093718614t_bool(X5056)
      | ~ is_fun2093718614t_bool(X5057)
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5056),X5057))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5057),X5056))
      | X5056 = X5057 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_284_order__antisym])]) ).

fof(i_0_2153,plain,
    ! [X5006,X5007] :
      ( ~ is_fun2093718614t_bool(X5006)
      | ~ is_fun2093718614t_bool(X5007)
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5006),X5007))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5007),X5006))
      | X5007 = X5006 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_xt1_I5_J])]) ).

fof(i_0_2154,plain,
    ! [X7436,X7437] :
      ( ~ is_fun1236654035i_bool(X7436)
      | ~ is_fun1236654035i_bool(X7437)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7436),X7437))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7437),X7436))
      | X7436 = X7437 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_909_equalityI])]) ).

fof(i_0_2155,plain,
    ! [X5256,X5257] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5256),X5257))
        | X5256 != X5257
        | ~ is_fun1236654035i_bool(X5256)
        | ~ is_fun1236654035i_bool(X5257) )
      & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5257),X5256))
        | X5256 != X5257
        | ~ is_fun1236654035i_bool(X5256)
        | ~ is_fun1236654035i_bool(X5257) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5256),X5257))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5257),X5256))
        | X5256 = X5257
        | ~ is_fun1236654035i_bool(X5256)
        | ~ is_fun1236654035i_bool(X5257) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_360_order__eq__iff])])]) ).

fof(i_0_2156,plain,
    ! [X5192,X5193] :
      ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5193),X5192))
        | X5193 = X5192
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5192),X5193))
        | ~ is_fun1236654035i_bool(X5192)
        | ~ is_fun1236654035i_bool(X5193) )
      & ( X5193 != X5192
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5193),X5192))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5192),X5193))
        | ~ is_fun1236654035i_bool(X5192)
        | ~ is_fun1236654035i_bool(X5193) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_332_order__antisym__conv])])]) ).

fof(i_0_2157,plain,
    ! [X5052,X5053] :
      ( ~ is_fun1236654035i_bool(X5052)
      | ~ is_fun1236654035i_bool(X5053)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5052),X5053))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5053),X5052))
      | X5052 = X5053 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_282_order__antisym])]) ).

fof(i_0_2158,plain,
    ! [X5002,X5003] :
      ( ~ is_fun1236654035i_bool(X5002)
      | ~ is_fun1236654035i_bool(X5003)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5002),X5003))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5003),X5002))
      | X5003 = X5002 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_262_xt1_I5_J])]) ).

fof(i_0_2159,plain,
    ! [X7434,X7435] :
      ( ~ is_fun961089132t_bool(X7434)
      | ~ is_fun961089132t_bool(X7435)
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7434),X7435))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7435),X7434))
      | X7434 = X7435 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_908_equalityI])]) ).

fof(i_0_2160,plain,
    ! [X5252,X5253] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5252),X5253))
        | X5252 != X5253
        | ~ is_fun961089132t_bool(X5252)
        | ~ is_fun961089132t_bool(X5253) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5253),X5252))
        | X5252 != X5253
        | ~ is_fun961089132t_bool(X5252)
        | ~ is_fun961089132t_bool(X5253) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5252),X5253))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5253),X5252))
        | X5252 = X5253
        | ~ is_fun961089132t_bool(X5252)
        | ~ is_fun961089132t_bool(X5253) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_358_order__eq__iff])])]) ).

fof(i_0_2161,plain,
    ! [X5188,X5189] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5189),X5188))
        | X5189 = X5188
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5188),X5189))
        | ~ is_fun961089132t_bool(X5188)
        | ~ is_fun961089132t_bool(X5189) )
      & ( X5189 != X5188
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5189),X5188))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5188),X5189))
        | ~ is_fun961089132t_bool(X5188)
        | ~ is_fun961089132t_bool(X5189) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_330_order__antisym__conv])])]) ).

fof(i_0_2162,plain,
    ! [X5048,X5049] :
      ( ~ is_fun961089132t_bool(X5048)
      | ~ is_fun961089132t_bool(X5049)
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5048),X5049))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5049),X5048))
      | X5048 = X5049 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_280_order__antisym])]) ).

fof(i_0_2163,plain,
    ! [X4998,X4999] :
      ( ~ is_fun961089132t_bool(X4998)
      | ~ is_fun961089132t_bool(X4999)
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4998),X4999))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4999),X4998))
      | X4999 = X4998 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_260_xt1_I5_J])]) ).

fof(i_0_2164,plain,
    ! [X7432,X7433] :
      ( ~ is_fun288122577l_bool(X7432)
      | ~ is_fun288122577l_bool(X7433)
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7432),X7433))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7433),X7432))
      | X7432 = X7433 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_907_equalityI])]) ).

fof(i_0_2165,plain,
    ! [X5250,X5251] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5250),X5251))
        | X5250 != X5251
        | ~ is_fun288122577l_bool(X5250)
        | ~ is_fun288122577l_bool(X5251) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5251),X5250))
        | X5250 != X5251
        | ~ is_fun288122577l_bool(X5250)
        | ~ is_fun288122577l_bool(X5251) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5250),X5251))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5251),X5250))
        | X5250 = X5251
        | ~ is_fun288122577l_bool(X5250)
        | ~ is_fun288122577l_bool(X5251) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_357_order__eq__iff])])]) ).

fof(i_0_2166,plain,
    ! [X5186,X5187] :
      ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5187),X5186))
        | X5187 = X5186
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5186),X5187))
        | ~ is_fun288122577l_bool(X5186)
        | ~ is_fun288122577l_bool(X5187) )
      & ( X5187 != X5186
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5187),X5186))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5186),X5187))
        | ~ is_fun288122577l_bool(X5186)
        | ~ is_fun288122577l_bool(X5187) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_329_order__antisym__conv])])]) ).

fof(i_0_2167,plain,
    ! [X5046,X5047] :
      ( ~ is_fun288122577l_bool(X5046)
      | ~ is_fun288122577l_bool(X5047)
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5046),X5047))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5047),X5046))
      | X5046 = X5047 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_279_order__antisym])]) ).

fof(i_0_2168,plain,
    ! [X4996,X4997] :
      ( ~ is_fun288122577l_bool(X4996)
      | ~ is_fun288122577l_bool(X4997)
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4996),X4997))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4997),X4996))
      | X4997 = X4996 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_259_xt1_I5_J])]) ).

fof(i_0_2169,plain,
    ! [X7428,X7429] :
      ( ~ is_fun279392540l_bool(X7428)
      | ~ is_fun279392540l_bool(X7429)
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7428),X7429))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7429),X7428))
      | X7428 = X7429 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_905_equalityI])]) ).

fof(i_0_2170,plain,
    ! [X5246,X5247] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5246),X5247))
        | X5246 != X5247
        | ~ is_fun279392540l_bool(X5246)
        | ~ is_fun279392540l_bool(X5247) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5247),X5246))
        | X5246 != X5247
        | ~ is_fun279392540l_bool(X5246)
        | ~ is_fun279392540l_bool(X5247) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5246),X5247))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5247),X5246))
        | X5246 = X5247
        | ~ is_fun279392540l_bool(X5246)
        | ~ is_fun279392540l_bool(X5247) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_355_order__eq__iff])])]) ).

fof(i_0_2171,plain,
    ! [X5182,X5183] :
      ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5183),X5182))
        | X5183 = X5182
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5182),X5183))
        | ~ is_fun279392540l_bool(X5182)
        | ~ is_fun279392540l_bool(X5183) )
      & ( X5183 != X5182
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5183),X5182))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5182),X5183))
        | ~ is_fun279392540l_bool(X5182)
        | ~ is_fun279392540l_bool(X5183) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_327_order__antisym__conv])])]) ).

fof(i_0_2172,plain,
    ! [X5042,X5043] :
      ( ~ is_fun279392540l_bool(X5042)
      | ~ is_fun279392540l_bool(X5043)
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5042),X5043))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5043),X5042))
      | X5042 = X5043 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_277_order__antisym])]) ).

fof(i_0_2173,plain,
    ! [X4992,X4993] :
      ( ~ is_fun279392540l_bool(X4992)
      | ~ is_fun279392540l_bool(X4993)
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4992),X4993))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4993),X4992))
      | X4993 = X4992 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_257_xt1_I5_J])]) ).

fof(i_0_2174,plain,
    ! [X7430,X7431] :
      ( ~ is_fun158382675l_bool(X7430)
      | ~ is_fun158382675l_bool(X7431)
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7430),X7431))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7431),X7430))
      | X7430 = X7431 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_906_equalityI])]) ).

fof(i_0_2175,plain,
    ! [X5248,X5249] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5248),X5249))
        | X5248 != X5249
        | ~ is_fun158382675l_bool(X5248)
        | ~ is_fun158382675l_bool(X5249) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5249),X5248))
        | X5248 != X5249
        | ~ is_fun158382675l_bool(X5248)
        | ~ is_fun158382675l_bool(X5249) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5248),X5249))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5249),X5248))
        | X5248 = X5249
        | ~ is_fun158382675l_bool(X5248)
        | ~ is_fun158382675l_bool(X5249) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_356_order__eq__iff])])]) ).

fof(i_0_2176,plain,
    ! [X5184,X5185] :
      ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5185),X5184))
        | X5185 = X5184
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5184),X5185))
        | ~ is_fun158382675l_bool(X5184)
        | ~ is_fun158382675l_bool(X5185) )
      & ( X5185 != X5184
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5185),X5184))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5184),X5185))
        | ~ is_fun158382675l_bool(X5184)
        | ~ is_fun158382675l_bool(X5185) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_328_order__antisym__conv])])]) ).

fof(i_0_2177,plain,
    ! [X5044,X5045] :
      ( ~ is_fun158382675l_bool(X5044)
      | ~ is_fun158382675l_bool(X5045)
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5044),X5045))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5045),X5044))
      | X5044 = X5045 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_278_order__antisym])]) ).

fof(i_0_2178,plain,
    ! [X4994,X4995] :
      ( ~ is_fun158382675l_bool(X4994)
      | ~ is_fun158382675l_bool(X4995)
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4994),X4995))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4995),X4994))
      | X4995 = X4994 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_258_xt1_I5_J])]) ).

fof(i_0_2179,plain,
    ! [X5966,X5967,X5968] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5967),X5968))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5966),X5968))
      | hAPP_nat_nat(hilber195283148at_nat(X5968,X5967),hAPP_nat_nat(X5967,X5966)) = X5966 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_617_inv__into__f__f])]) ).

fof(i_0_2180,plain,
    ! [X5973,X5974,X5975,X5976] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5975),X5976))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5974),X5976))
      | hAPP_nat_nat(X5975,X5974) != X5973
      | hAPP_nat_nat(hilber195283148at_nat(X5976,X5975),X5973) = X5974 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_619_inv__into__f__eq])]) ).

fof(i_0_2181,plain,
    ! [X5254,X5255] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5255),X5254))
        | ~ hBOOL(X5255)
        | ~ hBOOL(X5254) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5254),X5255))
        | ~ hBOOL(X5255)
        | ~ hBOOL(X5254) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5255),X5254))
        | hBOOL(X5255)
        | hBOOL(X5254) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5254),X5255))
        | hBOOL(X5255)
        | hBOOL(X5254) )
      & ( ~ hBOOL(X5255)
        | hBOOL(X5254)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5255),X5254))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5254),X5255)) )
      & ( ~ hBOOL(X5254)
        | hBOOL(X5255)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5255),X5254))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5254),X5255)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_359_order__eq__iff])])]) ).

fof(i_0_2182,plain,
    ! [X5190,X5191] :
      ( ( ~ hBOOL(X5191)
        | hBOOL(X5190)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5191),X5190))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5190),X5191)) )
      & ( ~ hBOOL(X5190)
        | hBOOL(X5191)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5191),X5190))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5190),X5191)) )
      & ( ~ hBOOL(X5191)
        | ~ hBOOL(X5190)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5191),X5190))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5190),X5191)) )
      & ( hBOOL(X5191)
        | hBOOL(X5190)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5191),X5190))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5190),X5191)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_331_order__antisym__conv])])]) ).

fof(i_0_2183,plain,
    ! [X5050,X5051] :
      ( ( ~ hBOOL(X5050)
        | hBOOL(X5051)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5051),X5050))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5050),X5051)) )
      & ( ~ hBOOL(X5051)
        | hBOOL(X5050)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5051),X5050))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5050),X5051)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_281_order__antisym])])]) ).

fof(i_0_2184,plain,
    ! [X5000,X5001] :
      ( ( ~ hBOOL(X5001)
        | hBOOL(X5000)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5001),X5000))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5000),X5001)) )
      & ( ~ hBOOL(X5000)
        | hBOOL(X5001)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5001),X5000))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5000),X5001)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_261_xt1_I5_J])])]) ).

fof(i_0_2185,plain,
    ! [X6101,X6102] :
      ( ~ is_fun1217980910e_indi(X6101)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X6102),top_to1576102282i_bool))
      | hAPP_A1637648121di_nat(X6102,hAPP_n1951273283e_indi(X6101,esk72_2(X6101,X6102))) != esk72_2(X6101,X6102)
      | hilber693666498di_nat(top_to1576102282i_bool,X6102) = X6101 ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_651_inj__imp__inv__eq])])])])]) ).

fof(i_0_2186,plain,
    ! [X4678,X4679,X4680] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4679),X4680))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4680),X4679))
      | hBOOL(X4678) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_130_order__less__imp__triv])]) ).

fof(i_0_2187,plain,
    ! [X4675,X4676,X4677] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4676),X4677))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4677),X4676))
      | hBOOL(X4675) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_129_order__less__imp__triv])]) ).

fof(i_0_2188,plain,
    ! [X4681,X4682,X4683] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4682),X4683))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4683),X4682))
      | hBOOL(X4681) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_131_order__less__imp__triv])]) ).

fof(i_0_2189,plain,
    ! [X4684,X4685,X4686] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4685),X4686))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4686),X4685))
      | hBOOL(X4684) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_132_order__less__imp__triv])]) ).

fof(i_0_2190,plain,
    ! [X5450,X5451] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5450),X5451))
        | X5450 = X5451
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5450),X5451)) )
      & ( X5450 != X5451
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5450),X5451))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5450),X5451)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1433])])]) ).

fof(i_0_2191,plain,
    ! [X7993,X7994,X7995] : hAPP_nat_nat(times_times_nat(X7993),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7994),X7995)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X7993),X7994)),hAPP_nat_nat(times_times_nat(X7993),X7995)),
    inference(variable_rename,[status(thm)],[fact_1150_add__mult__distrib2]) ).

fof(i_0_2192,plain,
    ! [X6104,X6105] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X6105),top_top_fun_nat_bool))
      | hAPP_nat_nat(X6105,hAPP_nat_nat(X6104,esk73_2(X6104,X6105))) != esk73_2(X6104,X6105)
      | hilber195283148at_nat(top_top_fun_nat_bool,X6105) = X6104 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_652_inj__imp__inv__eq])])]) ).

fof(i_0_2193,plain,
    ! [X7604,X7605] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7604),X7605))
        | X7604 != X7605 )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7605),X7604))
        | X7604 != X7605 )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7604),X7605))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7605),X7604))
        | X7604 = X7605 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_974_set__eq__subset])])]) ).

fof(i_0_2194,plain,
    ! [X7440,X7441] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7440),X7441))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7441),X7440))
      | X7440 = X7441 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_911_equalityI])]) ).

fof(i_0_2195,plain,
    ! [X5264,X5265] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5264),X5265))
        | X5264 != X5265 )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5265),X5264))
        | X5264 != X5265 )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5264),X5265))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5265),X5264))
        | X5264 = X5265 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_364_order__eq__iff])])]) ).

fof(i_0_2196,plain,
    ! [X5200,X5201] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5201),X5200))
        | X5201 = X5200
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5200),X5201)) )
      & ( X5201 != X5200
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5201),X5200))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5200),X5201)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_336_order__antisym__conv])])]) ).

fof(i_0_2197,plain,
    ! [X5060,X5061] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5060),X5061))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5061),X5060))
      | X5060 = X5061 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_286_order__antisym])]) ).

fof(i_0_2198,plain,
    ! [X5010,X5011] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5010),X5011))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5011),X5010))
      | X5011 = X5010 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_266_xt1_I5_J])]) ).

fof(i_0_2199,plain,
    ! [X7652,X7653] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7652),X7653))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7653),X7652))
      | X7652 = X7653 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_997_le__antisym])]) ).

fof(i_0_2200,plain,
    ! [X5262,X5263] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5262),X5263))
        | X5262 != X5263 )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5263),X5262))
        | X5262 != X5263 )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5262),X5263))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5263),X5262))
        | X5262 = X5263 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_363_order__eq__iff])])]) ).

fof(i_0_2201,plain,
    ! [X5198,X5199] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5199),X5198))
        | X5199 = X5198
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5198),X5199)) )
      & ( X5199 != X5198
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5199),X5198))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5198),X5199)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_335_order__antisym__conv])])]) ).

fof(i_0_2202,plain,
    ! [X5058,X5059] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5058),X5059))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5059),X5058))
      | X5058 = X5059 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_285_order__antisym])]) ).

fof(i_0_2203,plain,
    ! [X5008,X5009] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5008),X5009))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5009),X5008))
      | X5009 = X5008 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_265_xt1_I5_J])]) ).

fof(i_0_2204,plain,
    ! [X7799,X7800] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk492_2(X7799,X7800)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7799),X7800)) )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7799),esk492_2(X7799,X7800)) = X7800
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7799),X7800)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1058_less__imp__add__positive])])])]) ).

fof(i_0_2205,plain,
    ! [X7851,X7852] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7851),X7852))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7851),hAPP_nat_nat(suc,X7852))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1088_le__SucI])]) ).

fof(i_0_2206,plain,
    ! [X7892,X7893] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7892),X7893))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7892),hAPP_nat_nat(suc,X7893))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1105_le__imp__less__Suc])]) ).

fof(i_0_2207,plain,
    ! [X7829,X7830] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7829),X7830))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7829),hAPP_nat_nat(suc,X7830))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1077_less__SucI])]) ).

fof(i_0_2208,plain,
    ! [X4713,X4714] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4713),X4714))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4714),X4713)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1434])]) ).

fof(i_0_2209,plain,
    ! [X4705,X4706] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4705),X4706))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4706),X4705)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1435])]) ).

fof(i_0_2210,plain,
    ! [X4669,X4670] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4669),X4670))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4670),X4669)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1436])]) ).

fof(i_0_2211,plain,
    ! [X4661,X4662] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4661),X4662))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4662),X4661)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1437])]) ).

fof(i_0_2212,plain,
    ! [X4581,X4582] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4581),X4582))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4582),X4581)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1438])]) ).

fof(i_0_2213,plain,
    ! [X4711,X4712] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4711),X4712))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4712),X4711)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1439])]) ).

fof(i_0_2214,plain,
    ! [X4703,X4704] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4703),X4704))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4704),X4703)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1440])]) ).

fof(i_0_2215,plain,
    ! [X4667,X4668] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4667),X4668))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4668),X4667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1441])]) ).

fof(i_0_2216,plain,
    ! [X4659,X4660] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4659),X4660))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4660),X4659)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1442])]) ).

fof(i_0_2217,plain,
    ! [X4579,X4580] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4579),X4580))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4580),X4579)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1443])]) ).

fof(i_0_2218,plain,
    ! [X4715,X4716] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4715),X4716))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4716),X4715)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1444])]) ).

fof(i_0_2219,plain,
    ! [X4707,X4708] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4707),X4708))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4708),X4707)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1445])]) ).

fof(i_0_2220,plain,
    ! [X4671,X4672] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4671),X4672))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4672),X4671)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1446])]) ).

fof(i_0_2221,plain,
    ! [X4663,X4664] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4663),X4664))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4664),X4663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1447])]) ).

fof(i_0_2222,plain,
    ! [X4583,X4584] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4583),X4584))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4584),X4583)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1448])]) ).

fof(i_0_2223,plain,
    ! [X5318,X5319] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5318),X5319))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5319),X5318)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5319),X5318))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5318),X5319)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1449])]) ).

fof(i_0_2224,plain,
    ! [X5428,X5429] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5428),X5429))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5429),X5428)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1450])]) ).

fof(i_0_2225,plain,
    ! [X5316,X5317] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5316),X5317))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5317),X5316)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5317),X5316))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5316),X5317)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1451])]) ).

fof(i_0_2226,plain,
    ! [X4733,X4734] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4733),X4734))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4734),X4733))
        | X4733 = X4734 )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4734),X4733))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4733),X4734)) )
      & ( X4733 != X4734
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4733),X4734)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1452])])]) ).

fof(i_0_2227,plain,
    ! [X4717,X4718] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4717),X4718))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4718),X4717)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1453])]) ).

fof(i_0_2228,plain,
    ! [X4709,X4710] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4709),X4710))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4710),X4709)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1454])]) ).

fof(i_0_2229,plain,
    ! [X4673,X4674] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4673),X4674))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4674),X4673)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1455])]) ).

fof(i_0_2230,plain,
    ! [X4665,X4666] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4665),X4666))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4666),X4665)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1456])]) ).

fof(i_0_2231,plain,
    ! [X4585,X4586] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4585),X4586))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4586),X4585)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1457])]) ).

fof(i_0_2232,plain,
    ! [X7627,X7628,X7629] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | X7628 = X7629
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7628),X7629)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | X7628 = X7629
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7628),X7629)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7628),X7629)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7628),X7629)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | X7628 = X7629
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | X7628 = X7629
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X7627,X7629),X7628)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_987_nat__less__cases])])]) ).

fof(i_0_2233,plain,
    ! [X6453,X6454,X6455] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X6454),X6455))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6453),X6455))
      | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X6454),X6453)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_727_subset__inj__on])]) ).

fof(i_0_2234,plain,
    ! [X6450,X6451,X6452] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X6451),X6452))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6450),X6452))
      | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X6451),X6450)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_726_subset__inj__on])]) ).

fof(i_0_2235,plain,
    ! [X7695,X7696] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7695),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7695),X7696))),
    inference(variable_rename,[status(thm)],[fact_1014_le__add1]) ).

fof(i_0_2236,plain,
    ! [X7693,X7694] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7693),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7694),X7693))),
    inference(variable_rename,[status(thm)],[fact_1013_le__add2]) ).

fof(i_0_2237,plain,
    ! [X7632,X7633,X7634] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7632),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7633),X7634)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7633),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7632),X7634)),
    inference(variable_rename,[status(thm)],[fact_989_nat__add__left__commute]) ).

fof(i_0_2238,plain,
    ! [X6107] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6107),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6107),one_one_nat))),
    inference(variable_rename,[status(thm)],[fact_653_less__add__one]) ).

fof(i_0_2239,plain,
    ! [X7490,X7491] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7490),X7491))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7490),X7491))
        | X7490 = X7491
        | ~ is_fun961089132t_bool(X7490)
        | ~ is_fun961089132t_bool(X7491) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7490),X7491))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7490),X7491))
        | ~ is_fun961089132t_bool(X7490)
        | ~ is_fun961089132t_bool(X7491) )
      & ( X7490 != X7491
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7490),X7491))
        | ~ is_fun961089132t_bool(X7490)
        | ~ is_fun961089132t_bool(X7491) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_932_subset__iff__psubset__eq])])]) ).

fof(i_0_2240,plain,
    ! [X7476,X7477] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7476),X7477))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7476),X7477))
        | ~ is_fun961089132t_bool(X7476)
        | ~ is_fun961089132t_bool(X7477) )
      & ( X7476 != X7477
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7476),X7477))
        | ~ is_fun961089132t_bool(X7476)
        | ~ is_fun961089132t_bool(X7477) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7476),X7477))
        | X7476 = X7477
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7476),X7477))
        | ~ is_fun961089132t_bool(X7476)
        | ~ is_fun961089132t_bool(X7477) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_925_psubset__eq])])]) ).

fof(i_0_2241,plain,
    ! [X5502,X5503] :
      ( ~ is_fun961089132t_bool(X5502)
      | ~ is_fun961089132t_bool(X5503)
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5502),X5503))
      | X5503 = X5502
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5502),X5503)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_467_xt1_I11_J])]) ).

fof(i_0_2242,plain,
    ! [X5482,X5483] :
      ( ~ is_fun961089132t_bool(X5482)
      | ~ is_fun961089132t_bool(X5483)
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5482),X5483))
      | X5482 = X5483
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5482),X5483)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_457_order__le__neq__trans])]) ).

fof(i_0_2243,plain,
    ! [X5462,X5463] :
      ( ~ is_fun961089132t_bool(X5462)
      | ~ is_fun961089132t_bool(X5463)
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5462),X5463))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5462),X5463))
      | X5462 = X5463 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_order__le__imp__less__or__eq])]) ).

fof(i_0_2244,plain,
    ! [X5398,X5399] :
      ( ~ is_fun961089132t_bool(X5398)
      | ~ is_fun961089132t_bool(X5399)
      | X5398 = X5399
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5398),X5399))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5398),X5399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_415_order__neq__le__trans])]) ).

fof(i_0_2245,plain,
    ! [X5372,X5373] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5372),X5373))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5372),X5373))
        | X5372 = X5373
        | ~ is_fun961089132t_bool(X5372)
        | ~ is_fun961089132t_bool(X5373) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5372),X5373))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5372),X5373))
        | ~ is_fun961089132t_bool(X5372)
        | ~ is_fun961089132t_bool(X5373) )
      & ( X5372 != X5373
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5372),X5373))
        | ~ is_fun961089132t_bool(X5372)
        | ~ is_fun961089132t_bool(X5373) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_402_order__le__less])])]) ).

fof(i_0_2246,plain,
    ! [X5332,X5333] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5332),X5333))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5332),X5333))
        | ~ is_fun961089132t_bool(X5332)
        | ~ is_fun961089132t_bool(X5333) )
      & ( X5332 != X5333
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5332),X5333))
        | ~ is_fun961089132t_bool(X5332)
        | ~ is_fun961089132t_bool(X5333) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5332),X5333))
        | X5332 = X5333
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5332),X5333))
        | ~ is_fun961089132t_bool(X5332)
        | ~ is_fun961089132t_bool(X5333) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_382_order__less__le])])]) ).

fof(i_0_2247,plain,
    ! [X5418,X5419] :
      ( ~ is_fun961089132t_bool(X5418)
      | ~ is_fun961089132t_bool(X5419)
      | X5418 = X5419
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5419),X5418))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5419),X5418)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_425_xt1_I12_J])]) ).

fof(i_0_2248,plain,
    ! [X7484,X7485] :
      ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7484),X7485))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7484),X7485))
        | X7484 = X7485
        | ~ is_fun279392540l_bool(X7484)
        | ~ is_fun279392540l_bool(X7485) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7484),X7485))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7484),X7485))
        | ~ is_fun279392540l_bool(X7484)
        | ~ is_fun279392540l_bool(X7485) )
      & ( X7484 != X7485
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7484),X7485))
        | ~ is_fun279392540l_bool(X7484)
        | ~ is_fun279392540l_bool(X7485) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_929_subset__iff__psubset__eq])])]) ).

fof(i_0_2249,plain,
    ! [X7470,X7471] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7470),X7471))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7470),X7471))
        | ~ is_fun279392540l_bool(X7470)
        | ~ is_fun279392540l_bool(X7471) )
      & ( X7470 != X7471
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7470),X7471))
        | ~ is_fun279392540l_bool(X7470)
        | ~ is_fun279392540l_bool(X7471) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7470),X7471))
        | X7470 = X7471
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7470),X7471))
        | ~ is_fun279392540l_bool(X7470)
        | ~ is_fun279392540l_bool(X7471) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_922_psubset__eq])])]) ).

fof(i_0_2250,plain,
    ! [X5496,X5497] :
      ( ~ is_fun279392540l_bool(X5496)
      | ~ is_fun279392540l_bool(X5497)
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5496),X5497))
      | X5497 = X5496
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5496),X5497)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_464_xt1_I11_J])]) ).

fof(i_0_2251,plain,
    ! [X5476,X5477] :
      ( ~ is_fun279392540l_bool(X5476)
      | ~ is_fun279392540l_bool(X5477)
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5476),X5477))
      | X5476 = X5477
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5476),X5477)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_454_order__le__neq__trans])]) ).

fof(i_0_2252,plain,
    ! [X5456,X5457] :
      ( ~ is_fun279392540l_bool(X5456)
      | ~ is_fun279392540l_bool(X5457)
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5456),X5457))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5456),X5457))
      | X5456 = X5457 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_444_order__le__imp__less__or__eq])]) ).

fof(i_0_2253,plain,
    ! [X5392,X5393] :
      ( ~ is_fun279392540l_bool(X5392)
      | ~ is_fun279392540l_bool(X5393)
      | X5392 = X5393
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5392),X5393))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5392),X5393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_412_order__neq__le__trans])]) ).

fof(i_0_2254,plain,
    ! [X5366,X5367] :
      ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5366),X5367))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5366),X5367))
        | X5366 = X5367
        | ~ is_fun279392540l_bool(X5366)
        | ~ is_fun279392540l_bool(X5367) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5366),X5367))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5366),X5367))
        | ~ is_fun279392540l_bool(X5366)
        | ~ is_fun279392540l_bool(X5367) )
      & ( X5366 != X5367
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5366),X5367))
        | ~ is_fun279392540l_bool(X5366)
        | ~ is_fun279392540l_bool(X5367) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_399_order__le__less])])]) ).

fof(i_0_2255,plain,
    ! [X5326,X5327] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5326),X5327))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5326),X5327))
        | ~ is_fun279392540l_bool(X5326)
        | ~ is_fun279392540l_bool(X5327) )
      & ( X5326 != X5327
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5326),X5327))
        | ~ is_fun279392540l_bool(X5326)
        | ~ is_fun279392540l_bool(X5327) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5326),X5327))
        | X5326 = X5327
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5326),X5327))
        | ~ is_fun279392540l_bool(X5326)
        | ~ is_fun279392540l_bool(X5327) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_379_order__less__le])])]) ).

fof(i_0_2256,plain,
    ! [X5412,X5413] :
      ( ~ is_fun279392540l_bool(X5412)
      | ~ is_fun279392540l_bool(X5413)
      | X5412 = X5413
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5413),X5412))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5413),X5412)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_422_xt1_I12_J])]) ).

fof(i_0_2257,plain,
    ! [X7486,X7487] :
      ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7486),X7487))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7486),X7487))
        | X7486 = X7487
        | ~ is_fun158382675l_bool(X7486)
        | ~ is_fun158382675l_bool(X7487) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7486),X7487))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7486),X7487))
        | ~ is_fun158382675l_bool(X7486)
        | ~ is_fun158382675l_bool(X7487) )
      & ( X7486 != X7487
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7486),X7487))
        | ~ is_fun158382675l_bool(X7486)
        | ~ is_fun158382675l_bool(X7487) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_930_subset__iff__psubset__eq])])]) ).

fof(i_0_2258,plain,
    ! [X7472,X7473] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7472),X7473))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7472),X7473))
        | ~ is_fun158382675l_bool(X7472)
        | ~ is_fun158382675l_bool(X7473) )
      & ( X7472 != X7473
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7472),X7473))
        | ~ is_fun158382675l_bool(X7472)
        | ~ is_fun158382675l_bool(X7473) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7472),X7473))
        | X7472 = X7473
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7472),X7473))
        | ~ is_fun158382675l_bool(X7472)
        | ~ is_fun158382675l_bool(X7473) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_923_psubset__eq])])]) ).

fof(i_0_2259,plain,
    ! [X5498,X5499] :
      ( ~ is_fun158382675l_bool(X5498)
      | ~ is_fun158382675l_bool(X5499)
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5498),X5499))
      | X5499 = X5498
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5498),X5499)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_465_xt1_I11_J])]) ).

fof(i_0_2260,plain,
    ! [X5478,X5479] :
      ( ~ is_fun158382675l_bool(X5478)
      | ~ is_fun158382675l_bool(X5479)
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5478),X5479))
      | X5478 = X5479
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5478),X5479)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_455_order__le__neq__trans])]) ).

fof(i_0_2261,plain,
    ! [X5458,X5459] :
      ( ~ is_fun158382675l_bool(X5458)
      | ~ is_fun158382675l_bool(X5459)
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5458),X5459))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5458),X5459))
      | X5458 = X5459 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_445_order__le__imp__less__or__eq])]) ).

fof(i_0_2262,plain,
    ! [X5394,X5395] :
      ( ~ is_fun158382675l_bool(X5394)
      | ~ is_fun158382675l_bool(X5395)
      | X5394 = X5395
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5394),X5395))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5394),X5395)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_413_order__neq__le__trans])]) ).

fof(i_0_2263,plain,
    ! [X5368,X5369] :
      ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5368),X5369))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5368),X5369))
        | X5368 = X5369
        | ~ is_fun158382675l_bool(X5368)
        | ~ is_fun158382675l_bool(X5369) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5368),X5369))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5368),X5369))
        | ~ is_fun158382675l_bool(X5368)
        | ~ is_fun158382675l_bool(X5369) )
      & ( X5368 != X5369
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5368),X5369))
        | ~ is_fun158382675l_bool(X5368)
        | ~ is_fun158382675l_bool(X5369) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_400_order__le__less])])]) ).

fof(i_0_2264,plain,
    ! [X5328,X5329] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5328),X5329))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5328),X5329))
        | ~ is_fun158382675l_bool(X5328)
        | ~ is_fun158382675l_bool(X5329) )
      & ( X5328 != X5329
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5328),X5329))
        | ~ is_fun158382675l_bool(X5328)
        | ~ is_fun158382675l_bool(X5329) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5328),X5329))
        | X5328 = X5329
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5328),X5329))
        | ~ is_fun158382675l_bool(X5328)
        | ~ is_fun158382675l_bool(X5329) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_380_order__less__le])])]) ).

fof(i_0_2265,plain,
    ! [X5414,X5415] :
      ( ~ is_fun158382675l_bool(X5414)
      | ~ is_fun158382675l_bool(X5415)
      | X5414 = X5415
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5415),X5414))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5415),X5414)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_423_xt1_I12_J])]) ).

fof(i_0_2266,plain,
    ! [X7488,X7489] :
      ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7488),X7489))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7488),X7489))
        | X7488 = X7489
        | ~ is_fun288122577l_bool(X7488)
        | ~ is_fun288122577l_bool(X7489) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7488),X7489))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7488),X7489))
        | ~ is_fun288122577l_bool(X7488)
        | ~ is_fun288122577l_bool(X7489) )
      & ( X7488 != X7489
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7488),X7489))
        | ~ is_fun288122577l_bool(X7488)
        | ~ is_fun288122577l_bool(X7489) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_931_subset__iff__psubset__eq])])]) ).

fof(i_0_2267,plain,
    ! [X7474,X7475] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7474),X7475))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7474),X7475))
        | ~ is_fun288122577l_bool(X7474)
        | ~ is_fun288122577l_bool(X7475) )
      & ( X7474 != X7475
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7474),X7475))
        | ~ is_fun288122577l_bool(X7474)
        | ~ is_fun288122577l_bool(X7475) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7474),X7475))
        | X7474 = X7475
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7474),X7475))
        | ~ is_fun288122577l_bool(X7474)
        | ~ is_fun288122577l_bool(X7475) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_924_psubset__eq])])]) ).

fof(i_0_2268,plain,
    ! [X5500,X5501] :
      ( ~ is_fun288122577l_bool(X5500)
      | ~ is_fun288122577l_bool(X5501)
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5500),X5501))
      | X5501 = X5500
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5500),X5501)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_466_xt1_I11_J])]) ).

fof(i_0_2269,plain,
    ! [X5480,X5481] :
      ( ~ is_fun288122577l_bool(X5480)
      | ~ is_fun288122577l_bool(X5481)
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5480),X5481))
      | X5480 = X5481
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5480),X5481)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_456_order__le__neq__trans])]) ).

fof(i_0_2270,plain,
    ! [X5460,X5461] :
      ( ~ is_fun288122577l_bool(X5460)
      | ~ is_fun288122577l_bool(X5461)
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5460),X5461))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5460),X5461))
      | X5460 = X5461 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_446_order__le__imp__less__or__eq])]) ).

fof(i_0_2271,plain,
    ! [X5396,X5397] :
      ( ~ is_fun288122577l_bool(X5396)
      | ~ is_fun288122577l_bool(X5397)
      | X5396 = X5397
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5396),X5397))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5396),X5397)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_414_order__neq__le__trans])]) ).

fof(i_0_2272,plain,
    ! [X5370,X5371] :
      ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5370),X5371))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5370),X5371))
        | X5370 = X5371
        | ~ is_fun288122577l_bool(X5370)
        | ~ is_fun288122577l_bool(X5371) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5370),X5371))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5370),X5371))
        | ~ is_fun288122577l_bool(X5370)
        | ~ is_fun288122577l_bool(X5371) )
      & ( X5370 != X5371
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5370),X5371))
        | ~ is_fun288122577l_bool(X5370)
        | ~ is_fun288122577l_bool(X5371) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_401_order__le__less])])]) ).

fof(i_0_2273,plain,
    ! [X5330,X5331] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5330),X5331))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5330),X5331))
        | ~ is_fun288122577l_bool(X5330)
        | ~ is_fun288122577l_bool(X5331) )
      & ( X5330 != X5331
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5330),X5331))
        | ~ is_fun288122577l_bool(X5330)
        | ~ is_fun288122577l_bool(X5331) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5330),X5331))
        | X5330 = X5331
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5330),X5331))
        | ~ is_fun288122577l_bool(X5330)
        | ~ is_fun288122577l_bool(X5331) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_381_order__less__le])])]) ).

fof(i_0_2274,plain,
    ! [X5416,X5417] :
      ( ~ is_fun288122577l_bool(X5416)
      | ~ is_fun288122577l_bool(X5417)
      | X5416 = X5417
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5417),X5416))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5417),X5416)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_424_xt1_I12_J])]) ).

fof(i_0_2275,plain,
    ! [X7480,X7481] :
      ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7480),X7481))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7480),X7481))
        | X7480 = X7481
        | ~ is_fun1568535512t_bool(X7480)
        | ~ is_fun1568535512t_bool(X7481) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7480),X7481))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7480),X7481))
        | ~ is_fun1568535512t_bool(X7480)
        | ~ is_fun1568535512t_bool(X7481) )
      & ( X7480 != X7481
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7480),X7481))
        | ~ is_fun1568535512t_bool(X7480)
        | ~ is_fun1568535512t_bool(X7481) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_927_subset__iff__psubset__eq])])]) ).

fof(i_0_2276,plain,
    ! [X7466,X7467] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7466),X7467))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7466),X7467))
        | ~ is_fun1568535512t_bool(X7466)
        | ~ is_fun1568535512t_bool(X7467) )
      & ( X7466 != X7467
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7466),X7467))
        | ~ is_fun1568535512t_bool(X7466)
        | ~ is_fun1568535512t_bool(X7467) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7466),X7467))
        | X7466 = X7467
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7466),X7467))
        | ~ is_fun1568535512t_bool(X7466)
        | ~ is_fun1568535512t_bool(X7467) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_920_psubset__eq])])]) ).

fof(i_0_2277,plain,
    ! [X5492,X5493] :
      ( ~ is_fun1568535512t_bool(X5492)
      | ~ is_fun1568535512t_bool(X5493)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5492),X5493))
      | X5493 = X5492
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5492),X5493)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_462_xt1_I11_J])]) ).

fof(i_0_2278,plain,
    ! [X5472,X5473] :
      ( ~ is_fun1568535512t_bool(X5472)
      | ~ is_fun1568535512t_bool(X5473)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5472),X5473))
      | X5472 = X5473
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5472),X5473)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_452_order__le__neq__trans])]) ).

fof(i_0_2279,plain,
    ! [X5452,X5453] :
      ( ~ is_fun1568535512t_bool(X5452)
      | ~ is_fun1568535512t_bool(X5453)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5452),X5453))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5452),X5453))
      | X5452 = X5453 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_442_order__le__imp__less__or__eq])]) ).

fof(i_0_2280,plain,
    ! [X5388,X5389] :
      ( ~ is_fun1568535512t_bool(X5388)
      | ~ is_fun1568535512t_bool(X5389)
      | X5388 = X5389
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5388),X5389))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5388),X5389)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_410_order__neq__le__trans])]) ).

fof(i_0_2281,plain,
    ! [X5362,X5363] :
      ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5362),X5363))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5362),X5363))
        | X5362 = X5363
        | ~ is_fun1568535512t_bool(X5362)
        | ~ is_fun1568535512t_bool(X5363) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5362),X5363))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5362),X5363))
        | ~ is_fun1568535512t_bool(X5362)
        | ~ is_fun1568535512t_bool(X5363) )
      & ( X5362 != X5363
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5362),X5363))
        | ~ is_fun1568535512t_bool(X5362)
        | ~ is_fun1568535512t_bool(X5363) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_397_order__le__less])])]) ).

fof(i_0_2282,plain,
    ! [X5322,X5323] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5322),X5323))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5322),X5323))
        | ~ is_fun1568535512t_bool(X5322)
        | ~ is_fun1568535512t_bool(X5323) )
      & ( X5322 != X5323
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5322),X5323))
        | ~ is_fun1568535512t_bool(X5322)
        | ~ is_fun1568535512t_bool(X5323) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5322),X5323))
        | X5322 = X5323
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5322),X5323))
        | ~ is_fun1568535512t_bool(X5322)
        | ~ is_fun1568535512t_bool(X5323) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_377_order__less__le])])]) ).

fof(i_0_2283,plain,
    ! [X5408,X5409] :
      ( ~ is_fun1568535512t_bool(X5408)
      | ~ is_fun1568535512t_bool(X5409)
      | X5408 = X5409
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5409),X5408))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5409),X5408)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_420_xt1_I12_J])]) ).

fof(i_0_2284,plain,
    ! [X7482,X7483] :
      ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7482),X7483))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7482),X7483))
        | X7482 = X7483
        | ~ is_fun1236654035i_bool(X7482)
        | ~ is_fun1236654035i_bool(X7483) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7482),X7483))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7482),X7483))
        | ~ is_fun1236654035i_bool(X7482)
        | ~ is_fun1236654035i_bool(X7483) )
      & ( X7482 != X7483
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7482),X7483))
        | ~ is_fun1236654035i_bool(X7482)
        | ~ is_fun1236654035i_bool(X7483) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_928_subset__iff__psubset__eq])])]) ).

fof(i_0_2285,plain,
    ! [X7468,X7469] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7468),X7469))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7468),X7469))
        | ~ is_fun1236654035i_bool(X7468)
        | ~ is_fun1236654035i_bool(X7469) )
      & ( X7468 != X7469
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7468),X7469))
        | ~ is_fun1236654035i_bool(X7468)
        | ~ is_fun1236654035i_bool(X7469) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7468),X7469))
        | X7468 = X7469
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7468),X7469))
        | ~ is_fun1236654035i_bool(X7468)
        | ~ is_fun1236654035i_bool(X7469) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_921_psubset__eq])])]) ).

fof(i_0_2286,plain,
    ! [X5494,X5495] :
      ( ~ is_fun1236654035i_bool(X5494)
      | ~ is_fun1236654035i_bool(X5495)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5494),X5495))
      | X5495 = X5494
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5494),X5495)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_463_xt1_I11_J])]) ).

fof(i_0_2287,plain,
    ! [X5474,X5475] :
      ( ~ is_fun1236654035i_bool(X5474)
      | ~ is_fun1236654035i_bool(X5475)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5474),X5475))
      | X5474 = X5475
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5474),X5475)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_453_order__le__neq__trans])]) ).

fof(i_0_2288,plain,
    ! [X5454,X5455] :
      ( ~ is_fun1236654035i_bool(X5454)
      | ~ is_fun1236654035i_bool(X5455)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5454),X5455))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5454),X5455))
      | X5454 = X5455 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_443_order__le__imp__less__or__eq])]) ).

fof(i_0_2289,plain,
    ! [X5390,X5391] :
      ( ~ is_fun1236654035i_bool(X5390)
      | ~ is_fun1236654035i_bool(X5391)
      | X5390 = X5391
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5390),X5391))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5390),X5391)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_411_order__neq__le__trans])]) ).

fof(i_0_2290,plain,
    ! [X5364,X5365] :
      ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5364),X5365))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5364),X5365))
        | X5364 = X5365
        | ~ is_fun1236654035i_bool(X5364)
        | ~ is_fun1236654035i_bool(X5365) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5364),X5365))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5364),X5365))
        | ~ is_fun1236654035i_bool(X5364)
        | ~ is_fun1236654035i_bool(X5365) )
      & ( X5364 != X5365
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5364),X5365))
        | ~ is_fun1236654035i_bool(X5364)
        | ~ is_fun1236654035i_bool(X5365) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_398_order__le__less])])]) ).

fof(i_0_2291,plain,
    ! [X5324,X5325] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5324),X5325))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5324),X5325))
        | ~ is_fun1236654035i_bool(X5324)
        | ~ is_fun1236654035i_bool(X5325) )
      & ( X5324 != X5325
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5324),X5325))
        | ~ is_fun1236654035i_bool(X5324)
        | ~ is_fun1236654035i_bool(X5325) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5324),X5325))
        | X5324 = X5325
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5324),X5325))
        | ~ is_fun1236654035i_bool(X5324)
        | ~ is_fun1236654035i_bool(X5325) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_378_order__less__le])])]) ).

fof(i_0_2292,plain,
    ! [X5410,X5411] :
      ( ~ is_fun1236654035i_bool(X5410)
      | ~ is_fun1236654035i_bool(X5411)
      | X5410 = X5411
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5411),X5410))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5411),X5410)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_421_xt1_I12_J])]) ).

fof(i_0_2293,plain,
    ! [X5506,X5507] :
      ( ~ is_fun2093718614t_bool(X5506)
      | ~ is_fun2093718614t_bool(X5507)
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5506),X5507))
      | X5507 = X5506
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5506),X5507)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_469_xt1_I11_J])]) ).

fof(i_0_2294,plain,
    ! [X5486,X5487] :
      ( ~ is_fun2093718614t_bool(X5486)
      | ~ is_fun2093718614t_bool(X5487)
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5486),X5487))
      | X5486 = X5487
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5486),X5487)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_459_order__le__neq__trans])]) ).

fof(i_0_2295,plain,
    ! [X5466,X5467] :
      ( ~ is_fun2093718614t_bool(X5466)
      | ~ is_fun2093718614t_bool(X5467)
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5466),X5467))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5466),X5467))
      | X5466 = X5467 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_449_order__le__imp__less__or__eq])]) ).

fof(i_0_2296,plain,
    ! [X5402,X5403] :
      ( ~ is_fun2093718614t_bool(X5402)
      | ~ is_fun2093718614t_bool(X5403)
      | X5402 = X5403
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5402),X5403))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5402),X5403)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_417_order__neq__le__trans])]) ).

fof(i_0_2297,plain,
    ! [X5376,X5377] :
      ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5376),X5377))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5376),X5377))
        | X5376 = X5377
        | ~ is_fun2093718614t_bool(X5376)
        | ~ is_fun2093718614t_bool(X5377) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5376),X5377))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5376),X5377))
        | ~ is_fun2093718614t_bool(X5376)
        | ~ is_fun2093718614t_bool(X5377) )
      & ( X5376 != X5377
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5376),X5377))
        | ~ is_fun2093718614t_bool(X5376)
        | ~ is_fun2093718614t_bool(X5377) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_404_order__le__less])])]) ).

fof(i_0_2298,plain,
    ! [X5336,X5337] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5336),X5337))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5336),X5337))
        | ~ is_fun2093718614t_bool(X5336)
        | ~ is_fun2093718614t_bool(X5337) )
      & ( X5336 != X5337
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5336),X5337))
        | ~ is_fun2093718614t_bool(X5336)
        | ~ is_fun2093718614t_bool(X5337) )
      & ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5336),X5337))
        | X5336 = X5337
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5336),X5337))
        | ~ is_fun2093718614t_bool(X5336)
        | ~ is_fun2093718614t_bool(X5337) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_384_order__less__le])])]) ).

fof(i_0_2299,plain,
    ! [X5422,X5423] :
      ( ~ is_fun2093718614t_bool(X5422)
      | ~ is_fun2093718614t_bool(X5423)
      | X5422 = X5423
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5423),X5422))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5423),X5422)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_427_xt1_I12_J])]) ).

fof(i_0_2300,plain,
    ! [X5164,X5165,X5166] :
      ( ( ~ hBOOL(X5166)
        | ~ hBOOL(X5165)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5165),X5164))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5166),X5164)) )
      & ( hBOOL(X5166)
        | hBOOL(X5165)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5165),X5164))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5166),X5164)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_321_ord__eq__le__trans])])]) ).

fof(i_0_2301,plain,
    ! [X5074,X5075,X5076] :
      ( ( ~ hBOOL(X5075)
        | ~ hBOOL(X5074)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5074),X5076))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5075),X5076)) )
      & ( hBOOL(X5075)
        | hBOOL(X5074)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5074),X5076))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5075),X5076)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_291_xt1_I4_J])])]) ).

fof(i_0_2302,plain,
    ! [X5134,X5135,X5136] :
      ( ( ~ hBOOL(X5136)
        | ~ hBOOL(X5135)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5134),X5135))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5134),X5136)) )
      & ( hBOOL(X5136)
        | hBOOL(X5135)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5134),X5135))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5134),X5136)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_311_xt1_I3_J])])]) ).

fof(i_0_2303,plain,
    ! [X5104,X5105,X5106] :
      ( ( ~ hBOOL(X5106)
        | ~ hBOOL(X5104)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5105),X5104))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5105),X5106)) )
      & ( hBOOL(X5106)
        | hBOOL(X5104)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5105),X5104))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5105),X5106)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_301_ord__le__eq__trans])])]) ).

fof(i_0_2304,plain,
    ! [X8110,X8111] :
      ( hAPP_nat_nat(X8111,zero_zero_nat) != zero_zero_nat
      | hAPP_f22106695ol_nat(big_co387207925at_nat(X8111),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),X8110)) = hAPP_f22106695ol_nat(big_co387207925at_nat(X8111),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X8110)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1199_setsum__shift__lb__Suc0__0])]) ).

fof(i_0_2305,plain,
    ! [X7996,X7997,X7998] :
      ( ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X7996)),X7997) != hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X7996)),X7998)
        | X7997 = X7998 )
      & ( X7997 != X7998
        | hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X7996)),X7997) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X7996)),X7998) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1151_Suc__mult__cancel1])]) ).

fof(i_0_2306,plain,
    ! [X5504,X5505] :
      ( ( ~ hBOOL(X5505)
        | hBOOL(X5504)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5504),X5505))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5504),X5505)) )
      & ( ~ hBOOL(X5504)
        | hBOOL(X5505)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5504),X5505))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5504),X5505)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_468_xt1_I11_J])])]) ).

fof(i_0_2307,plain,
    ! [X5484,X5485] :
      ( ( ~ hBOOL(X5484)
        | hBOOL(X5485)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5484),X5485))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5484),X5485)) )
      & ( ~ hBOOL(X5485)
        | hBOOL(X5484)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5484),X5485))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5484),X5485)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_458_order__le__neq__trans])])]) ).

fof(i_0_2308,plain,
    ! [X5464,X5465] :
      ( ( ~ hBOOL(X5464)
        | hBOOL(X5465)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5464),X5465))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5464),X5465)) )
      & ( ~ hBOOL(X5465)
        | hBOOL(X5464)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5464),X5465))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5464),X5465)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_448_order__le__imp__less__or__eq])])]) ).

fof(i_0_2309,plain,
    ! [X5420,X5421] :
      ( ( ~ hBOOL(X5421)
        | hBOOL(X5420)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5420),X5421))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5420),X5421)) )
      & ( ~ hBOOL(X5420)
        | hBOOL(X5421)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5420),X5421))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5420),X5421)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_426_xt1_I12_J])])]) ).

fof(i_0_2310,plain,
    ! [X5400,X5401] :
      ( ( ~ hBOOL(X5401)
        | hBOOL(X5400)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5401),X5400))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5401),X5400)) )
      & ( ~ hBOOL(X5400)
        | hBOOL(X5401)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5401),X5400))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5401),X5400)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_416_order__neq__le__trans])])]) ).

fof(i_0_2311,plain,
    ! [X5374,X5375] :
      ( ( ~ hBOOL(X5374)
        | hBOOL(X5375)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5374),X5375))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5374),X5375)) )
      & ( ~ hBOOL(X5375)
        | hBOOL(X5374)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5374),X5375))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5374),X5375)) )
      & ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5374),X5375))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5374),X5375)) )
      & ( ~ hBOOL(X5374)
        | ~ hBOOL(X5375)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5374),X5375)) )
      & ( hBOOL(X5374)
        | hBOOL(X5375)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5374),X5375)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_403_order__le__less])])]) ).

fof(i_0_2312,plain,
    ! [X5334,X5335] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5334),X5335))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5334),X5335)) )
      & ( ~ hBOOL(X5334)
        | ~ hBOOL(X5335)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5334),X5335)) )
      & ( hBOOL(X5334)
        | hBOOL(X5335)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5334),X5335)) )
      & ( ~ hBOOL(X5334)
        | hBOOL(X5335)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5334),X5335))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5334),X5335)) )
      & ( ~ hBOOL(X5335)
        | hBOOL(X5334)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5334),X5335))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5334),X5335)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_383_order__less__le])])]) ).

fof(i_0_2313,plain,
    ! [X7492,X7493] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7492),X7493))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7492),X7493))
        | X7492 = X7493 )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7492),X7493))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7492),X7493)) )
      & ( X7492 != X7493
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7492),X7493)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_933_subset__iff__psubset__eq])])]) ).

fof(i_0_2314,plain,
    ! [X7478,X7479] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7478),X7479))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7478),X7479)) )
      & ( X7478 != X7479
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7478),X7479)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7478),X7479))
        | X7478 = X7479
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7478),X7479)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_926_psubset__eq])])]) ).

fof(i_0_2315,plain,
    ! [X5508,X5509] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5508),X5509))
      | X5509 = X5508
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5508),X5509)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_470_xt1_I11_J])]) ).

fof(i_0_2316,plain,
    ! [X5488,X5489] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5488),X5489))
      | X5488 = X5489
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5488),X5489)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_460_order__le__neq__trans])]) ).

fof(i_0_2317,plain,
    ! [X5468,X5469] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5468),X5469))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5468),X5469))
      | X5468 = X5469 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_450_order__le__imp__less__or__eq])]) ).

fof(i_0_2318,plain,
    ! [X5404,X5405] :
      ( X5404 = X5405
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5404),X5405))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5404),X5405)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_418_order__neq__le__trans])]) ).

fof(i_0_2319,plain,
    ! [X5378,X5379] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5378),X5379))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5378),X5379))
        | X5378 = X5379 )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5378),X5379))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5378),X5379)) )
      & ( X5378 != X5379
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5378),X5379)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_405_order__le__less])])]) ).

fof(i_0_2320,plain,
    ! [X5338,X5339] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5338),X5339))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5338),X5339)) )
      & ( X5338 != X5339
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5338),X5339)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5338),X5339))
        | X5338 = X5339
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5338),X5339)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_385_order__less__le])])]) ).

fof(i_0_2321,plain,
    ! [X5424,X5425] :
      ( X5424 = X5425
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5425),X5424))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5425),X5424)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_428_xt1_I12_J])]) ).

fof(i_0_2322,plain,
    ! [X7689,X7690] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7689),X7690))
      | X7689 = X7690
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7689),X7690)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1011_le__neq__implies__less])]) ).

fof(i_0_2323,plain,
    ! [X7685,X7686] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7685),X7686))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7685),X7686))
        | X7685 = X7686 )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7685),X7686))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7685),X7686)) )
      & ( X7685 != X7686
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7685),X7686)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1009_le__eq__less__or__eq])])]) ).

fof(i_0_2324,plain,
    ! [X7683,X7684] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7683),X7684))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7683),X7684)) )
      & ( X7683 != X7684
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7683),X7684)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7683),X7684))
        | X7683 = X7684
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7683),X7684)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1008_nat__less__le])])]) ).

fof(i_0_2325,plain,
    ! [X5510,X5511] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5510),X5511))
      | X5511 = X5510
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5510),X5511)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_471_xt1_I11_J])]) ).

fof(i_0_2326,plain,
    ! [X5490,X5491] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5490),X5491))
      | X5490 = X5491
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5490),X5491)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_461_order__le__neq__trans])]) ).

fof(i_0_2327,plain,
    ! [X5470,X5471] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5470),X5471))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5470),X5471))
      | X5470 = X5471 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_451_order__le__imp__less__or__eq])]) ).

fof(i_0_2328,plain,
    ! [X5406,X5407] :
      ( X5406 = X5407
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5406),X5407))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5406),X5407)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_419_order__neq__le__trans])]) ).

fof(i_0_2329,plain,
    ! [X5386,X5387] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5386),X5387))
        | X5386 = X5387
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5386),X5387)) )
      & ( X5386 != X5387
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5386),X5387))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5386),X5387)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1458])])]) ).

fof(i_0_2330,plain,
    ! [X5380,X5381] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5380),X5381))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5380),X5381))
        | X5380 = X5381 )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5380),X5381))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5380),X5381)) )
      & ( X5380 != X5381
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5380),X5381)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_406_order__le__less])])]) ).

fof(i_0_2331,plain,
    ! [X5340,X5341] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5340),X5341))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5340),X5341)) )
      & ( X5340 != X5341
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5340),X5341)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5340),X5341))
        | X5340 = X5341
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5340),X5341)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_386_order__less__le])])]) ).

fof(i_0_2332,plain,
    ! [X5426,X5427] :
      ( X5426 = X5427
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5427),X5426))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5427),X5426)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_429_xt1_I12_J])]) ).

fof(i_0_2333,plain,
    ! [X7579,X7580,X7581] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7580),X7581))
      | ~ hBOOL(hAPP_nat_bool(X7580,X7579))
      | hBOOL(hAPP_nat_bool(X7581,X7579)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_965_predicate1D])]) ).

fof(i_0_2334,plain,
    ! [X7601,X7602,X7603] :
      ( ~ hBOOL(hAPP_nat_bool(X7602,X7603))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7602),X7601))
      | hBOOL(hAPP_nat_bool(X7601,X7603)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_973_rev__predicate1D])]) ).

fof(i_0_2335,plain,
    ! [X7504,X7505] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X7504),X7505))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X7504),X7505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_939_psubset__imp__subset])]) ).

fof(i_0_2336,plain,
    ! [X5440,X5441] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X5440),X5441))
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5440),X5441)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_436_order__less__imp__le])]) ).

fof(i_0_2337,plain,
    ! [X7498,X7499] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X7498),X7499))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X7498),X7499)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_936_psubset__imp__subset])]) ).

fof(i_0_2338,plain,
    ! [X5434,X5435] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X5434),X5435))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5434),X5435)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_433_order__less__imp__le])]) ).

fof(i_0_2339,plain,
    ! [X7500,X7501] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X7500),X7501))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X7500),X7501)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_937_psubset__imp__subset])]) ).

fof(i_0_2340,plain,
    ! [X5436,X5437] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X5436),X5437))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5436),X5437)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_434_order__less__imp__le])]) ).

fof(i_0_2341,plain,
    ! [X7502,X7503] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X7502),X7503))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X7502),X7503)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_938_psubset__imp__subset])]) ).

fof(i_0_2342,plain,
    ! [X5438,X5439] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X5438),X5439))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5438),X5439)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_435_order__less__imp__le])]) ).

fof(i_0_2343,plain,
    ! [X7494,X7495] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X7494),X7495))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X7494),X7495)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_934_psubset__imp__subset])]) ).

fof(i_0_2344,plain,
    ! [X5430,X5431] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X5430),X5431))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5430),X5431)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_431_order__less__imp__le])]) ).

fof(i_0_2345,plain,
    ! [X7506,X7507] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X7506),X7507))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7506),X7507)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_940_psubset__imp__subset])]) ).

fof(i_0_2346,plain,
    ! [X5446,X5447] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5446),X5447))
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5446),X5447)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_439_order__less__imp__le])]) ).

fof(i_0_2347,plain,
    ! [X7496,X7497] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X7496),X7497))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X7496),X7497)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_935_psubset__imp__subset])]) ).

fof(i_0_2348,plain,
    ! [X5432,X5433] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X5432),X5433))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5432),X5433)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_432_order__less__imp__le])]) ).

fof(i_0_2349,plain,
    ! [X5444,X5445] :
      ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X5444),X5445))
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5444),X5445)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_438_order__less__imp__le])]) ).

fof(i_0_2350,plain,
    ! [X7741,X7742] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7741),X7742))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7741),X7742)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1027_termination__basic__simps_I5_J])]) ).

fof(i_0_2351,plain,
    ! [X7691,X7692] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7691),X7692))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7691),X7692)) )
      & ( X7691 != X7692
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7691),X7692)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1012_less__or__eq__imp__le])])]) ).

fof(i_0_2352,plain,
    ! [X7687,X7688] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7687),X7688))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7687),X7688)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1010_less__imp__le__nat])]) ).

fof(i_0_2353,plain,
    ! [X5448,X5449] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5448),X5449))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5448),X5449)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_440_order__less__imp__le])]) ).

fof(i_0_2354,plain,
    ! [X5442,X5443] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X5442),X5443))
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5442),X5443)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_437_order__less__imp__le])]) ).

fof(i_0_2355,plain,
    ! [X7697,X7698,X7700,X7701,X7702] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7697),X7698))
        | X7698 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7697),esk478_2(X7697,X7698)) )
      & ( X7701 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7700),X7702)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7700),X7701)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1015_le__iff__add])])])])]) ).

fof(i_0_2356,plain,
    ! [X7865] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7865),hAPP_nat_nat(suc,zero_zero_nat)))
        | X7865 = zero_zero_nat )
      & ( X7865 != zero_zero_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7865),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1095_less__Suc0])]) ).

fof(i_0_2357,plain,
    ! [X7901] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),X7901))) = hAPP_nat_nat(suc,X7901),
    inference(variable_rename,[status(thm)],[fact_1111_card__Collect__le__nat]) ).

fof(i_0_2358,plain,
    ! [X8062,X8063,X8064] :
      ( ( hAPP_nat_nat(times_times_nat(X8064),X8062) != hAPP_nat_nat(times_times_nat(X8064),X8063)
        | X8062 = X8063
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8064)) )
      & ( X8062 != X8063
        | hAPP_nat_nat(times_times_nat(X8064),X8062) = hAPP_nat_nat(times_times_nat(X8064),X8063)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X8064)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1178_nat__mult__eq__cancel1])])]) ).

fof(i_0_2359,plain,
    ! [X7932,X7933] :
      ( ( hBOOL(hAPP_nat_bool(X7932,hAPP_nat_nat(suc,esk504_1(X7932))))
        | hBOOL(hAPP_nat_bool(X7932,zero_zero_nat))
        | ~ hBOOL(hAPP_nat_bool(X7932,X7933)) )
      & ( ~ hBOOL(hAPP_nat_bool(X7932,esk504_1(X7932)))
        | hBOOL(hAPP_nat_bool(X7932,zero_zero_nat))
        | ~ hBOOL(hAPP_nat_bool(X7932,X7933)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1125_zero__induct])])])])])]) ).

fof(i_0_2360,plain,
    ! [X7752] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X7752))) = X7752,
    inference(variable_rename,[status(thm)],[fact_1036_card__Collect__less__nat]) ).

fof(i_0_2361,plain,
    ! [X7843,X7844] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X7843)),X7844) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7843),X7844)),
    inference(variable_rename,[status(thm)],[fact_1084_add__Suc]) ).

fof(i_0_2362,plain,
    ! [X7620,X7621] :
      ( X7620 = X7621
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7620),X7621))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7621),X7620)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1459])]) ).

fof(i_0_2363,plain,
    ! [X7618,X7619] :
      ( ( X7618 = X7619
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7618),X7619))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7619),X7618)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7618),X7619))
        | X7618 != X7619 )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7619),X7618))
        | X7618 != X7619 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_982_nat__neq__iff])])]) ).

fof(i_0_2364,plain,
    ! [X4735,X4736] :
      ( ( X4735 = X4736
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4735),X4736))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4736),X4735)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4735),X4736))
        | X4735 != X4736 )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4736),X4735))
        | X4735 != X4736 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_157_linorder__neq__iff])])]) ).

fof(i_0_2365,plain,
    ! [X4731,X4732] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4731),X4732))
      | X4731 = X4732
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4732),X4731)) ),
    inference(variable_rename,[status(thm)],[fact_155_linorder__less__linear]) ).

fof(i_0_2366,plain,
    ! [X4729,X4730] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4730),X4729))
        | X4730 = X4729
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4729),X4730)) )
      & ( X4730 != X4729
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4730),X4729))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4729),X4730)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1460])])]) ).

fof(i_0_2367,plain,
    ! [X4727,X4728] :
      ( X4727 = X4728
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4727),X4728))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4728),X4727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1461])]) ).

fof(i_0_2368,plain,
    ! [X4577,X4578] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4577),X4578))
      | X4577 = X4578
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4578),X4577)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1462])]) ).

fof(i_0_2369,plain,
    ! [X8053,X8054,X8055] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X8053),X8054)),X8055) = hAPP_nat_nat(times_times_nat(X8053),hAPP_nat_nat(times_times_nat(X8054),X8055)),
    inference(variable_rename,[status(thm)],[fact_1175_nat__mult__assoc]) ).

fof(i_0_2370,plain,
    ! [X7645,X7646] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7645),X7646))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7646),X7645)) ),
    inference(variable_rename,[status(thm)],[fact_994_nat__le__linear]) ).

fof(i_0_2371,plain,
    ! [X5266,X5267] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5266),X5267))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5267),X5266)) ),
    inference(variable_rename,[status(thm)],[fact_365_linorder__linear]) ).

fof(i_0_2372,plain,
    ! [X4936,X4937] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4936),X4937))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4937),X4936)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1463])]) ).

fof(i_0_2373,plain,
    ! [X5382,X5383] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5382),X5383))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5383),X5382)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1464])]) ).

fof(i_0_2374,plain,
    ! [X5384,X5385] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5384),X5385))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5385),X5384)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1465])]) ).

fof(i_0_2375,plain,
    ! [X5320,X5321] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5320),X5321))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5321),X5320)) ),
    inference(variable_rename,[status(thm)],[fact_376_linorder__le__less__linear]) ).

fof(i_0_2376,plain,
    ! [X7972] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7972),hAPP_nat_nat(times_times_nat(X7972),X7972))),
    inference(variable_rename,[status(thm)],[fact_1140_le__square]) ).

fof(i_0_2377,plain,
    ! [X4747,X4748] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4747),X4748))
        | hBOOL(hAPP_P606313927t_bool(X4748,X4747)) )
      & ( ~ hBOOL(hAPP_P606313927t_bool(X4748,X4747))
        | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4747),X4748)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_165_mem__def])]) ).

fof(i_0_2378,plain,
    ! [X4753,X4754] :
      ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4753),X4754))
        | hBOOL(hAPP_f592646513l_bool(X4754,X4753)) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(X4754,X4753))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4753),X4754)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_168_mem__def])]) ).

fof(i_0_2379,plain,
    ! [X4751,X4752] :
      ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4751),X4752))
        | hBOOL(hAPP_f312250286l_bool(X4752,X4751)) )
      & ( ~ hBOOL(hAPP_f312250286l_bool(X4752,X4751))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4751),X4752)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_167_mem__def])]) ).

fof(i_0_2380,plain,
    ! [X4749,X4750] :
      ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4749),X4750))
        | hBOOL(hAPP_f965095724l_bool(X4750,X4749)) )
      & ( ~ hBOOL(hAPP_f965095724l_bool(X4750,X4749))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4749),X4750)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_166_mem__def])]) ).

fof(i_0_2381,plain,
    ! [X4745,X4746] :
      ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4745),X4746))
        | hBOOL(hAPP_P1676879539t_bool(X4746,X4745)) )
      & ( ~ hBOOL(hAPP_P1676879539t_bool(X4746,X4745))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4745),X4746)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_164_mem__def])]) ).

fof(i_0_2382,plain,
    ! [X4755,X4756] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4755),X4756))
        | hBOOL(hAPP_nat_bool(X4756,X4755)) )
      & ( ~ hBOOL(hAPP_nat_bool(X4756,X4755))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4755),X4756)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_169_mem__def])]) ).

fof(i_0_2383,plain,
    ! [X4743,X4744] :
      ( ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4743),X4744))
        | hBOOL(hAPP_bool_bool(X4744,X4743)) )
      & ( ~ hBOOL(hAPP_bool_bool(X4744,X4743))
        | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4743),X4744)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_163_mem__def])]) ).

fof(i_0_2384,plain,
    ! [X4741,X4742] :
      ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4741),X4742))
        | hBOOL(hAPP_A1785763630i_bool(X4742,X4741)) )
      & ( ~ hBOOL(hAPP_A1785763630i_bool(X4742,X4741))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4741),X4742)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_162_mem__def])]) ).

fof(i_0_2385,plain,
    ! [X4480,X4481,X4482,X4483] :
      ( ( X4480 = X4482
        | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4480),X4481) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4482),X4483)
        | ~ is_Arr1861959080le_alt(X4480)
        | ~ is_Arr1861959080le_alt(X4481)
        | ~ is_Arr1861959080le_alt(X4482)
        | ~ is_Arr1861959080le_alt(X4483) )
      & ( X4481 = X4483
        | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4480),X4481) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4482),X4483)
        | ~ is_Arr1861959080le_alt(X4480)
        | ~ is_Arr1861959080le_alt(X4481)
        | ~ is_Arr1861959080le_alt(X4482)
        | ~ is_Arr1861959080le_alt(X4483) )
      & ( X4480 != X4482
        | X4481 != X4483
        | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4480),X4481) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4482),X4483)
        | ~ is_Arr1861959080le_alt(X4480)
        | ~ is_Arr1861959080le_alt(X4481)
        | ~ is_Arr1861959080le_alt(X4482)
        | ~ is_Arr1861959080le_alt(X4483) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_Pair__eq])])]) ).

fof(i_0_2386,plain,
    ! [X4476,X4477,X4478,X4479] :
      ( ( X4476 = X4478
        | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4476),X4477) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4478),X4479)
        | ~ is_Arr1861959080le_alt(X4476)
        | ~ is_Arr1861959080le_alt(X4477)
        | ~ is_Arr1861959080le_alt(X4478)
        | ~ is_Arr1861959080le_alt(X4479) )
      & ( X4477 = X4479
        | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4476),X4477) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4478),X4479)
        | ~ is_Arr1861959080le_alt(X4476)
        | ~ is_Arr1861959080le_alt(X4477)
        | ~ is_Arr1861959080le_alt(X4478)
        | ~ is_Arr1861959080le_alt(X4479) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_Pair__inject])])]) ).

fof(i_0_2387,plain,
    ! [X8099,X8100] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(X8099),X8100)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,X8099)),hAPP_nat_nat(suc,X8100)),
    inference(variable_rename,[status(thm)],[fact_1193_image__Suc__atLeastAtMost]) ).

fof(i_0_2388,plain,
    ! [X7943,X7944] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(X7943),X7944)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,X7943)),hAPP_nat_nat(suc,X7944)),
    inference(variable_rename,[status(thm)],[fact_1131_image__Suc__atLeastLessThan]) ).

fof(i_0_2389,plain,
    ! [X7845,X7846] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7845),hAPP_nat_nat(suc,X7846)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7845),X7846)),
    inference(variable_rename,[status(thm)],[fact_1085_add__Suc__right]) ).

fof(i_0_2390,plain,
    ! [X7841,X7842] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X7841)),X7842) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7841),hAPP_nat_nat(suc,X7842)),
    inference(variable_rename,[status(thm)],[fact_1083_add__Suc__shift]) ).

fof(i_0_2391,plain,
    ! [X8030,X8031] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X8030)),X8031) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8031),hAPP_nat_nat(times_times_nat(X8030),X8031)),
    inference(variable_rename,[status(thm)],[fact_1165_mult__Suc]) ).

fof(i_0_2392,plain,
    ! [X8073] : hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,X8073)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,X8073)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(variable_rename,[status(thm)],[fact_1183_nat_Osize_I4_J]) ).

fof(i_0_2393,plain,
    ! [X8072] : hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,X8072)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,X8072)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(variable_rename,[status(thm)],[fact_1181_nat_Osize_I2_J]) ).

fof(i_0_2394,plain,
    ! [X4783,X4784] :
      ( ~ is_Arr43961803e_indi(X4783)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X4784),top_to1576102282i_bool))
      | hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,X4784),hAPP_A1637648121di_nat(X4784,X4783)) = X4783 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_188_inv__f__f])]) ).

fof(i_0_2395,plain,
    ! [X4216,X4217,X4218] :
      ( ~ is_fun961089132t_bool(X4216)
      | ~ is_Arr1861959080le_alt(X4217)
      | ~ is_Arr1861959080le_alt(X4218)
      | is_fun961089132t_bool(arrow_1539419881_below(X4216,X4217,X4218)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow])]) ).

fof(i_0_2396,plain,
    ! [X4777,X4778,X4779] :
      ( ~ is_Arr43961803e_indi(X4777)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X4779),top_to1576102282i_bool))
      | hAPP_A1637648121di_nat(X4779,X4777) != X4778
      | hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,X4779),X4778) = X4777 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_186_inv__f__eq])]) ).

fof(i_0_2397,plain,
    ! [X7915] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7915))
      | X7915 = hAPP_nat_nat(suc,esk498_1(X7915)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1117_gr0__implies__Suc])])]) ).

fof(i_0_2398,plain,
    ! [X7861,X7863,X7864] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7861))
        | X7861 = hAPP_nat_nat(suc,esk493_1(X7861)) )
      & ( X7863 != hAPP_nat_nat(suc,X7864)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7863)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1094_gr0__conv__Suc])])])])]) ).

fof(i_0_2399,plain,
    ! [X4547] :
      ( ( ~ hBOOL(X4547)
        | hBOOL(top_top_bool)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4547),top_top_bool)) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(X4547)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4547),top_top_bool)) )
      & ( ~ hBOOL(X4547)
        | ~ hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4547),top_top_bool)) )
      & ( hBOOL(X4547)
        | hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X4547),top_top_bool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_less__top])])]) ).

fof(i_0_2400,plain,
    ! [X4785,X4786] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X4786),top_top_fun_nat_bool))
      | hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,X4786),hAPP_nat_nat(X4786,X4785)) = X4785 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_189_inv__f__f])]) ).

fof(i_0_2401,plain,
    ! [X8272,X8273,X8274] : hAPP_A1102281708t_bool(hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,X8272),X8273),X8274) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(X8272,X8274),X8273),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_074]) ).

fof(i_0_2402,plain,
    ! [X8229,X8230,X8231] : hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,X8229),X8230),X8231) = hAPP_A1941004017t_bool(hAPP_A621939144t_bool(X8229,X8231),X8230),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065]) ).

fof(i_0_2403,plain,
    ! [X8219,X8220,X8221] : hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,X8219),X8220),X8221) = hAPP_f1663053423t_bool(hAPP_A572596845t_bool(X8219,X8221),X8220),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062]) ).

fof(i_0_2404,plain,
    ! [X8129,X8130,X8131] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,X8129),X8130),X8131) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X8129,X8131),X8130),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U]) ).

fof(i_0_2405,plain,
    ! [X8222,X8223,X8224] : hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,X8222),X8223),X8224) = hAPP_f592646513l_bool(hAPP_P229966473l_bool(X8222,X8224),X8223),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_]) ).

fof(i_0_2406,plain,
    ! [X8232,X8233,X8234] : hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,X8232),X8233),X8234) = hAPP_f1749234559l_bool(hAPP_f566237389l_bool(X8232,X8234),X8233),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp]) ).

fof(i_0_2407,plain,
    ! [X8284,X8285,X8286] : hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,X8284),X8285),X8286) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(X8284,X8286),X8285),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn]) ).

fof(i_0_2408,plain,
    ! [X8263,X8264,X8265] : hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,X8263),X8264),X8265) = hAPP_f777333846l_bool(hAPP_f461621971l_bool(X8263,X8265),X8264),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__]) ).

fof(i_0_2409,plain,
    ! [X8151,X8152,X8153] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,X8151),X8152),X8153) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X8151,X8153),X8152),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).

fof(i_0_2410,plain,
    ! [X8132,X8133,X8134] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,X8132),X8133),X8134) = hAPP_nat_bool(hAPP_n1699378549t_bool(X8132,X8134),X8133),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).

fof(i_0_2411,plain,
    ! [X8238,X8239,X8240] : hAPP_A1677245848t_bool(hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,X8238),X8239),X8240) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(X8238,X8240),X8239),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_066]) ).

fof(i_0_2412,plain,
    ! [X8212,X8213,X8214] : hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,X8212),X8213),X8214) = hAPP_A568203993t_bool(hAPP_A1625428400t_bool(X8212,X8214),X8213),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059]) ).

fof(i_0_2413,plain,
    ! [X8157,X8158,X8159] : hAPP_A1785763630i_bool(hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,X8157),X8158),X8159) = hAPP_nat_bool(hAPP_A2046586321t_bool(X8157,X8159),X8158),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000]) ).

fof(i_0_2414,plain,
    ! [X8199,X8200,X8201] : hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,X8199),X8200),X8201) = hAPP_f592646513l_bool(hAPP_A187815023l_bool(X8199,X8201),X8200),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t]) ).

fof(i_0_2415,plain,
    ! [X4548] :
      ( ( X4548 = top_to565915683t_bool
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4548),top_to565915683t_bool))
        | ~ is_fun961089132t_bool(X4548) )
      & ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X4548),top_to565915683t_bool))
        | X4548 != top_to565915683t_bool
        | ~ is_fun961089132t_bool(X4548) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_67_less__top])])]) ).

fof(i_0_2416,plain,
    ! [X4544] :
      ( ( X4544 = top_to1853035173l_bool
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4544),top_to1853035173l_bool))
        | ~ is_fun279392540l_bool(X4544) )
      & ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X4544),top_to1853035173l_bool))
        | X4544 != top_to1853035173l_bool
        | ~ is_fun279392540l_bool(X4544) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_less__top])])]) ).

fof(i_0_2417,plain,
    ! [X4546] :
      ( ( X4546 = top_to1714702858l_bool
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4546),top_to1714702858l_bool))
        | ~ is_fun158382675l_bool(X4546) )
      & ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X4546),top_to1714702858l_bool))
        | X4546 != top_to1714702858l_bool
        | ~ is_fun158382675l_bool(X4546) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_65_less__top])])]) ).

fof(i_0_2418,plain,
    ! [X4545] :
      ( ( X4545 = top_to522745736l_bool
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4545),top_to522745736l_bool))
        | ~ is_fun288122577l_bool(X4545) )
      & ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X4545),top_to522745736l_bool))
        | X4545 != top_to522745736l_bool
        | ~ is_fun288122577l_bool(X4545) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_64_less__top])])]) ).

fof(i_0_2419,plain,
    ! [X4551] :
      ( ( X4551 = top_to1257323279t_bool
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4551),top_to1257323279t_bool))
        | ~ is_fun1568535512t_bool(X4551) )
      & ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4551),top_to1257323279t_bool))
        | X4551 != top_to1257323279t_bool
        | ~ is_fun1568535512t_bool(X4551) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_70_less__top])])]) ).

fof(i_0_2420,plain,
    ! [X4549] :
      ( ( X4549 = top_to1576102282i_bool
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4549),top_to1576102282i_bool))
        | ~ is_fun1236654035i_bool(X4549) )
      & ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4549),top_to1576102282i_bool))
        | X4549 != top_to1576102282i_bool
        | ~ is_fun1236654035i_bool(X4549) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_less__top])])]) ).

fof(i_0_2421,plain,
    ! [X4780,X4781,X4782] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X4782),top_top_fun_nat_bool))
      | hAPP_nat_nat(X4782,X4780) != X4781
      | hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,X4782),X4781) = X4780 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_187_inv__f__eq])]) ).

fof(i_0_2422,plain,
    ! [X8115,X8116] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X8115),X8116))
      | hBOOL(X8115) ),
    inference(variable_rename,[status(thm)],[i_0_1466]) ).

fof(i_0_2423,plain,
    ! [X8117,X8118] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X8117),X8118))
      | hBOOL(X8118) ),
    inference(variable_rename,[status(thm)],[i_0_1467]) ).

fof(i_0_2424,plain,
    ! [X4721,X4722] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4721),X4722))
      | X4721 != X4722 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_150_less__imp__neq])]) ).

fof(i_0_2425,plain,
    ! [X4697,X4698] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4697),X4698))
      | X4697 != X4698 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_138_order__less__imp__not__eq])]) ).

fof(i_0_2426,plain,
    ! [X4689,X4690] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4689),X4690))
      | X4690 != X4689 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_134_order__less__imp__not__eq2])]) ).

fof(i_0_2427,plain,
    ! [X4719,X4720] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4719),X4720))
      | X4719 != X4720 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_less__imp__neq])]) ).

fof(i_0_2428,plain,
    ! [X4695,X4696] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4695),X4696))
      | X4695 != X4696 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_order__less__imp__not__eq])]) ).

fof(i_0_2429,plain,
    ! [X4687,X4688] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4687),X4688))
      | X4688 != X4687 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_133_order__less__imp__not__eq2])]) ).

fof(i_0_2430,plain,
    ! [X4723,X4724] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4723),X4724))
      | X4723 != X4724 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_151_less__imp__neq])]) ).

fof(i_0_2431,plain,
    ! [X4699,X4700] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4699),X4700))
      | X4699 != X4700 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_139_order__less__imp__not__eq])]) ).

fof(i_0_2432,plain,
    ! [X4691,X4692] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4691),X4692))
      | X4692 != X4691 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_135_order__less__imp__not__eq2])]) ).

fof(i_0_2433,plain,
    ! [X7625,X7626] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7625),X7626))
      | X7625 != X7626 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_986_less__not__refl3])]) ).

fof(i_0_2434,plain,
    ! [X7623,X7624] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7623),X7624))
      | X7624 != X7623 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_985_less__not__refl2])]) ).

fof(i_0_2435,plain,
    ! [X4725,X4726] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4725),X4726))
      | X4725 != X4726 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_152_less__imp__neq])]) ).

fof(i_0_2436,plain,
    ! [X4701,X4702] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4701),X4702))
      | X4701 != X4702 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_140_order__less__imp__not__eq])]) ).

fof(i_0_2437,plain,
    ! [X4693,X4694] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4693),X4694))
      | X4694 != X4693 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_order__less__imp__not__eq2])]) ).

fof(i_0_2438,plain,
    ! [X5957,X5958,X5959] :
      ( ~ is_Arr43961803e_indi(X5957)
      | ~ is_Arr43961803e_indi(X5958)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5959),top_to1576102282i_bool))
      | hAPP_A1637648121di_nat(X5959,X5957) != hAPP_A1637648121di_nat(X5959,X5958)
      | X5957 = X5958 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_614_injD])]) ).

fof(i_0_2439,plain,
    ! [X5951,X5952,X5953] :
      ( ( hAPP_A1637648121di_nat(X5953,X5951) != hAPP_A1637648121di_nat(X5953,X5952)
        | X5951 = X5952
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5953),top_to1576102282i_bool))
        | ~ is_Arr43961803e_indi(X5951)
        | ~ is_Arr43961803e_indi(X5952) )
      & ( X5951 != X5952
        | hAPP_A1637648121di_nat(X5953,X5951) = hAPP_A1637648121di_nat(X5953,X5952)
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X5953),top_to1576102282i_bool))
        | ~ is_Arr43961803e_indi(X5951)
        | ~ is_Arr43961803e_indi(X5952) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_612_inj__eq])])]) ).

fof(i_0_2440,plain,
    ! [X7778,X7779] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7778),X7779))
      | X7779 != zero_zero_nat ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1047_gr__implies__not0])]) ).

fof(i_0_2441,plain,
    ! [X8121,X8122] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X8121),X8122))
      | X8121 = X8122 ),
    inference(variable_rename,[status(thm)],[i_0_1468]) ).

fof(i_0_2442,plain,
    ! [X7802] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7802),hAPP_nat_nat(suc,X7802))),
    inference(variable_rename,[status(thm)],[fact_1059_lessI]) ).

fof(i_0_2443,plain,
    ! [X5653] :
      ( ( ~ hBOOL(X5653)
        | hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X5653)) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(X5653)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X5653)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_533_top__le])])]) ).

fof(i_0_2444,plain,
    ! [X5644] :
      ( ( ~ hBOOL(X5644)
        | hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X5644)) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(X5644)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X5644)) )
      & ( ~ hBOOL(X5644)
        | ~ hBOOL(top_top_bool)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X5644)) )
      & ( hBOOL(X5644)
        | hBOOL(top_top_bool)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X5644)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_524_top__unique])])]) ).

fof(i_0_2445,plain,
    ! [X4738] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4738),X4738)),
    inference(variable_rename,[status(thm)],[i_0_1469]) ).

fof(i_0_2446,plain,
    ! [X4737] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4737),X4737)),
    inference(variable_rename,[status(thm)],[i_0_1470]) ).

fof(i_0_2447,plain,
    ! [X4739] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4739),X4739)),
    inference(variable_rename,[status(thm)],[i_0_1471]) ).

fof(i_0_2448,plain,
    ! [X7622] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7622),X7622)),
    inference(variable_rename,[status(thm)],[i_0_1472]) ).

fof(i_0_2449,plain,
    ! [X7617] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7617),X7617)),
    inference(variable_rename,[status(thm)],[i_0_1473]) ).

fof(i_0_2450,plain,
    ! [X4740] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4740),X4740)),
    inference(variable_rename,[status(thm)],[i_0_1474]) ).

fof(i_0_2451,plain,
    ! [X5654] :
      ( ~ is_fun961089132t_bool(X5654)
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),X5654))
      | X5654 = top_to565915683t_bool ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_534_top__le])]) ).

fof(i_0_2452,plain,
    ! [X5645] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),X5645))
        | X5645 = top_to565915683t_bool
        | ~ is_fun961089132t_bool(X5645) )
      & ( X5645 != top_to565915683t_bool
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),X5645))
        | ~ is_fun961089132t_bool(X5645) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_525_top__unique])])]) ).

fof(i_0_2453,plain,
    ! [X5650] :
      ( ~ is_fun279392540l_bool(X5650)
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),X5650))
      | X5650 = top_to1853035173l_bool ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_530_top__le])]) ).

fof(i_0_2454,plain,
    ! [X5641] :
      ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),X5641))
        | X5641 = top_to1853035173l_bool
        | ~ is_fun279392540l_bool(X5641) )
      & ( X5641 != top_to1853035173l_bool
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),X5641))
        | ~ is_fun279392540l_bool(X5641) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_521_top__unique])])]) ).

fof(i_0_2455,plain,
    ! [X5652] :
      ( ~ is_fun158382675l_bool(X5652)
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),X5652))
      | X5652 = top_to1714702858l_bool ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_532_top__le])]) ).

fof(i_0_2456,plain,
    ! [X5643] :
      ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),X5643))
        | X5643 = top_to1714702858l_bool
        | ~ is_fun158382675l_bool(X5643) )
      & ( X5643 != top_to1714702858l_bool
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),X5643))
        | ~ is_fun158382675l_bool(X5643) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_523_top__unique])])]) ).

fof(i_0_2457,plain,
    ! [X5651] :
      ( ~ is_fun288122577l_bool(X5651)
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),X5651))
      | X5651 = top_to522745736l_bool ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_531_top__le])]) ).

fof(i_0_2458,plain,
    ! [X5642] :
      ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),X5642))
        | X5642 = top_to522745736l_bool
        | ~ is_fun288122577l_bool(X5642) )
      & ( X5642 != top_to522745736l_bool
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),X5642))
        | ~ is_fun288122577l_bool(X5642) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_522_top__unique])])]) ).

fof(i_0_2459,plain,
    ! [X5658] :
      ( ~ is_fun1568535512t_bool(X5658)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),X5658))
      | X5658 = top_to1257323279t_bool ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_538_top__le])]) ).

fof(i_0_2460,plain,
    ! [X5649] :
      ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),X5649))
        | X5649 = top_to1257323279t_bool
        | ~ is_fun1568535512t_bool(X5649) )
      & ( X5649 != top_to1257323279t_bool
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),X5649))
        | ~ is_fun1568535512t_bool(X5649) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_529_top__unique])])]) ).

fof(i_0_2461,plain,
    ! [X5656] :
      ( ~ is_fun1236654035i_bool(X5656)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),X5656))
      | X5656 = top_to1576102282i_bool ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_536_top__le])]) ).

fof(i_0_2462,plain,
    ! [X5647] :
      ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),X5647))
        | X5647 = top_to1576102282i_bool
        | ~ is_fun1236654035i_bool(X5647) )
      & ( X5647 != top_to1576102282i_bool
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),X5647))
        | ~ is_fun1236654035i_bool(X5647) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_527_top__unique])])]) ).

fof(i_0_2463,plain,
    ! [X5655] :
      ( ~ is_fun2093718614t_bool(X5655)
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),X5655))
      | X5655 = top_to178429151t_bool ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_535_top__le])]) ).

fof(i_0_2464,plain,
    ! [X5646] :
      ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),X5646))
        | X5646 = top_to178429151t_bool
        | ~ is_fun2093718614t_bool(X5646) )
      & ( X5646 != top_to178429151t_bool
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),X5646))
        | ~ is_fun2093718614t_bool(X5646) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_526_top__unique])])]) ).

fof(i_0_2465,plain,
    ! [X7641,X7642,X7643] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7641),X7642) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7643),X7642)
        | X7641 = X7643 )
      & ( X7641 != X7643
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7641),X7642) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7643),X7642) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_992_nat__add__right__cancel])]) ).

fof(i_0_2466,plain,
    ! [X6465,X6466,X6467] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6465),X6466) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6467),X6466)
        | X6465 = X6467 )
      & ( X6465 != X6467
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6465),X6466) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6467),X6466) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_731_add__right__cancel])]) ).

fof(i_0_2467,plain,
    ! [X6456,X6457,X6458] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6456),X6457) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6458),X6457)
      | X6456 = X6458 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_728_add__right__imp__eq])]) ).

fof(i_0_2468,plain,
    ! [X7638,X7639,X7640] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7638),X7639) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7638),X7640)
        | X7639 = X7640 )
      & ( X7639 != X7640
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7638),X7639) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7638),X7640) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_991_nat__add__left__cancel])]) ).

fof(i_0_2469,plain,
    ! [X6468,X6469,X6470] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6468),X6469) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6468),X6470)
        | X6469 = X6470 )
      & ( X6469 != X6470
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6468),X6469) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6468),X6470) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_732_add__left__cancel])]) ).

fof(i_0_2470,plain,
    ! [X6462,X6463,X6464] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6462),X6463) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6462),X6464)
      | X6463 = X6464 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_730_add__left__imp__eq])]) ).

fof(i_0_2471,plain,
    ! [X6459,X6460,X6461] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6459),X6460) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6459),X6461)
      | X6460 = X6461 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_729_add__imp__eq])]) ).

fof(i_0_2472,plain,
    ! [X8028,X8029] : hAPP_nat_nat(times_times_nat(X8028),hAPP_nat_nat(suc,X8029)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8028),hAPP_nat_nat(times_times_nat(X8028),X8029)),
    inference(variable_rename,[status(thm)],[fact_1164_mult__Suc__right]) ).

fof(i_0_2473,plain,
    ! [X8275,X8276,X8277] : hAPP_A1102281708t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(X8275),X8276),X8277) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(X8275,X8277),hAPP_A1677245848t_bool(X8276,X8277)),
    inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_075]) ).

fof(i_0_2474,plain,
    ! [X8135,X8136,X8137] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBS_nat_bool_bool(X8135),X8136),X8137) = hAPP_bool_bool(hAPP_n1006566506l_bool(X8135,X8137),hAPP_nat_bool(X8136,X8137)),
    inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).

fof(i_0_2475,plain,
    ! [X8241,X8242,X8243] : hAPP_A1677245848t_bool(hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(X8241),X8242),X8243) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(X8241,X8243),hAPP_A1677245848t_bool(X8242,X8243)),
    inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000]) ).

fof(i_0_2476,plain,
    ! [X4550] :
      ( ( X4550 = top_top_fun_nat_bool
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4550),top_top_fun_nat_bool)) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4550),top_top_fun_nat_bool))
        | X4550 != top_top_fun_nat_bool ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_69_less__top])]) ).

fof(i_0_2477,plain,
    ! [X7787] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7787),zero_zero_nat))
        | X7787 = zero_zero_nat )
      & ( X7787 != zero_zero_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7787),zero_zero_nat)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1053_le__0__eq])]) ).

fof(i_0_2478,plain,
    ! [X7805] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X7805))),
    inference(variable_rename,[status(thm)],[fact_1061_zero__less__Suc]) ).

fof(i_0_2479,plain,
    ! [X7777] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7777),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[i_0_1475]) ).

fof(i_0_2480,plain,
    ! [X7775] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7775),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[i_0_1476]) ).

fof(i_0_2481,plain,
    ! [X7773] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7773),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[i_0_1477]) ).

fof(i_0_2482,plain,
    ! [X7776] :
      ( ( X7776 = zero_zero_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7776)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7776))
        | X7776 != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1045_neq0__conv])]) ).

fof(i_0_2483,plain,
    ! [X5657] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),X5657))
      | X5657 = top_top_fun_nat_bool ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_537_top__le])]) ).

fof(i_0_2484,plain,
    ! [X5648] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),X5648))
        | X5648 = top_top_fun_nat_bool )
      & ( X5648 != top_top_fun_nat_bool
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),X5648)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_528_top__unique])]) ).

fof(i_0_2485,plain,
    ! [X4540] : ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),X4540)),
    inference(variable_rename,[status(thm)],[i_0_1478]) ).

fof(i_0_2486,plain,
    ! [X4536] : ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),X4536)),
    inference(variable_rename,[status(thm)],[i_0_1479]) ).

fof(i_0_2487,plain,
    ! [X4538] : ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),X4538)),
    inference(variable_rename,[status(thm)],[i_0_1480]) ).

fof(i_0_2488,plain,
    ! [X4537] : ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),X4537)),
    inference(variable_rename,[status(thm)],[i_0_1481]) ).

fof(i_0_2489,plain,
    ! [X4543] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),X4543)),
    inference(variable_rename,[status(thm)],[i_0_1482]) ).

fof(i_0_2490,plain,
    ! [X4542] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),X4542)),
    inference(variable_rename,[status(thm)],[i_0_1483]) ).

fof(i_0_2491,plain,
    ! [X4541] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),X4541)),
    inference(variable_rename,[status(thm)],[i_0_1484]) ).

fof(i_0_2492,plain,
    ! [X4539] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),X4539)),
    inference(variable_rename,[status(thm)],[i_0_1485]) ).

fof(i_0_2493,plain,
    ! [X5960,X5961,X5962] :
      ( ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5962),top_top_fun_nat_bool))
      | hAPP_nat_nat(X5962,X5960) != hAPP_nat_nat(X5962,X5961)
      | X5960 = X5961 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_615_injD])]) ).

fof(i_0_2494,plain,
    ! [X5954,X5955,X5956] :
      ( ( hAPP_nat_nat(X5956,X5954) != hAPP_nat_nat(X5956,X5955)
        | X5954 = X5955
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5956),top_top_fun_nat_bool)) )
      & ( X5954 != X5955
        | hAPP_nat_nat(X5956,X5954) = hAPP_nat_nat(X5956,X5955)
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X5956),top_top_fun_nat_bool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_613_inj__eq])])]) ).

fof(i_0_2495,plain,
    ! [X8079,X8080] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(X8079),X8080))),
    inference(variable_rename,[status(thm)],[fact_1189_finite__atLeastAtMost]) ).

fof(i_0_2496,plain,
    ! [X7968,X7969] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(X7968),X7969))),
    inference(variable_rename,[status(thm)],[fact_1138_finite__greaterThanLessThan]) ).

fof(i_0_2497,plain,
    ! [X7966,X7967] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(X7966),X7967))),
    inference(variable_rename,[status(thm)],[fact_1137_finite__greaterThanAtMost]) ).

fof(i_0_2498,plain,
    ! [X7938,X7939] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(X7938),X7939))),
    inference(variable_rename,[status(thm)],[fact_1128_finite__atLeastLessThan]) ).

fof(i_0_2499,plain,
    ! [X7872,X7873] :
      ( ( X7872 = zero_zero_nat
        | X7872 = hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7872),X7873) != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( X7873 = hAPP_nat_nat(suc,zero_zero_nat)
        | X7872 = hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7872),X7873) != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( X7872 = zero_zero_nat
        | X7873 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7872),X7873) != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( X7873 = hAPP_nat_nat(suc,zero_zero_nat)
        | X7873 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7872),X7873) != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( X7872 != hAPP_nat_nat(suc,zero_zero_nat)
        | X7873 != zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7872),X7873) = hAPP_nat_nat(suc,zero_zero_nat) )
      & ( X7872 != zero_zero_nat
        | X7873 != hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7872),X7873) = hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1097_add__is__1])])]) ).

fof(i_0_2500,plain,
    ! [X7874,X7875] :
      ( ( X7874 = zero_zero_nat
        | X7874 = hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7874),X7875) )
      & ( X7875 = hAPP_nat_nat(suc,zero_zero_nat)
        | X7874 = hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7874),X7875) )
      & ( X7874 = zero_zero_nat
        | X7875 = zero_zero_nat
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7874),X7875) )
      & ( X7875 = hAPP_nat_nat(suc,zero_zero_nat)
        | X7875 = zero_zero_nat
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7874),X7875) )
      & ( X7874 != hAPP_nat_nat(suc,zero_zero_nat)
        | X7875 != zero_zero_nat
        | hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7874),X7875) )
      & ( X7874 != zero_zero_nat
        | X7875 != hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7874),X7875) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1098_one__is__add])])]) ).

fof(i_0_2501,plain,
    ! [X8281,X8282,X8283] : hAPP_A1455239488t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(X8281),X8282),X8283) = hAPP_b1588041841t_bool(X8281,hAPP_A1785763630i_bool(X8282,X8283)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_]) ).

fof(i_0_2502,plain,
    ! [X8266,X8267,X8268] : hAPP_A1553574765l_bool(hAPP_f156764033l_bool(cOMBB_2112722489le_alt(X8266),X8267),X8268) = hAPP_f1539445765l_bool(X8266,hAPP_A1505516597le_alt(X8267,X8268)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__]) ).

fof(i_0_2503,plain,
    ! [X8269,X8270,X8271] : hAPP_A621939144t_bool(hAPP_f210227915t_bool(cOMBB_1769989562e_indi(X8269),X8270),X8271) = hAPP_f344580165t_bool(X8269,hAPP_A1677245848t_bool(X8270,X8271)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_073]) ).

fof(i_0_2504,plain,
    ! [X8278,X8279,X8280] : hAPP_A572596845t_bool(hAPP_f1324249913t_bool(cOMBB_747702273le_alt(X8278),X8279),X8280) = hAPP_f653880381t_bool(X8278,hAPP_A1553574765l_bool(X8279,X8280)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___076]) ).

fof(i_0_2505,plain,
    ! [X8252,X8253,X8254] : hAPP_A1625428400t_bool(hAPP_f721938099t_bool(cOMBB_2032668066e_indi(X8252),X8253),X8254) = hAPP_f393984045t_bool(X8252,hAPP_A1677245848t_bool(X8253,X8254)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp]) ).

fof(i_0_2506,plain,
    ! [X8154,X8155,X8156] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(X8154),X8155),X8156) = hAPP_b589554111l_bool(X8154,hAPP_nat_bool(X8155,X8156)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo]) ).

fof(i_0_2507,plain,
    ! [X8167,X8168,X8169] : hAPP_A2046586321t_bool(hAPP_f224734595t_bool(cOMBB_1883918730e_indi(X8167),X8168),X8169) = hAPP_n1699378549t_bool(X8167,hAPP_A1637648121di_nat(X8168,X8169)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__049]) ).

fof(i_0_2508,plain,
    ! [X8164,X8165,X8166] : hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(X8164),X8165),X8166) = hAPP_n215258509l_bool(X8164,hAPP_nat_nat(X8165,X8166)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO]) ).

fof(i_0_2509,plain,
    ! [X8148,X8149,X8150] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(X8148),X8149),X8150) = hAPP_n1699378549t_bool(X8148,hAPP_nat_nat(X8149,X8150)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).

fof(i_0_2510,plain,
    ! [X8235,X8236,X8237] : hAPP_A187815023l_bool(hAPP_f1539445765l_bool(cOMBB_84213429le_alt(X8235),X8236),X8237) = hAPP_P229966473l_bool(X8235,hAPP_A702847159le_alt(X8236,X8237)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_]) ).

fof(i_0_2511,plain,
    ! [X8113,X8114] :
      ( ~ hBOOL(X8114)
      | ~ hBOOL(X8113)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X8114),X8113)) ),
    inference(variable_rename,[status(thm)],[i_0_1486]) ).

fof(i_0_2512,plain,
    ! [X5234,X5235] :
      ( ( ~ hBOOL(X5235)
        | ~ hBOOL(X5234)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5235),X5234)) )
      & ( hBOOL(X5235)
        | hBOOL(X5234)
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5235),X5234)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_349_order__eq__refl])])]) ).

fof(i_0_2513,plain,
    ! [X8172,X8173] :
      ( ~ is_fun961089132t_bool(X8172)
      | hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),X8172),X8173) = X8172 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp])]) ).

fof(i_0_2514,plain,
    ! [X8174,X8175] :
      ( ~ is_fun961089132t_bool(X8175)
      | hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fFalse),X8174),X8175) = X8175 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp])]) ).

fof(i_0_2515,plain,
    ! [X8101,X8102] : hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,X8101)),X8102) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(X8101),X8102),
    inference(variable_rename,[status(thm)],[fact_1194_atLeastSucAtMost__greaterThanAtMost]) ).

fof(i_0_2516,plain,
    ! [X7970,X7971] : hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,X7970)),X7971) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(X7970),X7971),
    inference(variable_rename,[status(thm)],[fact_1139_atLeastSucLessThan__greaterThanLessThan]) ).

fof(i_0_2517,plain,
    ! [X6119] :
      ( ( hAPP_nat_nat(X6119,esk76_1(X6119)) = hAPP_nat_nat(X6119,esk77_1(X6119))
        | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X6119),top_top_fun_nat_bool)) )
      & ( esk76_1(X6119) != esk77_1(X6119)
        | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X6119),top_top_fun_nat_bool)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_657_injI])])])]) ).

fof(i_0_2518,plain,
    ! [X6116] :
      ( ( is_Arr43961803e_indi(esk74_1(X6116))
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X6116),top_to1576102282i_bool)) )
      & ( is_Arr43961803e_indi(esk75_1(X6116))
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X6116),top_to1576102282i_bool)) )
      & ( hAPP_A1637648121di_nat(X6116,esk74_1(X6116)) = hAPP_A1637648121di_nat(X6116,esk75_1(X6116))
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X6116),top_to1576102282i_bool)) )
      & ( esk74_1(X6116) != esk75_1(X6116)
        | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X6116),top_to1576102282i_bool)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_656_injI])])])]) ).

fof(i_0_2519,plain,
    ! [X5232,X5233] :
      ( X5232 != X5233
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5232),X5233)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_348_order__eq__refl])]) ).

fof(i_0_2520,plain,
    ! [X5226,X5227] :
      ( X5226 != X5227
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5226),X5227)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_345_order__eq__refl])]) ).

fof(i_0_2521,plain,
    ! [X5228,X5229] :
      ( X5228 != X5229
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5228),X5229)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_346_order__eq__refl])]) ).

fof(i_0_2522,plain,
    ! [X5230,X5231] :
      ( X5230 != X5231
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5230),X5231)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_347_order__eq__refl])]) ).

fof(i_0_2523,plain,
    ! [X5238,X5239] :
      ( X5238 != X5239
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5238),X5239)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_351_order__eq__refl])]) ).

fof(i_0_2524,plain,
    ! [X7599,X7600] :
      ( X7599 != X7600
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7599),X7600)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_972_equalityD1])]) ).

fof(i_0_2525,plain,
    ! [X7544,X7545] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7544),X7545))
        | X7544 != X7545 )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7545),X7544))
        | X7544 != X7545 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1487])])]) ).

fof(i_0_2526,plain,
    ! [X5244,X5245] :
      ( X5244 != X5245
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5244),X5245)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_354_order__eq__refl])]) ).

fof(i_0_2527,plain,
    ! [X7597,X7598] :
      ( X7597 != X7598
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7598),X7597)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_971_equalityD2])]) ).

fof(i_0_2528,plain,
    ! [X5236,X5237] :
      ( X5236 != X5237
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5236),X5237)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_350_order__eq__refl])]) ).

fof(i_0_2529,plain,
    ! [X5240,X5241] :
      ( X5240 != X5241
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5240),X5241)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_352_order__eq__refl])]) ).

fof(i_0_2530,plain,
    ! [X7647,X7648] :
      ( X7647 != X7648
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7647),X7648)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_995_eq__imp__le])]) ).

fof(i_0_2531,plain,
    ! [X5242,X5243] :
      ( X5242 != X5243
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5242),X5243)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_353_order__eq__refl])]) ).

fof(i_0_2532,plain,
    ! [X8123,X8124] :
      ( X8123 != X8124
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X8123),X8124)) ),
    inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__Nat__Onat_T]) ).

fof(i_0_2533,plain,
    ! [X4925] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4925),X4925)),
    inference(variable_rename,[status(thm)],[fact_229_order__refl]) ).

fof(i_0_2534,plain,
    ! [X4922] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4922),X4922)),
    inference(variable_rename,[status(thm)],[fact_226_order__refl]) ).

fof(i_0_2535,plain,
    ! [X4923] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4923),X4923)),
    inference(variable_rename,[status(thm)],[fact_227_order__refl]) ).

fof(i_0_2536,plain,
    ! [X4924] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4924),X4924)),
    inference(variable_rename,[status(thm)],[fact_228_order__refl]) ).

fof(i_0_2537,plain,
    ! [X4928] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4928),X4928)),
    inference(variable_rename,[status(thm)],[fact_232_order__refl]) ).

fof(i_0_2538,plain,
    ! [X7606] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7606),X7606)),
    inference(variable_rename,[status(thm)],[fact_975_subset__refl]) ).

fof(i_0_2539,plain,
    ! [X4931] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4931),X4931)),
    inference(variable_rename,[status(thm)],[fact_235_order__refl]) ).

fof(i_0_2540,plain,
    ! [X4927] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4927),X4927)),
    inference(variable_rename,[status(thm)],[fact_231_order__refl]) ).

fof(i_0_2541,plain,
    ! [X4929] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4929),X4929)),
    inference(variable_rename,[status(thm)],[fact_233_order__refl]) ).

fof(i_0_2542,plain,
    ! [X7644] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7644),X7644)),
    inference(variable_rename,[status(thm)],[fact_993_le__refl]) ).

fof(i_0_2543,plain,
    ! [X4930] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4930),X4930)),
    inference(variable_rename,[status(thm)],[fact_234_order__refl]) ).

fof(i_0_2544,plain,
    ! [X4926] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4926),X4926)),
    inference(variable_rename,[status(thm)],[fact_230_order__refl]) ).

fof(i_0_2545,plain,
    ! [X7630,X7631] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7630),X7631) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7631),X7630),
    inference(variable_rename,[status(thm)],[fact_988_nat__add__commute]) ).

fof(i_0_2546,plain,
    ! [X4524] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4524),top_to565915683t_bool)),
    inference(variable_rename,[status(thm)],[fact_43_iso__tuple__UNIV__I]) ).

fof(i_0_2547,plain,
    ! [X4516] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4516),top_to565915683t_bool)),
    inference(variable_rename,[status(thm)],[fact_35_UNIV__I]) ).

fof(i_0_2548,plain,
    ! [X6446] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X6446),top_to565915683t_bool)),
    inference(variable_rename,[status(thm)],[fact_722_subset__UNIV]) ).

fof(i_0_2549,plain,
    ! [X5636] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X5636),top_to565915683t_bool)),
    inference(variable_rename,[status(thm)],[fact_516_top__greatest]) ).

fof(i_0_2550,plain,
    ! [X6443] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X6443),top_to1853035173l_bool)),
    inference(variable_rename,[status(thm)],[fact_719_subset__UNIV]) ).

fof(i_0_2551,plain,
    ! [X5632] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X5632),top_to1853035173l_bool)),
    inference(variable_rename,[status(thm)],[fact_512_top__greatest]) ).

fof(i_0_2552,plain,
    ! [X4527] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4527),top_to1853035173l_bool)),
    inference(variable_rename,[status(thm)],[fact_46_iso__tuple__UNIV__I]) ).

fof(i_0_2553,plain,
    ! [X4519] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4519),top_to1853035173l_bool)),
    inference(variable_rename,[status(thm)],[fact_38_UNIV__I]) ).

fof(i_0_2554,plain,
    ! [X6445] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X6445),top_to1714702858l_bool)),
    inference(variable_rename,[status(thm)],[fact_721_subset__UNIV]) ).

fof(i_0_2555,plain,
    ! [X5634] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X5634),top_to1714702858l_bool)),
    inference(variable_rename,[status(thm)],[fact_514_top__greatest]) ).

fof(i_0_2556,plain,
    ! [X4526] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4526),top_to1714702858l_bool)),
    inference(variable_rename,[status(thm)],[fact_45_iso__tuple__UNIV__I]) ).

fof(i_0_2557,plain,
    ! [X4518] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4518),top_to1714702858l_bool)),
    inference(variable_rename,[status(thm)],[fact_37_UNIV__I]) ).

fof(i_0_2558,plain,
    ! [X6444] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X6444),top_to522745736l_bool)),
    inference(variable_rename,[status(thm)],[fact_720_subset__UNIV]) ).

fof(i_0_2559,plain,
    ! [X5633] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X5633),top_to522745736l_bool)),
    inference(variable_rename,[status(thm)],[fact_513_top__greatest]) ).

fof(i_0_2560,plain,
    ! [X4525] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4525),top_to522745736l_bool)),
    inference(variable_rename,[status(thm)],[fact_44_iso__tuple__UNIV__I]) ).

fof(i_0_2561,plain,
    ! [X4517] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4517),top_to522745736l_bool)),
    inference(variable_rename,[status(thm)],[fact_36_UNIV__I]) ).

fof(i_0_2562,plain,
    ! [X6449] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X6449),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[fact_725_subset__UNIV]) ).

fof(i_0_2563,plain,
    ! [X5640] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X5640),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[fact_520_top__greatest]) ).

fof(i_0_2564,plain,
    ! [X4523] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4523),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[fact_42_iso__tuple__UNIV__I]) ).

fof(i_0_2565,plain,
    ! [X4515] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4515),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[fact_34_UNIV__I]) ).

fof(i_0_2566,plain,
    ! [X6448] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6448),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[fact_724_subset__UNIV]) ).

fof(i_0_2567,plain,
    ! [X5639] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5639),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[fact_519_top__greatest]) ).

fof(i_0_2568,plain,
    ! [X4528] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4528),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[fact_47_iso__tuple__UNIV__I]) ).

fof(i_0_2569,plain,
    ! [X4520] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4520),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[fact_39_UNIV__I]) ).

fof(i_0_2570,plain,
    ! [X4521] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4521),top_to1647826457l_bool)),
    inference(variable_rename,[status(thm)],[fact_40_iso__tuple__UNIV__I]) ).

fof(i_0_2571,plain,
    ! [X4513] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4513),top_to1647826457l_bool)),
    inference(variable_rename,[status(thm)],[fact_32_UNIV__I]) ).

fof(i_0_2572,plain,
    ! [X6447] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X6447),top_to1576102282i_bool)),
    inference(variable_rename,[status(thm)],[fact_723_subset__UNIV]) ).

fof(i_0_2573,plain,
    ! [X5638] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X5638),top_to1576102282i_bool)),
    inference(variable_rename,[status(thm)],[fact_518_top__greatest]) ).

fof(i_0_2574,plain,
    ! [X4522] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4522),top_to1576102282i_bool)),
    inference(variable_rename,[status(thm)],[fact_41_iso__tuple__UNIV__I]) ).

fof(i_0_2575,plain,
    ! [X4514] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4514),top_to1576102282i_bool)),
    inference(variable_rename,[status(thm)],[fact_33_UNIV__I]) ).

fof(i_0_2576,plain,
    ! [X5637] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X5637),top_to178429151t_bool)),
    inference(variable_rename,[status(thm)],[fact_517_top__greatest]) ).

fof(i_0_2577,plain,
    ! [X5635] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X5635),top_top_bool)),
    inference(variable_rename,[status(thm)],[fact_515_top__greatest]) ).

fof(i_0_2578,plain,
    ! [X7780] :
      ( X7780 = zero_zero_nat
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X7780)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1048_gr0I])]) ).

fof(i_0_2579,plain,
    ! [X7788] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X7788)),
    inference(variable_rename,[status(thm)],[fact_1054_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_2580,plain,
    ! [X7774] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X7774)),
    inference(variable_rename,[status(thm)],[fact_1043_le0]) ).

fof(i_0_2581,plain,
    ! [X8009,X8010] :
      ( ( X8009 = hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(times_times_nat(X8009),X8010) != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( X8010 = hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(times_times_nat(X8009),X8010) != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( X8009 != hAPP_nat_nat(suc,zero_zero_nat)
        | X8010 != hAPP_nat_nat(suc,zero_zero_nat)
        | hAPP_nat_nat(times_times_nat(X8009),X8010) = hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1157_mult__eq__1__iff])])]) ).

fof(i_0_2582,plain,
    ! [X7999,X8000,X8001] :
      ( ( hAPP_nat_nat(times_times_nat(X7999),X8000) != hAPP_nat_nat(times_times_nat(X8001),X8000)
        | X7999 = X8001
        | X8000 = zero_zero_nat )
      & ( X7999 != X8001
        | hAPP_nat_nat(times_times_nat(X7999),X8000) = hAPP_nat_nat(times_times_nat(X8001),X8000) )
      & ( X8000 != zero_zero_nat
        | hAPP_nat_nat(times_times_nat(X7999),X8000) = hAPP_nat_nat(times_times_nat(X8001),X8000) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1152_mult__cancel2])])]) ).

fof(i_0_2583,plain,
    ! [X8065,X8066,X8067] :
      ( ( hAPP_nat_nat(times_times_nat(X8065),X8066) != hAPP_nat_nat(times_times_nat(X8065),X8067)
        | X8065 = zero_zero_nat
        | X8066 = X8067 )
      & ( X8065 != zero_zero_nat
        | hAPP_nat_nat(times_times_nat(X8065),X8066) = hAPP_nat_nat(times_times_nat(X8065),X8067) )
      & ( X8066 != X8067
        | hAPP_nat_nat(times_times_nat(X8065),X8066) = hAPP_nat_nat(times_times_nat(X8065),X8067) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1179_nat__mult__eq__cancel__disj])])]) ).

fof(i_0_2584,plain,
    ! [X8002,X8003,X8004] :
      ( ( hAPP_nat_nat(times_times_nat(X8002),X8003) != hAPP_nat_nat(times_times_nat(X8002),X8004)
        | X8003 = X8004
        | X8002 = zero_zero_nat )
      & ( X8003 != X8004
        | hAPP_nat_nat(times_times_nat(X8002),X8003) = hAPP_nat_nat(times_times_nat(X8002),X8004) )
      & ( X8002 != zero_zero_nat
        | hAPP_nat_nat(times_times_nat(X8002),X8003) = hAPP_nat_nat(times_times_nat(X8002),X8004) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1153_mult__cancel1])])]) ).

fof(i_0_2585,plain,
    ( is_fun961089132t_bool(esk483_0)
    & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk483_0),arrow_1681063817le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_1030_linear__alt])]) ).

fof(i_0_2586,plain,
    ! [X8081,X8082] : hAPP_n1699378549t_bool(ord_at4362885an_nat(X8081),hAPP_nat_nat(suc,X8082)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(X8081),X8082),
    inference(variable_rename,[status(thm)],[fact_1190_atLeastLessThanSuc__atLeastAtMost]) ).

fof(i_0_2587,plain,
    ! [X7785,X7786] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7785),X7786) != X7785
      | X7786 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1052_add__eq__self__zero])]) ).

fof(i_0_2588,plain,
    ! [X7783,X7784] :
      ( ( X7783 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7783),X7784) != zero_zero_nat )
      & ( X7784 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7783),X7784) != zero_zero_nat )
      & ( X7783 != zero_zero_nat
        | X7784 != zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7783),X7784) = zero_zero_nat ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1051_add__is__0])])]) ).

fof(i_0_2589,plain,
    ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(esk506_0),top_to1576102282i_bool))
    & hAPP_f2026336507t_bool(image_579431497di_nat(esk506_0),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12])])]) ).

fof(i_0_2590,plain,
    ! [X8109] : hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,X8109)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,X8109),
    inference(variable_rename,[status(thm)],[fact_1198_atLeast__Suc__greaterThan]) ).

fof(i_0_2591,plain,
    ! [X7917] : hAPP_nat_nat(suc,X7917) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7917),one_one_nat),
    inference(variable_rename,[status(thm)],[fact_1118_Suc__eq__plus1]) ).

fof(i_0_2592,plain,
    ! [X7900] : hAPP_n1699378549t_bool(ord_less_nat,X7900) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X7900)),
    inference(variable_rename,[status(thm)],[fact_1110_less__eq__Suc__le__raw]) ).

fof(i_0_2593,plain,
    ! [X7918] : hAPP_nat_nat(suc,X7918) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X7918),
    inference(variable_rename,[status(thm)],[fact_1119_Suc__eq__plus1__left]) ).

fof(i_0_2594,plain,
    ! [X4532] :
      ( ( ~ hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X4532))
        | hBOOL(top_top_bool) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X4532)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_top__apply])]) ).

fof(i_0_2595,plain,
    ! [X4529] :
      ( ( ~ hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X4529))
        | hBOOL(top_top_bool) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X4529)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_top__apply])]) ).

fof(i_0_2596,plain,
    ! [X4531] :
      ( ( ~ hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X4531))
        | hBOOL(top_top_bool) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X4531)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_top__apply])]) ).

fof(i_0_2597,plain,
    ! [X4530] :
      ( ( ~ hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X4530))
        | hBOOL(top_top_bool) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X4530)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_49_top__apply])]) ).

fof(i_0_2598,plain,
    ! [X4535] :
      ( ( ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X4535))
        | hBOOL(top_top_bool) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X4535)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_top__apply])]) ).

fof(i_0_2599,plain,
    ! [X4534] :
      ( ( ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X4534))
        | hBOOL(top_top_bool) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X4534)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_53_top__apply])]) ).

fof(i_0_2600,plain,
    ! [X4533] :
      ( ( ~ hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X4533))
        | hBOOL(top_top_bool) )
      & ( ~ hBOOL(top_top_bool)
        | hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X4533)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_52_top__apply])]) ).

fof(i_0_2601,plain,
    ! [X8183,X8184] :
      ( ~ is_fun1568535512t_bool(X8183)
      | hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,X8183),X8184) = X8183 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_050])]) ).

fof(i_0_2602,plain,
    ! [X8191,X8192] :
      ( ~ is_fun1236654035i_bool(X8191)
      | hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,X8191),X8192) = X8191 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___052])]) ).

fof(i_0_2603,plain,
    ! [X8170,X8171] :
      ( ~ is_bool(X8170)
      | hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_alt,X8170),X8171) = X8170 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe])]) ).

fof(i_0_2604,plain,
    ! [X8195,X8196] :
      ( ~ is_fun1568535512t_bool(X8195)
      | hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,X8195),X8196) = X8195 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_054])]) ).

fof(i_0_2605,plain,
    ! [X8204,X8205] :
      ( ~ is_fun1236654035i_bool(X8204)
      | hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,X8204),X8205) = X8204 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___056])]) ).

fof(i_0_2606,plain,
    ! [X8177,X8178] :
      ( ~ is_bool(X8177)
      | hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,X8177),X8178) = X8177 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_])]) ).

fof(i_0_2607,plain,
    ! [X8255,X8256] :
      ( ~ is_fun1568535512t_bool(X8255)
      | hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,X8255),X8256) = X8255 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_069])]) ).

fof(i_0_2608,plain,
    ! [X8259,X8260] :
      ( ~ is_fun1236654035i_bool(X8259)
      | hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,X8259),X8260) = X8259 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___071])]) ).

fof(i_0_2609,plain,
    ! [X8244,X8245] :
      ( ~ is_bool(X8244)
      | hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_bool,X8244),X8245) = X8244 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__])]) ).

fof(i_0_2610,plain,
    ! [X8246,X8247] :
      ( ~ is_fun279392540l_bool(X8246)
      | hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,X8246),X8247) = X8246 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_067])]) ).

fof(i_0_2611,plain,
    ! [X8215,X8216] :
      ( ~ is_fun1568535512t_bool(X8215)
      | hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,X8215),X8216) = X8215 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_060])]) ).

fof(i_0_2612,plain,
    ! [X8225,X8226] :
      ( ~ is_fun1236654035i_bool(X8225)
      | hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,X8225),X8226) = X8225 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___063])]) ).

fof(i_0_2613,plain,
    ! [X8202,X8203] :
      ( ~ is_bool(X8202)
      | hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_bool,X8202),X8203) = X8202 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel])]) ).

fof(i_0_2614,plain,
    ! [X8185,X8186] :
      ( ~ is_fun961089132t_bool(X8185)
      | hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,X8185),X8186) = X8185 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051])]) ).

fof(i_0_2615,plain,
    ! [X8197,X8198] :
      ( ~ is_fun279392540l_bool(X8197)
      | hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,X8197),X8198) = X8197 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_055])]) ).

fof(i_0_2616,plain,
    ! [X8257,X8258] :
      ( ~ is_fun158382675l_bool(X8257)
      | hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,X8257),X8258) = X8257 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_070])]) ).

fof(i_0_2617,plain,
    ! [X8217,X8218] :
      ( ~ is_fun288122577l_bool(X8217)
      | hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,X8217),X8218) = X8217 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_061])]) ).

fof(i_0_2618,plain,
    ! [X8127,X8128] :
      ( ~ is_bool(X8127)
      | hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,X8127),X8128) = X8127 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U])]) ).

fof(i_0_2619,plain,
    ! [X8146,X8147] :
      ( ~ is_fun1568535512t_bool(X8146)
      | hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,X8146),X8147) = X8146 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00])]) ).

fof(i_0_2620,plain,
    ! [X8160,X8161] :
      ( ~ is_fun1236654035i_bool(X8160)
      | hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,X8160),X8161) = X8160 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__])]) ).

fof(i_0_2621,plain,
    ! [X8125,X8126] :
      ( ~ is_bool(X8125)
      | hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,X8125),X8126) = X8125 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U])]) ).

fof(i_0_2622,plain,
    ! [X8181,X8182] :
      ( ~ is_fun961089132t_bool(X8181)
      | hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,X8181),X8182) = X8181 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp])]) ).

fof(i_0_2623,plain,
    ! [X8189,X8190] :
      ( ~ is_fun279392540l_bool(X8189)
      | hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,X8189),X8190) = X8189 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe])]) ).

fof(i_0_2624,plain,
    ! [X8250,X8251] :
      ( ~ is_fun158382675l_bool(X8250)
      | hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,X8250),X8251) = X8250 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel])]) ).

fof(i_0_2625,plain,
    ! [X8210,X8211] :
      ( ~ is_fun288122577l_bool(X8210)
      | hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,X8210),X8211) = X8210 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn])]) ).

fof(i_0_2626,plain,
    ! [X8193,X8194] :
      ( ~ is_fun961089132t_bool(X8193)
      | hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X8193),X8194) = X8193 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_053])]) ).

fof(i_0_2627,plain,
    ! [X8206,X8207] :
      ( ~ is_fun279392540l_bool(X8206)
      | hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,X8206),X8207) = X8206 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057])]) ).

fof(i_0_2628,plain,
    ! [X8261,X8262] :
      ( ~ is_fun158382675l_bool(X8261)
      | hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,X8261),X8262) = X8261 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_072])]) ).

fof(i_0_2629,plain,
    ! [X8227,X8228] :
      ( ~ is_fun288122577l_bool(X8227)
      | hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,X8227),X8228) = X8227 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_064])]) ).

fof(i_0_2630,plain,
    ! [X8142,X8143] :
      ( ~ is_bool(X8142)
      | hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,X8142),X8143) = X8142 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn])]) ).

fof(i_0_2631,hypothesis,
    ! [X4405,X4406] :
      ( ~ is_fun279392540l_bool(X4405)
      | ~ is_fun961089132t_bool(X4406)
      | is_bool(hAPP_f592646513l_bool(X4405,X4406)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039])]) ).

fof(i_0_2632,plain,
    ! [X4233,X4234] :
      ( ~ is_fun1236654035i_bool(X4233)
      | ~ is_Arr43961803e_indi(X4234)
      | is_bool(hAPP_A1785763630i_bool(X4233,X4234)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O])]) ).

fof(i_0_2633,plain,
    ! [X7808,X7809] :
      ( ( hAPP_nat_nat(suc,X7808) != hAPP_nat_nat(suc,X7809)
        | X7808 = X7809 )
      & ( X7808 != X7809
        | hAPP_nat_nat(suc,X7808) = hAPP_nat_nat(suc,X7809) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1063_nat_Oinject])]) ).

fof(i_0_2634,plain,
    ! [X7806,X7807] :
      ( hAPP_nat_nat(suc,X7806) != hAPP_nat_nat(suc,X7807)
      | X7806 = X7807 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1062_Suc__inject])]) ).

fof(i_0_2635,plain,
    ! [X8051,X8052] : hAPP_nat_nat(times_times_nat(X8051),X8052) = hAPP_nat_nat(times_times_nat(X8052),X8051),
    inference(variable_rename,[status(thm)],[fact_1174_nat__mult__commute]) ).

fof(i_0_2636,plain,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    inference(fof_simplification,[status(thm)],[fact_1034_infinite__UNIV__nat]) ).

fof(i_0_2637,plain,
    ! [X8138,X8139] : hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,X8138),X8139) = X8138,
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__On]) ).

fof(i_0_2638,plain,
    ! [X8187,X8188] : hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,X8187),X8188) = X8187,
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc]) ).

fof(i_0_2639,plain,
    ! [X8248,X8249] : hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,X8248),X8249) = X8248,
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_068]) ).

fof(i_0_2640,plain,
    ! [X8208,X8209] : hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,X8208),X8209) = X8208,
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_058]) ).

fof(i_0_2641,plain,
    ! [X8144,X8145] : hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,X8144),X8145) = X8144,
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product_]) ).

fof(i_0_2642,plain,
    ! [X8162,X8163] : hAPP_A2046586321t_bool(hAPP_f1491725936t_bool(cOMBK_847149194e_indi,X8162),X8163) = X8162,
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___]) ).

fof(i_0_2643,plain,
    ! [X8179,X8180] : hAPP_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_alt,X8179),X8180) = X8179,
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It]) ).

fof(i_0_2644,plain,
    ! [X8140,X8141] : hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,X8140),X8141) = X8140,
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).

fof(i_0_2645,plain,
    ! [X4225,X4226] :
      ( ~ is_fun1236654035i_bool(X4225)
      | is_fun1217980910e_indi(hilber693666498di_nat(X4225,X4226)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu])]) ).

fof(i_0_2646,plain,
    ! [X4411,X4412] :
      ( ~ is_fun961089132t_bool(X4412)
      | is_fun1568535512t_bool(hAPP_f1710744577t_bool(X4411,X4412)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___042])]) ).

fof(i_0_2647,plain,
    ! [X4325,X4326] :
      ( ~ is_fun1568535512t_bool(X4326)
      | is_fun1568535512t_bool(hAPP_f427533077t_bool(X4325,X4326)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I])]) ).

fof(i_0_2648,plain,
    ! [X4247,X4248] :
      ( ~ is_bool(X4248)
      | is_fun1568535512t_bool(hAPP_b1096750261t_bool(X4247,X4248)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob])]) ).

fof(i_0_2649,plain,
    ! [X4407,X4408] :
      ( ~ is_fun961089132t_bool(X4408)
      | is_fun2093718614t_bool(hAPP_f1617919085t_bool(X4407,X4408)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040])]) ).

fof(i_0_2650,plain,
    ! [X4419,X4420] :
      ( ~ is_fun961089132t_bool(X4419)
      | is_bool(hAPP_P606313927t_bool(X4419,X4420)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__045])]) ).

fof(i_0_2651,plain,
    ! [X4397,X4398] :
      ( ~ is_fun279392540l_bool(X4398)
      | is_bool(hAPP_f1749234559l_bool(X4397,X4398)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_036])]) ).

fof(i_0_2652,plain,
    ! [X4379,X4380] :
      ( ~ is_fun158382675l_bool(X4380)
      | is_bool(hAPP_f250445784l_bool(X4379,X4380)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_030])]) ).

fof(i_0_2653,plain,
    ! [X4339,X4340] :
      ( ~ is_fun158382675l_bool(X4339)
      | is_bool(hAPP_f312250286l_bool(X4339,X4340)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_024])]) ).

fof(i_0_2654,plain,
    ! [X4333,X4334] :
      ( ~ is_fun288122577l_bool(X4334)
      | is_bool(hAPP_f777333846l_bool(X4333,X4334)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_021])]) ).

fof(i_0_2655,plain,
    ! [X4323,X4324] :
      ( ~ is_fun1568535512t_bool(X4324)
      | is_bool(hAPP_f2028818269l_bool(X4323,X4324)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__])]) ).

fof(i_0_2656,plain,
    ! [X4295,X4296] :
      ( ~ is_fun288122577l_bool(X4295)
      | is_bool(hAPP_f965095724l_bool(X4295,X4296)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__011])]) ).

fof(i_0_2657,plain,
    ! [X4289,X4290] :
      ( ~ is_fun1236654035i_bool(X4290)
      | is_bool(hAPP_f1599966040l_bool(X4289,X4290)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_])]) ).

fof(i_0_2658,plain,
    ! [X4287,X4288] :
      ( ~ is_fun2093718614t_bool(X4288)
      | is_bool(hAPP_f324780729l_bool(X4287,X4288)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___008])]) ).

fof(i_0_2659,plain,
    ! [X4275,X4276] :
      ( ~ is_fun1568535512t_bool(X4275)
      | is_bool(hAPP_P1676879539t_bool(X4275,X4276)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool])]) ).

fof(i_0_2660,plain,
    ! [X4243,X4244] :
      ( ~ is_bool(X4244)
      | is_bool(hAPP_bool_bool(X4243,X4244)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool])]) ).

fof(i_0_2661,plain,
    ! [X4227,X4228] :
      ( ~ is_Arr1861959080le_alt(X4228)
      | is_bool(hAPP_A862370221t_bool(X4227,X4228)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob])]) ).

fof(i_0_2662,plain,
    ! [X4403,X4404] :
      ( ~ is_fun961089132t_bool(X4404)
      | is_Arr43961803e_indi(hAPP_f1582908258e_indi(X4403,X4404)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__])]) ).

fof(i_0_2663,plain,
    ! [X4257,X4258] :
      ( ~ is_fun1217980910e_indi(X4257)
      | is_Arr43961803e_indi(hAPP_n1951273283e_indi(X4257,X4258)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oi])]) ).

fof(i_0_2664,plain,
    ! [X4409,X4410] :
      ( ~ is_fun961089132t_bool(X4410)
      | is_fun1236654035i_bool(hAPP_f244157820i_bool(X4409,X4410)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___041])]) ).

fof(i_0_2665,plain,
    ! [X4291,X4292] :
      ( ~ is_fun1236654035i_bool(X4292)
      | is_fun1236654035i_bool(hAPP_f580451669i_bool(X4291,X4292)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__009])]) ).

fof(i_0_2666,plain,
    ! [X4245,X4246] :
      ( ~ is_bool(X4246)
      | is_fun1236654035i_bool(hAPP_b1337486384i_bool(X4245,X4246)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnf])]) ).

fof(i_0_2667,plain,
    ! [X4415,X4416] :
      ( ~ is_fun961089132t_bool(X4416)
      | is_fun961089132t_bool(hAPP_f515126293t_bool(X4415,X4416)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___044])]) ).

fof(i_0_2668,plain,
    ! [X4255,X4256] :
      ( ~ is_bool(X4256)
      | is_fun961089132t_bool(hAPP_b1703662281t_bool(X4255,X4256)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel])]) ).

fof(i_0_2669,plain,
    ! [X4241,X4242] :
      ( ~ is_Arr43961803e_indi(X4242)
      | is_fun961089132t_bool(hAPP_A1677245848t_bool(X4241,X4242)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_006])]) ).

fof(i_0_2670,plain,
    ! [X4231,X4232] :
      ( ~ is_Arr1861959080le_alt(X4232)
      | is_fun961089132t_bool(hAPP_A568203993t_bool(X4231,X4232)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003])]) ).

fof(i_0_2671,plain,
    ! [X4335,X4336] :
      ( ~ is_fun288122577l_bool(X4336)
      | is_fun288122577l_bool(hAPP_f146009813l_bool(X4335,X4336)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_022])]) ).

fof(i_0_2672,plain,
    ! [X4249,X4250] :
      ( ~ is_bool(X4250)
      | is_fun288122577l_bool(hAPP_b1048178734l_bool(X4249,X4250)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell])]) ).

fof(i_0_2673,plain,
    ! [X4235,X4236] :
      ( ~ is_Arr43961803e_indi(X4236)
      | is_fun288122577l_bool(hAPP_A1952883197l_bool(X4235,X4236)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It])]) ).

fof(i_0_2674,plain,
    ! [X4219,X4220] :
      ( ~ is_fun1236654035i_bool(X4219)
      | is_fun288122577l_bool(pi_Arr990697634t_bool(X4219,X4220)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc_])]) ).

fof(i_0_2675,plain,
    ! [X4413,X4414] :
      ( ~ is_fun961089132t_bool(X4414)
      | is_fun279392540l_bool(hAPP_f863359027l_bool(X4413,X4414)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___043])]) ).

fof(i_0_2676,plain,
    ! [X4399,X4400] :
      ( ~ is_fun279392540l_bool(X4400)
      | is_fun279392540l_bool(hAPP_f111185985l_bool(X4399,X4400)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_037])]) ).

fof(i_0_2677,plain,
    ! [X4253,X4254] :
      ( ~ is_bool(X4254)
      | is_fun279392540l_bool(hAPP_b1812770943l_bool(X4253,X4254)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__])]) ).

fof(i_0_2678,plain,
    ! [X4239,X4240] :
      ( ~ is_Arr43961803e_indi(X4240)
      | is_fun279392540l_bool(hAPP_A60074736l_bool(X4239,X4240)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_005])]) ).

fof(i_0_2679,plain,
    ! [X4229,X4230] :
      ( ~ is_Arr1861959080le_alt(X4230)
      | is_fun279392540l_bool(hAPP_A187815023l_bool(X4229,X4230)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc])]) ).

fof(i_0_2680,plain,
    ! [X4223,X4224] :
      ( ~ is_fun961089132t_bool(X4223)
      | is_fun279392540l_bool(pi_Pro666468413t_bool(X4223,X4224)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa])]) ).

fof(i_0_2681,plain,
    ! [X4381,X4382] :
      ( ~ is_fun158382675l_bool(X4382)
      | is_fun158382675l_bool(hAPP_f1765205l_bool(X4381,X4382)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_031])]) ).

fof(i_0_2682,plain,
    ! [X4251,X4252] :
      ( ~ is_bool(X4252)
      | is_fun158382675l_bool(hAPP_b517355696l_bool(X4251,X4252)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___])]) ).

fof(i_0_2683,plain,
    ! [X4237,X4238] :
      ( ~ is_Arr43961803e_indi(X4238)
      | is_fun158382675l_bool(hAPP_A1112981887l_bool(X4237,X4238)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_004])]) ).

fof(i_0_2684,plain,
    ! [X4221,X4222] :
      ( ~ is_fun288122577l_bool(X4221)
      | is_fun158382675l_bool(pi_fun150026276t_bool(X4221,X4222)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oin])]) ).

fof(i_0_2685,plain,
    ! [X8035,X8036] :
      ( X8035 != hAPP_nat_nat(times_times_nat(X8035),X8036)
      | X8036 = one_one_nat
      | X8035 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1167_mult__eq__self__implies__10])]) ).

fof(i_0_2686,plain,
    ! [X7860] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),X7860)),
    inference(variable_rename,[status(thm)],[fact_1093_inj__Suc]) ).

fof(i_0_2687,plain,
    ! [X5826] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),X5826)),
    inference(variable_rename,[status(thm)],[fact_580_inj__on__id2]) ).

fof(i_0_2688,plain,
    ! [X7782] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X7782),zero_zero_nat) = X7782,
    inference(variable_rename,[status(thm)],[fact_1050_Nat_Oadd__0__right]) ).

fof(i_0_2689,plain,
    ! [X8005,X8006] :
      ( ( hAPP_nat_nat(times_times_nat(X8005),X8006) != zero_zero_nat
        | X8005 = zero_zero_nat
        | X8006 = zero_zero_nat )
      & ( X8005 != zero_zero_nat
        | hAPP_nat_nat(times_times_nat(X8005),X8006) = zero_zero_nat )
      & ( X8006 != zero_zero_nat
        | hAPP_nat_nat(times_times_nat(X8005),X8006) = zero_zero_nat ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1154_mult__is__0])])]) ).

fof(i_0_2690,plain,
    ! [X7781] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X7781) = X7781,
    inference(variable_rename,[status(thm)],[fact_1049_plus__nat_Oadd__0]) ).

fof(i_0_2691,plain,
    ! [X4914] : pi_Pro666468413t_bool(X4914,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool)) = top_to1853035173l_bool,
    inference(variable_rename,[status(thm)],[fact_222_Pi__UNIV]) ).

fof(i_0_2692,plain,
    ! [X4915] : pi_fun150026276t_bool(X4915,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool,
    inference(variable_rename,[status(thm)],[fact_223_Pi__UNIV]) ).

fof(i_0_2693,plain,
    ! [X4916] : pi_Arr990697634t_bool(X4916,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool,
    inference(variable_rename,[status(thm)],[fact_224_Pi__UNIV]) ).

fof(i_0_2694,plain,
    ! [X7984,X7985] :
      ( ( X7984 = one_one_nat
        | hAPP_nat_nat(times_times_nat(X7984),X7985) != one_one_nat )
      & ( X7985 = one_one_nat
        | hAPP_nat_nat(times_times_nat(X7984),X7985) != one_one_nat )
      & ( X7984 != one_one_nat
        | X7985 != one_one_nat
        | hAPP_nat_nat(times_times_nat(X7984),X7985) = one_one_nat ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1145_nat__mult__eq__1__iff])])]) ).

fof(i_0_2695,plain,
    ! [X7987,X7988] :
      ( ( X7987 = one_one_nat
        | one_one_nat != hAPP_nat_nat(times_times_nat(X7987),X7988) )
      & ( X7988 = one_one_nat
        | one_one_nat != hAPP_nat_nat(times_times_nat(X7987),X7988) )
      & ( X7987 != one_one_nat
        | X7988 != one_one_nat
        | one_one_nat = hAPP_nat_nat(times_times_nat(X7987),X7988) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1147_nat__1__eq__mult__iff])])]) ).

fof(i_0_2696,plain,
    ! [X4423,X4424] : is_fun1568535512t_bool(hAPP_P332578347t_bool(X4423,X4424)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__047]) ).

fof(i_0_2697,plain,
    ! [X4343,X4344] : is_fun1568535512t_bool(hAPP_f1866147972t_bool(X4343,X4344)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_026]) ).

fof(i_0_2698,plain,
    ! [X4313,X4314] : is_fun1568535512t_bool(hAPP_f1061584978t_bool(X4313,X4314)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Product__]) ).

fof(i_0_2699,plain,
    ! [X4299,X4300] : is_fun1568535512t_bool(hAPP_f1891021702t_bool(X4299,X4300)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__013]) ).

fof(i_0_2700,plain,
    ! [X4265,X4266] : is_fun1568535512t_bool(hAPP_n454528608t_bool(X4265,X4266)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo]) ).

fof(i_0_2701,plain,
    ! [X4309,X4310] : is_fun2093718614t_bool(hAPP_f861874780t_bool(X4309,X4310)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow____]) ).

fof(i_0_2702,plain,
    ! [X4261,X4262] : is_fun2093718614t_bool(hAPP_n539120590t_bool(X4261,X4262)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn]) ).

fof(i_0_2703,plain,
    ! [X4401,X4402] : is_bool(hAPP_f22590837l_bool(X4401,X4402)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_038]) ).

fof(i_0_2704,plain,
    ! [X4395,X4396] : is_bool(hAPP_f1306865520l_bool(X4395,X4396)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn]) ).

fof(i_0_2705,plain,
    ! [X4393,X4394] : is_bool(hAPP_f866275871l_bool(X4393,X4394)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_035]) ).

fof(i_0_2706,plain,
    ! [X4391,X4392] : is_bool(hAPP_f167218729l_bool(X4391,X4392)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_034]) ).

fof(i_0_2707,plain,
    ! [X4389,X4390] : is_bool(hAPP_f560831258l_bool(X4389,X4390)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel]) ).

fof(i_0_2708,plain,
    ! [X4387,X4388] : is_bool(hAPP_f1644647260l_bool(X4387,X4388)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_033]) ).

fof(i_0_2709,plain,
    ! [X4385,X4386] : is_bool(hAPP_f859154022l_bool(X4385,X4386)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_032]) ).

fof(i_0_2710,plain,
    ! [X4383,X4384] : is_bool(hAPP_f10461143l_bool(X4383,X4384)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell]) ).

fof(i_0_2711,plain,
    ! [X4377,X4378] : is_bool(hAPP_f770608346l_bool(X4377,X4378)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_029]) ).

fof(i_0_2712,plain,
    ! [X4375,X4376] : is_bool(hAPP_f597137892l_bool(X4375,X4376)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_028]) ).

fof(i_0_2713,plain,
    ! [X4373,X4374] : is_bool(hAPP_f1725204053l_bool(X4373,X4374)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf]) ).

fof(i_0_2714,plain,
    ! [X4371,X4372] : is_bool(hAPP_f415146997l_bool(X4371,X4372)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_]) ).

fof(i_0_2715,plain,
    ! [X4369,X4370] : is_bool(hAPP_f1846209297l_bool(X4369,X4370)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It]) ).

fof(i_0_2716,plain,
    ! [X4367,X4368] : is_bool(hAPP_f1508442332l_bool(X4367,X4368)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc]) ).

fof(i_0_2717,plain,
    ! [X4365,X4366] : is_bool(hAPP_f844512602l_bool(X4365,X4366)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__]) ).

fof(i_0_2718,plain,
    ! [X4363,X4364] : is_bool(hAPP_f339859954l_bool(X4363,X4364)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_]) ).

fof(i_0_2719,plain,
    ! [X4361,X4362] : is_bool(hAPP_f537623936l_bool(X4361,X4362)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_]) ).

fof(i_0_2720,plain,
    ! [X4359,X4360] : is_bool(hAPP_f1637334154l_bool(X4359,X4360)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).

fof(i_0_2721,plain,
    ! [X4357,X4358] : is_bool(hAPP_f795156475l_bool(X4357,X4358)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__]) ).

fof(i_0_2722,plain,
    ! [X4355,X4356] : is_bool(hAPP_f1351174655l_bool(X4355,X4356)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____]) ).

fof(i_0_2723,plain,
    ! [X4353,X4354] : is_bool(hAPP_f817604743l_bool(X4353,X4354)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____]) ).

fof(i_0_2724,plain,
    ! [X4351,X4352] : is_bool(hAPP_f651410150l_bool(X4351,X4352)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O]) ).

fof(i_0_2725,plain,
    ! [X4349,X4350] : is_bool(hAPP_f599145828l_bool(X4349,X4350)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M]) ).

fof(i_0_2726,plain,
    ! [X4347,X4348] : is_bool(hAPP_f67777128l_bool(X4347,X4348)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_]) ).

fof(i_0_2727,plain,
    ! [X4345,X4346] : is_bool(hAPP_f1837019376l_bool(X4345,X4346)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_027]) ).

fof(i_0_2728,plain,
    ! [X4331,X4332] : is_bool(hAPP_f785974231l_bool(X4331,X4332)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_020]) ).

fof(i_0_2729,plain,
    ! [X4329,X4330] : is_bool(hAPP_f1252760917l_bool(X4329,X4330)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_019]) ).

fof(i_0_2730,plain,
    ! [X4327,X4328] : is_bool(hAPP_f1632652727l_bool(X4327,X4328)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O]) ).

fof(i_0_2731,plain,
    ! [X4307,X4308] : is_bool(hAPP_f54304608l_bool(X4307,X4308)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(i_0_2732,plain,
    ! [X4305,X4306] : is_bool(hAPP_f387058535l_bool(X4305,X4306)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(i_0_2733,plain,
    ! [X4285,X4286] : is_bool(hAPP_f2013399995l_bool(X4285,X4286)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__]) ).

fof(i_0_2734,plain,
    ! [X4259,X4260] : is_bool(hAPP_nat_bool(X4259,X4260)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).

fof(i_0_2735,plain,
    ! [X4417,X4418] : is_Arr43961803e_indi(hAPP_P710098616e_indi(X4417,X4418)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_]) ).

fof(i_0_2736,plain,
    ! [X4337,X4338] : is_Arr43961803e_indi(hAPP_f1693298207e_indi(X4337,X4338)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_023]) ).

fof(i_0_2737,plain,
    ! [X4293,X4294] : is_Arr43961803e_indi(hAPP_f836059805e_indi(X4293,X4294)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__010]) ).

fof(i_0_2738,plain,
    ! [X4421,X4422] : is_fun1236654035i_bool(hAPP_P1875867302i_bool(X4421,X4422)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__046]) ).

fof(i_0_2739,plain,
    ! [X4341,X4342] : is_fun1236654035i_bool(hAPP_f1552576127i_bool(X4341,X4342)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025]) ).

fof(i_0_2740,plain,
    ! [X4311,X4312] : is_fun1236654035i_bool(hAPP_f632777549i_bool(X4311,X4312)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow_____016]) ).

fof(i_0_2741,plain,
    ! [X4297,X4298] : is_fun1236654035i_bool(hAPP_f1948454017i_bool(X4297,X4298)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__012]) ).

fof(i_0_2742,plain,
    ! [X4263,X4264] : is_fun1236654035i_bool(hAPP_n821919323i_bool(X4263,X4264)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007]) ).

fof(i_0_2743,plain,
    ! [X4321,X4322] : is_fun961089132t_bool(hAPP_f899613158t_bool(X4321,X4322)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc_]) ).

fof(i_0_2744,hypothesis,
    ! [X4303,X4304] : is_fun961089132t_bool(hAPP_f412050202t_bool(X4303,X4304)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__015]) ).

fof(i_0_2745,plain,
    ! [X4283,X4284] : is_fun961089132t_bool(hAPP_P1341894483t_bool(X4283,X4284)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde]) ).

fof(i_0_2746,plain,
    ! [X4273,X4274] : is_fun961089132t_bool(hAPP_n588788980t_bool(X4273,X4274)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell]) ).

fof(i_0_2747,plain,
    ! [X4315,X4316] : is_fun288122577l_bool(hAPP_f226010187l_bool(X4315,X4316)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__]) ).

fof(i_0_2748,plain,
    ! [X4277,X4278] : is_fun288122577l_bool(hAPP_P254387896l_bool(X4277,X4278)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order]) ).

fof(i_0_2749,plain,
    ! [X4267,X4268] : is_fun288122577l_bool(hAPP_n2095207769l_bool(X4267,X4268)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle]) ).

fof(i_0_2750,hypothesis,
    ! [X4425,X4426] : is_fun279392540l_bool(hAPP_P229966473l_bool(X4425,X4426)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048]) ).

fof(i_0_2751,plain,
    ! [X4319,X4320] : is_fun279392540l_bool(hAPP_f769545506l_bool(X4319,X4320)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___018]) ).

fof(i_0_2752,plain,
    ! [X4301,X4302] : is_fun279392540l_bool(hAPP_f1277514478l_bool(X4301,X4302)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__014]) ).

fof(i_0_2753,plain,
    ! [X4281,X4282] : is_fun279392540l_bool(hAPP_P1294997365l_bool(X4281,X4282)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro]) ).

fof(i_0_2754,plain,
    ! [X4271,X4272] : is_fun279392540l_bool(hAPP_n1674354836l_bool(X4271,X4272)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___]) ).

fof(i_0_2755,plain,
    ! [X4317,X4318] : is_fun158382675l_bool(hAPP_f1449238989l_bool(X4317,X4318)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___017]) ).

fof(i_0_2756,plain,
    ! [X4279,X4280] : is_fun158382675l_bool(hAPP_P1171466554l_bool(X4279,X4280)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow]) ).

fof(i_0_2757,plain,
    ! [X4269,X4270] : is_fun158382675l_bool(hAPP_n295497947l_bool(X4269,X4270)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____]) ).

fof(i_0_2758,plain,
    ! [X4509] : hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X4509)),
    inference(variable_rename,[status(thm)],[fact_28_top1I]) ).

fof(i_0_2759,plain,
    ! [X4506] : hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X4506)),
    inference(variable_rename,[status(thm)],[fact_25_top1I]) ).

fof(i_0_2760,plain,
    ! [X4508] : hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X4508)),
    inference(variable_rename,[status(thm)],[fact_27_top1I]) ).

fof(i_0_2761,plain,
    ! [X4507] : hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X4507)),
    inference(variable_rename,[status(thm)],[fact_26_top1I]) ).

fof(i_0_2762,plain,
    ! [X4512] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X4512)),
    inference(variable_rename,[status(thm)],[fact_31_top1I]) ).

fof(i_0_2763,plain,
    ! [X4511] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X4511)),
    inference(variable_rename,[status(thm)],[fact_30_top1I]) ).

fof(i_0_2764,plain,
    ! [X4510] : hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X4510)),
    inference(variable_rename,[status(thm)],[fact_29_top1I]) ).

fof(i_0_2765,plain,
    ! [X7810] : hAPP_nat_nat(suc,X7810) != X7810,
    inference(variable_rename,[status(thm)],[fact_1064_Suc__n__not__n]) ).

fof(i_0_2766,plain,
    ! [X7811] : X7811 != hAPP_nat_nat(suc,X7811),
    inference(variable_rename,[status(thm)],[fact_1065_n__not__Suc__n]) ).

fof(i_0_2767,plain,
    ! [X7930] :
      ( X7930 = zero_zero_nat
      | X7930 = hAPP_nat_nat(suc,esk503_1(X7930)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1124_nat_Oexhaust])])]) ).

fof(i_0_2768,plain,
    ! [X7928] :
      ( X7928 = zero_zero_nat
      | X7928 = hAPP_nat_nat(suc,esk502_1(X7928)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1123_not0__implies__Suc])])]) ).

fof(i_0_2769,plain,
    ! [X4757] :
      ( ~ is_fun1568535512t_bool(X4757)
      | hAPP_f427533077t_bool(collect_Product_unit,X4757) = X4757 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_170_Collect__def])]) ).

fof(i_0_2770,plain,
    ! [X4758] :
      ( ~ is_fun1236654035i_bool(X4758)
      | hAPP_f580451669i_bool(collec1611109369e_indi,X4758) = X4758 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_171_Collect__def])]) ).

fof(i_0_2771,plain,
    ! [X7815] : hAPP_nat_nat(suc,X7815) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[fact_1069_Suc__not__Zero]) ).

fof(i_0_2772,plain,
    ! [X7814] : hAPP_nat_nat(suc,X7814) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[fact_1068_nat_Osimps_I3_J]) ).

fof(i_0_2773,plain,
    ! [X7812] : hAPP_nat_nat(suc,X7812) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[fact_1066_Suc__neq__Zero]) ).

fof(i_0_2774,plain,
    ! [X7817] : zero_zero_nat != hAPP_nat_nat(suc,X7817),
    inference(variable_rename,[status(thm)],[fact_1071_Zero__not__Suc]) ).

fof(i_0_2775,plain,
    ! [X7816] : zero_zero_nat != hAPP_nat_nat(suc,X7816),
    inference(variable_rename,[status(thm)],[fact_1070_nat_Osimps_I2_J]) ).

fof(i_0_2776,plain,
    ! [X7813] : zero_zero_nat != hAPP_nat_nat(suc,X7813),
    inference(variable_rename,[status(thm)],[fact_1067_Zero__neq__Suc]) ).

fof(i_0_2777,plain,
    ! [X7986] : hAPP_nat_nat(times_times_nat(X7986),one_one_nat) = X7986,
    inference(variable_rename,[status(thm)],[fact_1146_nat__mult__1__right]) ).

fof(i_0_2778,plain,
    ! [X8007] : hAPP_nat_nat(times_times_nat(X8007),zero_zero_nat) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[fact_1155_mult__0__right]) ).

fof(i_0_2779,plain,
    ! [X7989] : hAPP_nat_nat(times_times_nat(one_one_nat),X7989) = X7989,
    inference(variable_rename,[status(thm)],[fact_1148_nat__mult__1]) ).

fof(i_0_2780,plain,
    ! [X8008] : hAPP_nat_nat(times_times_nat(zero_zero_nat),X8008) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[fact_1156_mult__0]) ).

fof(i_0_2781,plain,
    ! [X8074] : hAPP_nat_nat(size_size_nat,X8074) = X8074,
    inference(variable_rename,[status(thm)],[fact_1184_nat__size]) ).

fof(i_0_2782,plain,
    ! [X8120] : hAPP_nat_nat(cOMBI_nat,X8120) = X8120,
    inference(variable_rename,[status(thm)],[help_COMBI_1_1_COMBI_000tc__Nat__Onat_U]) ).

fof(i_0_2783,plain,
    ! [X4759] : hAPP_f800510211t_bool(collect_nat,X4759) = X4759,
    inference(variable_rename,[status(thm)],[fact_172_Collect__def]) ).

fof(i_0_2784,plain,
    ! [X8176] :
      ( ~ is_bool(X8176)
      | X8176 = fTrue
      | X8176 = fFalse ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp])]) ).

fof(i_0_2785,plain,
    ! [X8119] :
      ( ~ is_bool(X8119)
      | X8119 = fTrue
      | X8119 = fFalse ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])]) ).

fof(i_0_2786,plain,
    ! [X8112] :
      ( ~ is_bool(X8112)
      | X8112 = fTrue
      | X8112 = fFalse ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fTrue_1_1_T])]) ).

fof(i_0_2787,plain,
    ~ hBOOL(fFalse),
    inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).

cnf(i_0_2788,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_1488]),
    [final] ).

cnf(i_0_2789,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_1489]),
    [final] ).

cnf(i_0_2790,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_1490]),
    [final] ).

cnf(i_0_2791,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1488]),
    [final] ).

cnf(i_0_2792,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1489]),
    [final] ).

cnf(i_0_2793,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | X5 = X1
    | X4 = X2
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A1677245848t_bool(X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1491]),
    [final] ).

cnf(i_0_2794,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | X2 = X4
    | X1 = X5
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A1677245848t_bool(X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1491]),
    [final] ).

cnf(i_0_2795,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X5),X6)),hAPP_f412050202t_bool(f,X4)))
    | X2 = X5
    | X1 = X6
    | X5 = X6
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X5),X6)),hAPP_A1677245848t_bool(X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X6)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1492]),
    [final] ).

cnf(i_0_2796,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A1677245848t_bool(X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1493]),
    [final] ).

cnf(i_0_2797,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A1677245848t_bool(X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1493]),
    [final] ).

cnf(i_0_2798,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))) ),
    inference(split_conjunct,[status(thm)],[i_0_1490]),
    [final] ).

cnf(i_0_2799,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    inference(split_conjunct,[status(thm)],[fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]),
    [final] ).

cnf(i_0_2800,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    inference(split_conjunct,[status(thm)],[fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]),
    [final] ).

cnf(i_0_2801,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    inference(split_conjunct,[status(thm)],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]),
    [final] ).

cnf(i_0_2802,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))),arrow_1721807329e_Prof)),
    inference(split_conjunct,[status(thm)],[fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai]),
    [final] ).

cnf(i_0_2803,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A1677245848t_bool(X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | X5 = X1
    | X4 = X2
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1491]),
    [final] ).

cnf(i_0_2804,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A1677245848t_bool(X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | X2 = X4
    | X1 = X5
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1491]),
    [final] ).

cnf(i_0_2805,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X5),X6)),hAPP_A1677245848t_bool(X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X5),X6)),hAPP_f412050202t_bool(f,X4)))
    | X2 = X5
    | X1 = X6
    | X5 = X6
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X6)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1492]),
    [final] ).

cnf(i_0_2806,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A1677245848t_bool(X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1493]),
    [final] ).

cnf(i_0_2807,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_A1677245848t_bool(X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1493]),
    [final] ).

cnf(i_0_2808,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk28_0),one_one_nat)))),lab)),lba)))),
    inference(split_conjunct,[status(thm)],[i_0_1494]),
    [final] ).

cnf(i_0_2809,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk27_0),one_one_nat)))),lab)),lba)))),
    inference(split_conjunct,[status(thm)],[i_0_1495]),
    [final] ).

cnf(i_0_2810,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))),
    inference(split_conjunct,[status(thm)],[fact_183_n_I3_J]),
    [final] ).

cnf(i_0_2811,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X5)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X4,esk9_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X5,esk9_5(X3,X4,X5,X1,X2))))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_2812,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X5)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X5,esk9_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X4,esk9_5(X3,X5,X4,X1,X2))))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_2813,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X4)),hAPP_f412050202t_bool(f,X5)))
    | X1 = X4
    | X2 = X4
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X4)),hAPP_A1677245848t_bool(X5,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1497]),
    [final] ).

cnf(i_0_2814,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X1)),hAPP_f412050202t_bool(f,X5)))
    | X4 = X2
    | X1 = X2
    | X4 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X1)),hAPP_A1677245848t_bool(X5,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1497]),
    [final] ).

cnf(i_0_2815,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk28_0)) ),
    inference(split_conjunct,[status(thm)],[i_0_1494]),
    [final] ).

cnf(i_0_2816,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk27_0)) ),
    inference(split_conjunct,[status(thm)],[i_0_1495]),
    [final] ).

cnf(i_0_2817,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),n)) ),
    inference(split_conjunct,[status(thm)],[i_0_1498]),
    [final] ).

cnf(i_0_2818,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),X1))),lab)),lba)),arrow_1721807329e_Prof)),
    inference(split_conjunct,[status(thm)],[i_0_1499]),
    [final] ).

cnf(i_0_2819,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X5)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X4,esk9_5(X3,X4,X5,X1,X2))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X5,esk9_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X4)))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_2820,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X5)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X5,esk9_5(X3,X5,X4,X1,X2))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X4,esk9_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X4)))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_2821,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X4)),hAPP_f412050202t_bool(f,X5)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk3_5(X5,X3,X4,X1,X2))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X4)),hAPP_A1677245848t_bool(X5,esk3_5(X5,X3,X4,X1,X2))))
    | X1 = X4
    | X2 = X4
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1497]),
    [final] ).

cnf(i_0_2822,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X1)),hAPP_f412050202t_bool(f,X5)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X1)),hAPP_A1677245848t_bool(X5,esk3_5(X3,X5,X2,X4,X1))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk3_5(X3,X5,X2,X4,X1))))
    | X4 = X2
    | X1 = X2
    | X4 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1497]),
    [final] ).

cnf(i_0_2823,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | is_Arr43961803e_indi(esk1_6(X3,X6,X1,X2,X4,X5))
    | X5 = X1
    | X4 = X2
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1491]),
    [final] ).

cnf(i_0_2824,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | is_Arr43961803e_indi(esk1_6(X6,X3,X4,X5,X1,X2))
    | X2 = X4
    | X1 = X5
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1491]),
    [final] ).

cnf(i_0_2825,plain,
    ( is_Arr43961803e_indi(esk2_6(X1,X2,X3,X4,X5,X6))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),hAPP_f412050202t_bool(f,X1)))
    | X6 = X3
    | X5 = X4
    | X3 = X4
    | X5 = X6
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X5),X6)),hAPP_f412050202t_bool(f,X2)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X2),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_1492]),
    [final] ).

cnf(i_0_2826,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | is_Arr43961803e_indi(esk4_6(X3,X6,X1,X2,X4,X5))
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1493]),
    [final] ).

cnf(i_0_2827,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X5)),hAPP_f412050202t_bool(f,X6)))
    | is_Arr43961803e_indi(esk4_6(X6,X3,X4,X5,X1,X2))
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X6),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1493]),
    [final] ).

cnf(i_0_2828,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X1,esk245_4(X2,X1,X3,X4))),hAPP_f899613158t_bool(X1,esk244_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1500]),
    [final] ).

cnf(i_0_2829,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X1,esk410_4(X1,X2,X3,X4))),hAPP_f899613158t_bool(X1,esk411_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1501]),
    [final] ).

cnf(i_0_2830,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X1,esk227_4(X2,X1,X3,X4))),hAPP_n588788980t_bool(X1,esk226_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1502]),
    [final] ).

cnf(i_0_2831,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,esk203_4(X2,X1,X3,X4))),hAPP_n588788980t_bool(X1,esk202_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1503]),
    [final] ).

cnf(i_0_2832,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X1,esk392_4(X1,X2,X3,X4))),hAPP_n588788980t_bool(X1,esk393_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1504]),
    [final] ).

cnf(i_0_2833,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,esk466_4(X1,X2,X3,X4))),hAPP_n588788980t_bool(X1,esk467_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1505]),
    [final] ).

cnf(i_0_2834,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X1,esk239_4(X2,X1,X3,X4))),hAPP_f769545506l_bool(X1,esk238_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1506]),
    [final] ).

cnf(i_0_2835,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X1,esk404_4(X1,X2,X3,X4))),hAPP_f769545506l_bool(X1,esk405_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1507]),
    [final] ).

cnf(i_0_2836,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X1,esk221_4(X2,X1,X3,X4))),hAPP_n1674354836l_bool(X1,esk220_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1508]),
    [final] ).

cnf(i_0_2837,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,esk197_4(X2,X1,X3,X4))),hAPP_n1674354836l_bool(X1,esk196_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1509]),
    [final] ).

cnf(i_0_2838,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X1,esk386_4(X1,X2,X3,X4))),hAPP_n1674354836l_bool(X1,esk387_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1510]),
    [final] ).

cnf(i_0_2839,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,esk460_4(X1,X2,X3,X4))),hAPP_n1674354836l_bool(X1,esk461_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1511]),
    [final] ).

cnf(i_0_2840,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X1,esk241_4(X2,X1,X3,X4))),hAPP_f1449238989l_bool(X1,esk240_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1512]),
    [final] ).

cnf(i_0_2841,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X1,esk406_4(X1,X2,X3,X4))),hAPP_f1449238989l_bool(X1,esk407_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1513]),
    [final] ).

cnf(i_0_2842,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X1,esk223_4(X2,X1,X3,X4))),hAPP_n295497947l_bool(X1,esk222_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1514]),
    [final] ).

cnf(i_0_2843,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,esk199_4(X2,X1,X3,X4))),hAPP_n295497947l_bool(X1,esk198_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1515]),
    [final] ).

cnf(i_0_2844,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X1,esk388_4(X1,X2,X3,X4))),hAPP_n295497947l_bool(X1,esk389_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1516]),
    [final] ).

cnf(i_0_2845,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,esk462_4(X1,X2,X3,X4))),hAPP_n295497947l_bool(X1,esk463_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1517]),
    [final] ).

cnf(i_0_2846,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X1,esk243_4(X2,X1,X3,X4))),hAPP_f226010187l_bool(X1,esk242_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1518]),
    [final] ).

cnf(i_0_2847,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X1,esk408_4(X1,X2,X3,X4))),hAPP_f226010187l_bool(X1,esk409_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1519]),
    [final] ).

cnf(i_0_2848,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X1,esk225_4(X2,X1,X3,X4))),hAPP_n2095207769l_bool(X1,esk224_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1520]),
    [final] ).

cnf(i_0_2849,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,esk201_4(X2,X1,X3,X4))),hAPP_n2095207769l_bool(X1,esk200_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1521]),
    [final] ).

cnf(i_0_2850,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X1,esk390_4(X1,X2,X3,X4))),hAPP_n2095207769l_bool(X1,esk391_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1522]),
    [final] ).

cnf(i_0_2851,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,esk464_4(X1,X2,X3,X4))),hAPP_n2095207769l_bool(X1,esk465_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_2852,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X1,esk235_4(X2,X1,X3,X4))),hAPP_f1061584978t_bool(X1,esk234_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1524]),
    [final] ).

cnf(i_0_2853,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X1,esk400_4(X1,X2,X3,X4))),hAPP_f1061584978t_bool(X1,esk401_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1525]),
    [final] ).

cnf(i_0_2854,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X1,esk217_4(X2,X1,X3,X4))),hAPP_n454528608t_bool(X1,esk216_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1526]),
    [final] ).

cnf(i_0_2855,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,esk193_4(X2,X1,X3,X4))),hAPP_n454528608t_bool(X1,esk192_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1527]),
    [final] ).

cnf(i_0_2856,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X1,esk382_4(X1,X2,X3,X4))),hAPP_n454528608t_bool(X1,esk383_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1528]),
    [final] ).

cnf(i_0_2857,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,esk456_4(X1,X2,X3,X4))),hAPP_n454528608t_bool(X1,esk457_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_2858,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X1,esk265_4(X2,X1,X3,X4))),hAPP_f1363542492t_bool(X1,esk264_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1530]),
    [final] ).

cnf(i_0_2859,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X1,esk430_4(X1,X2,X3,X4))),hAPP_f1363542492t_bool(X1,esk431_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1531]),
    [final] ).

cnf(i_0_2860,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X1,esk257_4(X2,X1,X3,X4))),hAPP_f856106132t_bool(X1,esk256_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1532]),
    [final] ).

cnf(i_0_2861,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X1,esk422_4(X1,X2,X3,X4))),hAPP_f856106132t_bool(X1,esk423_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1533]),
    [final] ).

cnf(i_0_2862,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X1,esk255_4(X2,X1,X3,X4))),hAPP_f985923321t_bool(X1,esk254_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1534]),
    [final] ).

cnf(i_0_2863,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X1,esk420_4(X1,X2,X3,X4))),hAPP_f985923321t_bool(X1,esk421_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1535]),
    [final] ).

cnf(i_0_2864,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X1,esk253_4(X2,X1,X3,X4))),hAPP_f839525755t_bool(X1,esk252_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1536]),
    [final] ).

cnf(i_0_2865,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X1,esk418_4(X1,X2,X3,X4))),hAPP_f839525755t_bool(X1,esk419_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1537]),
    [final] ).

cnf(i_0_2866,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X1,esk251_4(X2,X1,X3,X4))),hAPP_f464145314t_bool(X1,esk250_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1538]),
    [final] ).

cnf(i_0_2867,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X1,esk416_4(X1,X2,X3,X4))),hAPP_f464145314t_bool(X1,esk417_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1539]),
    [final] ).

cnf(i_0_2868,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,esk261_4(X2,X1,X3,X4))),hAPP_f2026336507t_bool(X1,esk260_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1540]),
    [final] ).

cnf(i_0_2869,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,esk189_4(X2,X1,X3,X4))),hAPP_f2026336507t_bool(X1,esk188_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1541]),
    [final] ).

cnf(i_0_2870,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,esk426_4(X1,X2,X3,X4))),hAPP_f2026336507t_bool(X1,esk427_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1542]),
    [final] ).

cnf(i_0_2871,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,esk452_4(X1,X2,X3,X4))),hAPP_f2026336507t_bool(X1,esk453_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1543]),
    [final] ).

cnf(i_0_2872,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,esk263_4(X2,X1,X3,X4))),hAPP_f543204480t_bool(X1,esk262_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1544]),
    [final] ).

cnf(i_0_2873,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,esk187_4(X2,X1,X3,X4))),hAPP_f543204480t_bool(X1,esk186_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1545]),
    [final] ).

cnf(i_0_2874,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,esk428_4(X1,X2,X3,X4))),hAPP_f543204480t_bool(X1,esk429_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1546]),
    [final] ).

cnf(i_0_2875,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,esk450_4(X1,X2,X3,X4))),hAPP_f543204480t_bool(X1,esk451_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1547]),
    [final] ).

cnf(i_0_2876,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X1,esk259_4(X2,X1,X3,X4))),hAPP_b1013836512t_bool(X1,esk258_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1548]),
    [final] ).

cnf(i_0_2877,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X1,esk424_4(X1,X2,X3,X4))),hAPP_b1013836512t_bool(X1,esk425_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1549]),
    [final] ).

cnf(i_0_2878,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X1,esk233_4(X2,X1,X3,X4))),hAPP_f800510211t_bool(X1,esk232_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1550]),
    [final] ).

cnf(i_0_2879,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,esk185_4(X2,X1,X3,X4))),hAPP_f800510211t_bool(X1,esk184_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1551]),
    [final] ).

cnf(i_0_2880,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X1,esk398_4(X1,X2,X3,X4))),hAPP_f800510211t_bool(X1,esk399_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1552]),
    [final] ).

cnf(i_0_2881,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,esk448_4(X1,X2,X3,X4))),hAPP_f800510211t_bool(X1,esk449_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1553]),
    [final] ).

cnf(i_0_2882,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,esk215_4(X2,X1,X3,X4))),hAPP_n1699378549t_bool(X1,esk214_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1554]),
    [final] ).

cnf(i_0_2883,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,esk191_4(X2,X1,X3,X4))),hAPP_n1699378549t_bool(X1,esk190_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1555]),
    [final] ).

cnf(i_0_2884,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,esk380_4(X1,X2,X3,X4))),hAPP_n1699378549t_bool(X1,esk381_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1556]),
    [final] ).

cnf(i_0_2885,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,esk454_4(X1,X2,X3,X4))),hAPP_n1699378549t_bool(X1,esk455_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1557]),
    [final] ).

cnf(i_0_2886,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X1,esk237_4(X2,X1,X3,X4))),hAPP_f632777549i_bool(X1,esk236_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1558]),
    [final] ).

cnf(i_0_2887,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X1,esk402_4(X1,X2,X3,X4))),hAPP_f632777549i_bool(X1,esk403_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1559]),
    [final] ).

cnf(i_0_2888,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X1,esk219_4(X2,X1,X3,X4))),hAPP_n821919323i_bool(X1,esk218_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1560]),
    [final] ).

cnf(i_0_2889,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,esk195_4(X2,X1,X3,X4))),hAPP_n821919323i_bool(X1,esk194_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1561]),
    [final] ).

cnf(i_0_2890,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X1,esk384_4(X1,X2,X3,X4))),hAPP_n821919323i_bool(X1,esk385_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1562]),
    [final] ).

cnf(i_0_2891,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,esk458_4(X1,X2,X3,X4))),hAPP_n821919323i_bool(X1,esk459_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1563]),
    [final] ).

cnf(i_0_2892,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X1,esk249_4(X2,X1,X3,X4))),hAPP_f861874780t_bool(X1,esk248_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1564]),
    [final] ).

cnf(i_0_2893,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X1,esk414_4(X1,X2,X3,X4))),hAPP_f861874780t_bool(X1,esk415_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1565]),
    [final] ).

cnf(i_0_2894,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X1,esk231_4(X2,X1,X3,X4))),hAPP_n539120590t_bool(X1,esk230_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1566]),
    [final] ).

cnf(i_0_2895,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,esk207_4(X2,X1,X3,X4))),hAPP_n539120590t_bool(X1,esk206_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2896,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X1,esk396_4(X1,X2,X3,X4))),hAPP_n539120590t_bool(X1,esk397_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1568]),
    [final] ).

cnf(i_0_2897,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,esk470_4(X1,X2,X3,X4))),hAPP_n539120590t_bool(X1,esk471_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1569]),
    [final] ).

cnf(i_0_2898,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X1,esk281_4(X2,X1,X3,X4))),hAPP_f1358350510ol_nat(X1,esk280_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2899,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X1,esk446_4(X1,X2,X3,X4))),hAPP_f1358350510ol_nat(X1,esk447_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1571]),
    [final] ).

cnf(i_0_2900,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X1,esk273_4(X2,X1,X3,X4))),hAPP_f816335862ol_nat(X1,esk272_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2901,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X1,esk438_4(X1,X2,X3,X4))),hAPP_f816335862ol_nat(X1,esk439_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1573]),
    [final] ).

cnf(i_0_2902,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X1,esk271_4(X2,X1,X3,X4))),hAPP_f897066961ol_nat(X1,esk270_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1574]),
    [final] ).

cnf(i_0_2903,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X1,esk436_4(X1,X2,X3,X4))),hAPP_f897066961ol_nat(X1,esk437_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1575]),
    [final] ).

cnf(i_0_2904,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X1,esk269_4(X2,X1,X3,X4))),hAPP_f1695077327ol_nat(X1,esk268_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1576]),
    [final] ).

cnf(i_0_2905,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X1,esk434_4(X1,X2,X3,X4))),hAPP_f1695077327ol_nat(X1,esk435_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1577]),
    [final] ).

cnf(i_0_2906,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X1,esk267_4(X2,X1,X3,X4))),hAPP_f1313392232ol_nat(X1,esk266_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1578]),
    [final] ).

cnf(i_0_2907,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X1,esk432_4(X1,X2,X3,X4))),hAPP_f1313392232ol_nat(X1,esk433_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1579]),
    [final] ).

cnf(i_0_2908,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,esk279_4(X2,X1,X3,X4))),hAPP_f2030293770ol_nat(X1,esk278_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1580]),
    [final] ).

cnf(i_0_2909,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,esk211_4(X2,X1,X3,X4))),hAPP_f2030293770ol_nat(X1,esk210_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1581]),
    [final] ).

cnf(i_0_2910,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,esk444_4(X1,X2,X3,X4))),hAPP_f2030293770ol_nat(X1,esk445_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1582]),
    [final] ).

cnf(i_0_2911,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,esk474_4(X1,X2,X3,X4))),hAPP_f2030293770ol_nat(X1,esk475_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1583]),
    [final] ).

cnf(i_0_2912,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X1,esk209_4(X2,X1,X3,X4))),hAPP_f22106695ol_nat(X1,esk208_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1584]),
    [final] ).

cnf(i_0_2913,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X1,esk472_4(X1,X2,X3,X4))),hAPP_f22106695ol_nat(X1,esk473_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1585]),
    [final] ).

cnf(i_0_2914,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X1,esk275_4(X2,X1,X3,X4))),hAPP_bool_nat(X1,esk274_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1586]),
    [final] ).

cnf(i_0_2915,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X1,esk440_4(X1,X2,X3,X4))),hAPP_bool_nat(X1,esk441_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1587]),
    [final] ).

cnf(i_0_2916,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,esk277_4(X2,X1,X3,X4))),hAPP_f2120083535ol_nat(X1,esk276_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1588]),
    [final] ).

cnf(i_0_2917,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X2)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,esk213_4(X2,X1,X3,X4))),hAPP_f2120083535ol_nat(X1,esk212_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1589]),
    [final] ).

cnf(i_0_2918,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,esk442_4(X1,X2,X3,X4))),hAPP_f2120083535ol_nat(X1,esk443_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1590]),
    [final] ).

cnf(i_0_2919,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,esk476_4(X1,X2,X3,X4))),hAPP_f2120083535ol_nat(X1,esk477_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1591]),
    [final] ).

cnf(i_0_2920,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X1,esk247_4(X2,X1,X3,X4))),hAPP_f54304608l_bool(X1,esk246_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1592]),
    [final] ).

cnf(i_0_2921,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X1,esk412_4(X1,X2,X3,X4))),hAPP_f54304608l_bool(X1,esk413_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1593]),
    [final] ).

cnf(i_0_2922,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk229_4(X2,X1,X3,X4))),hAPP_nat_bool(X1,esk228_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1594]),
    [final] ).

cnf(i_0_2923,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X2)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,esk205_4(X2,X1,X3,X4))),hAPP_nat_bool(X1,esk204_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1595]),
    [final] ).

cnf(i_0_2924,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk394_4(X1,X2,X3,X4))),hAPP_nat_bool(X1,esk395_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1596]),
    [final] ).

cnf(i_0_2925,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,esk468_4(X1,X2,X3,X4))),hAPP_nat_bool(X1,esk469_4(X1,X2,X3,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1597]),
    [final] ).

cnf(i_0_2926,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_f899613158t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X1,esk139_4(X2,X1,X3,X4))),hAPP_f899613158t_bool(X1,esk138_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_f899613158t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1598]),
    [final] ).

cnf(i_0_2927,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_n588788980t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X1,esk121_4(X2,X1,X3,X4))),hAPP_n588788980t_bool(X1,esk120_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_n588788980t_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1599]),
    [final] ).

cnf(i_0_2928,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_n588788980t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,esk97_4(X2,X1,X3,X4))),hAPP_n588788980t_bool(X1,esk96_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),hAPP_n588788980t_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1600]),
    [final] ).

cnf(i_0_2929,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X3),hAPP_f899613158t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(X1,esk342_4(X2,X3,X1,X4))),hAPP_f899613158t_bool(X1,esk343_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X3),hAPP_f899613158t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1601]),
    [final] ).

cnf(i_0_2930,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X3),hAPP_n588788980t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X1,esk324_4(X2,X3,X1,X4))),hAPP_n588788980t_bool(X1,esk325_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X3),hAPP_n588788980t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2931,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X3),hAPP_n588788980t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,esk300_4(X2,X3,X1,X4))),hAPP_n588788980t_bool(X1,esk301_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),hAPP_n588788980t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1603]),
    [final] ).

cnf(i_0_2932,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_f769545506l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X1,esk133_4(X2,X1,X3,X4))),hAPP_f769545506l_bool(X1,esk132_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_f769545506l_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1604]),
    [final] ).

cnf(i_0_2933,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_n1674354836l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X1,esk115_4(X2,X1,X3,X4))),hAPP_n1674354836l_bool(X1,esk114_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_n1674354836l_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1605]),
    [final] ).

cnf(i_0_2934,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_n1674354836l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,esk91_4(X2,X1,X3,X4))),hAPP_n1674354836l_bool(X1,esk90_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),hAPP_n1674354836l_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1606]),
    [final] ).

cnf(i_0_2935,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X3),hAPP_f769545506l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(X1,esk336_4(X2,X3,X1,X4))),hAPP_f769545506l_bool(X1,esk337_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X3),hAPP_f769545506l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1607]),
    [final] ).

cnf(i_0_2936,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X3),hAPP_n1674354836l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X1,esk318_4(X2,X3,X1,X4))),hAPP_n1674354836l_bool(X1,esk319_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X3),hAPP_n1674354836l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1608]),
    [final] ).

cnf(i_0_2937,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X3),hAPP_n1674354836l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,esk294_4(X2,X3,X1,X4))),hAPP_n1674354836l_bool(X1,esk295_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),hAPP_n1674354836l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1609]),
    [final] ).

cnf(i_0_2938,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_f1449238989l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X1,esk135_4(X2,X1,X3,X4))),hAPP_f1449238989l_bool(X1,esk134_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_f1449238989l_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1610]),
    [final] ).

cnf(i_0_2939,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_n295497947l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X1,esk117_4(X2,X1,X3,X4))),hAPP_n295497947l_bool(X1,esk116_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_n295497947l_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1611]),
    [final] ).

cnf(i_0_2940,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_n295497947l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,esk93_4(X2,X1,X3,X4))),hAPP_n295497947l_bool(X1,esk92_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),hAPP_n295497947l_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1612]),
    [final] ).

cnf(i_0_2941,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X3),hAPP_f1449238989l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(X1,esk338_4(X2,X3,X1,X4))),hAPP_f1449238989l_bool(X1,esk339_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X3),hAPP_f1449238989l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1613]),
    [final] ).

cnf(i_0_2942,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X3),hAPP_n295497947l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X1,esk320_4(X2,X3,X1,X4))),hAPP_n295497947l_bool(X1,esk321_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X3),hAPP_n295497947l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1614]),
    [final] ).

cnf(i_0_2943,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X3),hAPP_n295497947l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,esk296_4(X2,X3,X1,X4))),hAPP_n295497947l_bool(X1,esk297_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),hAPP_n295497947l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_2944,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_f226010187l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X1,esk137_4(X2,X1,X3,X4))),hAPP_f226010187l_bool(X1,esk136_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_f226010187l_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_2945,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_n2095207769l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X1,esk119_4(X2,X1,X3,X4))),hAPP_n2095207769l_bool(X1,esk118_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_n2095207769l_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_2946,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_n2095207769l_bool(X1,X4)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,esk95_4(X2,X1,X3,X4))),hAPP_n2095207769l_bool(X1,esk94_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),hAPP_n2095207769l_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1618]),
    [final] ).

cnf(i_0_2947,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X3),hAPP_f226010187l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(X1,esk340_4(X2,X3,X1,X4))),hAPP_f226010187l_bool(X1,esk341_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X3),hAPP_f226010187l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1619]),
    [final] ).

cnf(i_0_2948,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X3),hAPP_n2095207769l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X1,esk322_4(X2,X3,X1,X4))),hAPP_n2095207769l_bool(X1,esk323_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X3),hAPP_n2095207769l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1620]),
    [final] ).

cnf(i_0_2949,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X3),hAPP_n2095207769l_bool(X1,X2)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,esk298_4(X2,X3,X1,X4))),hAPP_n2095207769l_bool(X1,esk299_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),hAPP_n2095207769l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1621]),
    [final] ).

cnf(i_0_2950,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_f1061584978t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X1,esk129_4(X2,X1,X3,X4))),hAPP_f1061584978t_bool(X1,esk128_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_f1061584978t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1622]),
    [final] ).

cnf(i_0_2951,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_n454528608t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X1,esk111_4(X2,X1,X3,X4))),hAPP_n454528608t_bool(X1,esk110_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_n454528608t_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1623]),
    [final] ).

cnf(i_0_2952,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_n454528608t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,esk87_4(X2,X1,X3,X4))),hAPP_n454528608t_bool(X1,esk86_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),hAPP_n454528608t_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1624]),
    [final] ).

cnf(i_0_2953,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),hAPP_f1061584978t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(X1,esk332_4(X2,X3,X1,X4))),hAPP_f1061584978t_bool(X1,esk333_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),hAPP_f1061584978t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1625]),
    [final] ).

cnf(i_0_2954,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),hAPP_n454528608t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X1,esk314_4(X2,X3,X1,X4))),hAPP_n454528608t_bool(X1,esk315_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),hAPP_n454528608t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1626]),
    [final] ).

cnf(i_0_2955,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),hAPP_n454528608t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,esk290_4(X2,X3,X1,X4))),hAPP_n454528608t_bool(X1,esk291_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),hAPP_n454528608t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1627]),
    [final] ).

cnf(i_0_2956,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f1363542492t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X1,esk159_4(X2,X1,X3,X4))),hAPP_f1363542492t_bool(X1,esk158_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f1363542492t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1628]),
    [final] ).

cnf(i_0_2957,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f856106132t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X1,esk151_4(X2,X1,X3,X4))),hAPP_f856106132t_bool(X1,esk150_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f856106132t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1629]),
    [final] ).

cnf(i_0_2958,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f985923321t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X1,esk149_4(X2,X1,X3,X4))),hAPP_f985923321t_bool(X1,esk148_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f985923321t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1630]),
    [final] ).

cnf(i_0_2959,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f839525755t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X1,esk147_4(X2,X1,X3,X4))),hAPP_f839525755t_bool(X1,esk146_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f839525755t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1631]),
    [final] ).

cnf(i_0_2960,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f464145314t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X1,esk145_4(X2,X1,X3,X4))),hAPP_f464145314t_bool(X1,esk144_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f464145314t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1632]),
    [final] ).

cnf(i_0_2961,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,esk155_4(X2,X1,X3,X4))),hAPP_f2026336507t_bool(X1,esk154_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1633]),
    [final] ).

cnf(i_0_2962,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,esk83_4(X2,X1,X3,X4))),hAPP_f2026336507t_bool(X1,esk82_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f2026336507t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1634]),
    [final] ).

cnf(i_0_2963,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,esk157_4(X2,X1,X3,X4))),hAPP_f543204480t_bool(X1,esk156_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1635]),
    [final] ).

cnf(i_0_2964,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,esk81_4(X2,X1,X3,X4))),hAPP_f543204480t_bool(X1,esk80_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f543204480t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1636]),
    [final] ).

cnf(i_0_2965,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_b1013836512t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X1,esk153_4(X2,X1,X3,X4))),hAPP_b1013836512t_bool(X1,esk152_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_b1013836512t_bool(X1,X3)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1637]),
    [final] ).

cnf(i_0_2966,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f800510211t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X1,esk127_4(X2,X1,X3,X4))),hAPP_f800510211t_bool(X1,esk126_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f800510211t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1638]),
    [final] ).

cnf(i_0_2967,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f800510211t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,esk79_4(X2,X1,X3,X4))),hAPP_f800510211t_bool(X1,esk78_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1639]),
    [final] ).

cnf(i_0_2968,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_n1699378549t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,esk109_4(X2,X1,X3,X4))),hAPP_n1699378549t_bool(X1,esk108_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_n1699378549t_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1640]),
    [final] ).

cnf(i_0_2969,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_n1699378549t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,esk85_4(X2,X1,X3,X4))),hAPP_n1699378549t_bool(X1,esk84_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_n1699378549t_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1641]),
    [final] ).

cnf(i_0_2970,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f1363542492t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(X1,esk362_4(X2,X3,X1,X4))),hAPP_f1363542492t_bool(X1,esk363_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f1363542492t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1642]),
    [final] ).

cnf(i_0_2971,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f856106132t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(X1,esk354_4(X2,X3,X1,X4))),hAPP_f856106132t_bool(X1,esk355_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f856106132t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1643]),
    [final] ).

cnf(i_0_2972,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f985923321t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(X1,esk352_4(X2,X3,X1,X4))),hAPP_f985923321t_bool(X1,esk353_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f985923321t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1644]),
    [final] ).

cnf(i_0_2973,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f839525755t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(X1,esk350_4(X2,X3,X1,X4))),hAPP_f839525755t_bool(X1,esk351_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f839525755t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1645]),
    [final] ).

cnf(i_0_2974,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f464145314t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(X1,esk348_4(X2,X3,X1,X4))),hAPP_f464145314t_bool(X1,esk349_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f464145314t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1646]),
    [final] ).

cnf(i_0_2975,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f2026336507t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,esk358_4(X2,X3,X1,X4))),hAPP_f2026336507t_bool(X1,esk359_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f2026336507t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1647]),
    [final] ).

cnf(i_0_2976,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f2026336507t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,esk286_4(X2,X3,X1,X4))),hAPP_f2026336507t_bool(X1,esk287_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),hAPP_f2026336507t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1648]),
    [final] ).

cnf(i_0_2977,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f543204480t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,esk360_4(X2,X3,X1,X4))),hAPP_f543204480t_bool(X1,esk361_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f543204480t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_2978,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f543204480t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,esk284_4(X2,X3,X1,X4))),hAPP_f543204480t_bool(X1,esk285_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),hAPP_f543204480t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_2979,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_b1013836512t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(X1,esk356_4(X2,X3,X1,X4))),hAPP_b1013836512t_bool(X1,esk357_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_b1013836512t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1651]),
    [final] ).

cnf(i_0_2980,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f800510211t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X1,esk330_4(X2,X3,X1,X4))),hAPP_f800510211t_bool(X1,esk331_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f800510211t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1652]),
    [final] ).

cnf(i_0_2981,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_f800510211t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,esk282_4(X2,X3,X1,X4))),hAPP_f800510211t_bool(X1,esk283_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),hAPP_f800510211t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1653]),
    [final] ).

cnf(i_0_2982,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_n1699378549t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,esk312_4(X2,X3,X1,X4))),hAPP_n1699378549t_bool(X1,esk313_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_n1699378549t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1654]),
    [final] ).

cnf(i_0_2983,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),hAPP_n1699378549t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,esk288_4(X2,X3,X1,X4))),hAPP_n1699378549t_bool(X1,esk289_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),hAPP_n1699378549t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1655]),
    [final] ).

cnf(i_0_2984,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_f632777549i_bool(X1,X4)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X1,esk131_4(X2,X1,X3,X4))),hAPP_f632777549i_bool(X1,esk130_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_f632777549i_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1656]),
    [final] ).

cnf(i_0_2985,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_n821919323i_bool(X1,X4)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X1,esk113_4(X2,X1,X3,X4))),hAPP_n821919323i_bool(X1,esk112_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_n821919323i_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1657]),
    [final] ).

cnf(i_0_2986,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_n821919323i_bool(X1,X4)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,esk89_4(X2,X1,X3,X4))),hAPP_n821919323i_bool(X1,esk88_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),hAPP_n821919323i_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1658]),
    [final] ).

cnf(i_0_2987,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),hAPP_f632777549i_bool(X1,X2)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(X1,esk334_4(X2,X3,X1,X4))),hAPP_f632777549i_bool(X1,esk335_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),hAPP_f632777549i_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1659]),
    [final] ).

cnf(i_0_2988,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),hAPP_n821919323i_bool(X1,X2)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X1,esk316_4(X2,X3,X1,X4))),hAPP_n821919323i_bool(X1,esk317_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),hAPP_n821919323i_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1660]),
    [final] ).

cnf(i_0_2989,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),hAPP_n821919323i_bool(X1,X2)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,esk292_4(X2,X3,X1,X4))),hAPP_n821919323i_bool(X1,esk293_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),hAPP_n821919323i_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1661]),
    [final] ).

cnf(i_0_2990,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_f861874780t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X1,esk143_4(X2,X1,X3,X4))),hAPP_f861874780t_bool(X1,esk142_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_f861874780t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1662]),
    [final] ).

cnf(i_0_2991,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_n539120590t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X1,esk125_4(X2,X1,X3,X4))),hAPP_n539120590t_bool(X1,esk124_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_n539120590t_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1663]),
    [final] ).

cnf(i_0_2992,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_n539120590t_bool(X1,X4)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,esk101_4(X2,X1,X3,X4))),hAPP_n539120590t_bool(X1,esk100_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),hAPP_n539120590t_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_2993,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X3),hAPP_f861874780t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(X1,esk346_4(X2,X3,X1,X4))),hAPP_f861874780t_bool(X1,esk347_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X3),hAPP_f861874780t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1665]),
    [final] ).

cnf(i_0_2994,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X3),hAPP_n539120590t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X1,esk328_4(X2,X3,X1,X4))),hAPP_n539120590t_bool(X1,esk329_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X3),hAPP_n539120590t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1666]),
    [final] ).

cnf(i_0_2995,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X3),hAPP_n539120590t_bool(X1,X2)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,esk304_4(X2,X3,X1,X4))),hAPP_n539120590t_bool(X1,esk305_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),hAPP_n539120590t_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1667]),
    [final] ).

cnf(i_0_2996,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1358350510ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X1,esk175_4(X2,X1,X3,X4))),hAPP_f1358350510ol_nat(X1,esk174_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1358350510ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1668]),
    [final] ).

cnf(i_0_2997,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f816335862ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X1,esk167_4(X2,X1,X3,X4))),hAPP_f816335862ol_nat(X1,esk166_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f816335862ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1669]),
    [final] ).

cnf(i_0_2998,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f897066961ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X1,esk165_4(X2,X1,X3,X4))),hAPP_f897066961ol_nat(X1,esk164_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f897066961ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1670]),
    [final] ).

cnf(i_0_2999,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1695077327ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X1,esk163_4(X2,X1,X3,X4))),hAPP_f1695077327ol_nat(X1,esk162_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1695077327ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1671]),
    [final] ).

cnf(i_0_3000,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1313392232ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X1,esk161_4(X2,X1,X3,X4))),hAPP_f1313392232ol_nat(X1,esk160_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1313392232ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1672]),
    [final] ).

cnf(i_0_3001,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,esk173_4(X2,X1,X3,X4))),hAPP_f2030293770ol_nat(X1,esk172_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1673]),
    [final] ).

cnf(i_0_3002,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,esk105_4(X2,X1,X3,X4))),hAPP_f2030293770ol_nat(X1,esk104_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2030293770ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1674]),
    [final] ).

cnf(i_0_3003,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f22106695ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X1,esk103_4(X2,X1,X3,X4))),hAPP_f22106695ol_nat(X1,esk102_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f22106695ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1675]),
    [final] ).

cnf(i_0_3004,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_bool_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X1,esk169_4(X2,X1,X3,X4))),hAPP_bool_nat(X1,esk168_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_bool_nat(X1,X3)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1676]),
    [final] ).

cnf(i_0_3005,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,esk171_4(X2,X1,X3,X4))),hAPP_f2120083535ol_nat(X1,esk170_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_3006,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X1,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,esk107_4(X2,X1,X3,X4))),hAPP_f2120083535ol_nat(X1,esk106_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2120083535ol_nat(X1,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1678]),
    [final] ).

cnf(i_0_3007,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f1358350510ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(X1,esk378_4(X2,X3,X1,X4))),hAPP_f1358350510ol_nat(X1,esk379_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f1358350510ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1679]),
    [final] ).

cnf(i_0_3008,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f816335862ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(X1,esk370_4(X2,X3,X1,X4))),hAPP_f816335862ol_nat(X1,esk371_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f816335862ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1680]),
    [final] ).

cnf(i_0_3009,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f897066961ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(X1,esk368_4(X2,X3,X1,X4))),hAPP_f897066961ol_nat(X1,esk369_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f897066961ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1681]),
    [final] ).

cnf(i_0_3010,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f1695077327ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(X1,esk366_4(X2,X3,X1,X4))),hAPP_f1695077327ol_nat(X1,esk367_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f1695077327ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1682]),
    [final] ).

cnf(i_0_3011,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f1313392232ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(X1,esk364_4(X2,X3,X1,X4))),hAPP_f1313392232ol_nat(X1,esk365_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f1313392232ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1683]),
    [final] ).

cnf(i_0_3012,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f2030293770ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,esk376_4(X2,X3,X1,X4))),hAPP_f2030293770ol_nat(X1,esk377_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f2030293770ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1684]),
    [final] ).

cnf(i_0_3013,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f2030293770ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,esk308_4(X2,X3,X1,X4))),hAPP_f2030293770ol_nat(X1,esk309_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_f2030293770ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1685]),
    [final] ).

cnf(i_0_3014,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f22106695ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X1,esk306_4(X2,X3,X1,X4))),hAPP_f22106695ol_nat(X1,esk307_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_f22106695ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1686]),
    [final] ).

cnf(i_0_3015,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_bool_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(X1,esk372_4(X2,X3,X1,X4))),hAPP_bool_nat(X1,esk373_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_bool_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1687]),
    [final] ).

cnf(i_0_3016,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f2120083535ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,esk374_4(X2,X3,X1,X4))),hAPP_f2120083535ol_nat(X1,esk375_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f2120083535ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1688]),
    [final] ).

cnf(i_0_3017,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_f2120083535ol_nat(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,esk310_4(X2,X3,X1,X4))),hAPP_f2120083535ol_nat(X1,esk311_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_f2120083535ol_nat(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1689]),
    [final] ).

cnf(i_0_3018,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_f54304608l_bool(X1,X4)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X1,esk141_4(X2,X1,X3,X4))),hAPP_f54304608l_bool(X1,esk140_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_f54304608l_bool(X1,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1690]),
    [final] ).

cnf(i_0_3019,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_nat_bool(X1,X4)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk123_4(X2,X1,X3,X4))),hAPP_nat_bool(X1,esk122_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_nat_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1691]),
    [final] ).

cnf(i_0_3020,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_nat_bool(X1,X4)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,esk99_4(X2,X1,X3,X4))),hAPP_nat_bool(X1,esk98_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),hAPP_nat_bool(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1692]),
    [final] ).

cnf(i_0_3021,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X3),hAPP_f54304608l_bool(X1,X2)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(X1,esk344_4(X2,X3,X1,X4))),hAPP_f54304608l_bool(X1,esk345_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X3),hAPP_f54304608l_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1693]),
    [final] ).

cnf(i_0_3022,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X3),hAPP_nat_bool(X1,X2)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk326_4(X2,X3,X1,X4))),hAPP_nat_bool(X1,esk327_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X3),hAPP_nat_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1694]),
    [final] ).

cnf(i_0_3023,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X3),hAPP_nat_bool(X1,X2)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,esk302_4(X2,X3,X1,X4))),hAPP_nat_bool(X1,esk303_4(X2,X3,X1,X4))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),hAPP_nat_bool(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1695]),
    [final] ).

cnf(i_0_3024,plain,
    ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),X1))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X2))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X1))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X2)))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1696]),
    [final] ).

cnf(i_0_3025,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_f412050202t_bool(f,X4)))
    | X2 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_A1677245848t_bool(X4,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1697]),
    [final] ).

cnf(i_0_3026,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_f412050202t_bool(f,X4)))
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_A1677245848t_bool(X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1697]),
    [final] ).

cnf(i_0_3027,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_f412050202t_bool(f,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_A1677245848t_bool(X4,esk5_4(X3,X4,X2,X1))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk5_4(X3,X4,X2,X1))))
    | X2 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1697]),
    [final] ).

cnf(i_0_3028,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_f412050202t_bool(f,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_A1677245848t_bool(X4,esk5_4(X4,X3,X1,X2))))
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1697]),
    [final] ).

cnf(i_0_3029,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X1)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1698]),
    [final] ).

cnf(i_0_3030,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1))
    | hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),X1))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X2)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X1))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X2))))) ),
    inference(split_conjunct,[status(thm)],[i_0_1699]),
    [final] ).

cnf(i_0_3031,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3032,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X4,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A1677245848t_bool(X3,esk14_4(X4,X3,X1,X2))))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1701]),
    [final] ).

cnf(i_0_3033,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3034,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3035,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3036,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3037,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X5)))
    | is_Arr43961803e_indi(esk9_5(X3,X4,X5,X1,X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X4)))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_3038,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X5)))
    | is_Arr43961803e_indi(esk9_5(X3,X5,X4,X1,X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(X3,X4)))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_3039,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X1)),hAPP_f412050202t_bool(f,X5)))
    | is_Arr43961803e_indi(esk3_5(X3,X5,X2,X4,X1))
    | X4 = X2
    | X1 = X2
    | X4 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1497]),
    [final] ).

cnf(i_0_3040,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X4)),hAPP_f412050202t_bool(f,X5)))
    | is_Arr43961803e_indi(esk3_5(X5,X3,X4,X1,X2))
    | X1 = X4
    | X2 = X4
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X5),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1497]),
    [final] ).

cnf(i_0_3041,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X1)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),X2)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1698]),
    [final] ).

cnf(i_0_3042,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk410_4(X1,X2,X3,X4)),esk411_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1501]),
    [final] ).

cnf(i_0_3043,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk245_4(X1,X2,X3,X4)),esk244_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1500]),
    [final] ).

cnf(i_0_3044,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk392_4(X1,X2,X3,X4)),esk393_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1504]),
    [final] ).

cnf(i_0_3045,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk466_4(X1,X2,X3,X4)),esk467_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1505]),
    [final] ).

cnf(i_0_3046,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk227_4(X1,X2,X3,X4)),esk226_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1502]),
    [final] ).

cnf(i_0_3047,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk203_4(X1,X2,X3,X4)),esk202_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1503]),
    [final] ).

cnf(i_0_3048,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk404_4(X1,X2,X3,X4)),esk405_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1507]),
    [final] ).

cnf(i_0_3049,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk239_4(X1,X2,X3,X4)),esk238_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1506]),
    [final] ).

cnf(i_0_3050,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk386_4(X1,X2,X3,X4)),esk387_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1510]),
    [final] ).

cnf(i_0_3051,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk460_4(X1,X2,X3,X4)),esk461_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1511]),
    [final] ).

cnf(i_0_3052,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk221_4(X1,X2,X3,X4)),esk220_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1508]),
    [final] ).

cnf(i_0_3053,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk197_4(X1,X2,X3,X4)),esk196_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1509]),
    [final] ).

cnf(i_0_3054,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk406_4(X1,X2,X3,X4)),esk407_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1513]),
    [final] ).

cnf(i_0_3055,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk241_4(X1,X2,X3,X4)),esk240_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1512]),
    [final] ).

cnf(i_0_3056,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk388_4(X1,X2,X3,X4)),esk389_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1516]),
    [final] ).

cnf(i_0_3057,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk462_4(X1,X2,X3,X4)),esk463_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1517]),
    [final] ).

cnf(i_0_3058,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk223_4(X1,X2,X3,X4)),esk222_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1514]),
    [final] ).

cnf(i_0_3059,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk199_4(X1,X2,X3,X4)),esk198_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1515]),
    [final] ).

cnf(i_0_3060,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk408_4(X1,X2,X3,X4)),esk409_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1519]),
    [final] ).

cnf(i_0_3061,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk243_4(X1,X2,X3,X4)),esk242_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1518]),
    [final] ).

cnf(i_0_3062,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk390_4(X1,X2,X3,X4)),esk391_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1522]),
    [final] ).

cnf(i_0_3063,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk464_4(X1,X2,X3,X4)),esk465_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_3064,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk225_4(X1,X2,X3,X4)),esk224_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1520]),
    [final] ).

cnf(i_0_3065,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk201_4(X1,X2,X3,X4)),esk200_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1521]),
    [final] ).

cnf(i_0_3066,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk400_4(X1,X2,X3,X4)),esk401_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1525]),
    [final] ).

cnf(i_0_3067,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk235_4(X1,X2,X3,X4)),esk234_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1524]),
    [final] ).

cnf(i_0_3068,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk382_4(X1,X2,X3,X4)),esk383_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1528]),
    [final] ).

cnf(i_0_3069,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk456_4(X1,X2,X3,X4)),esk457_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_3070,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk217_4(X1,X2,X3,X4)),esk216_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1526]),
    [final] ).

cnf(i_0_3071,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk193_4(X1,X2,X3,X4)),esk192_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1527]),
    [final] ).

cnf(i_0_3072,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk430_4(X1,X2,X3,X4)),esk431_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1531]),
    [final] ).

cnf(i_0_3073,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk265_4(X1,X2,X3,X4)),esk264_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1530]),
    [final] ).

cnf(i_0_3074,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk422_4(X1,X2,X3,X4)),esk423_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1533]),
    [final] ).

cnf(i_0_3075,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk257_4(X1,X2,X3,X4)),esk256_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1532]),
    [final] ).

cnf(i_0_3076,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk420_4(X1,X2,X3,X4)),esk421_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1535]),
    [final] ).

cnf(i_0_3077,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk255_4(X1,X2,X3,X4)),esk254_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1534]),
    [final] ).

cnf(i_0_3078,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk418_4(X1,X2,X3,X4)),esk419_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1537]),
    [final] ).

cnf(i_0_3079,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk253_4(X1,X2,X3,X4)),esk252_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1536]),
    [final] ).

cnf(i_0_3080,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk416_4(X1,X2,X3,X4)),esk417_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1539]),
    [final] ).

cnf(i_0_3081,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk251_4(X1,X2,X3,X4)),esk250_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1538]),
    [final] ).

cnf(i_0_3082,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk426_4(X1,X2,X3,X4)),esk427_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1542]),
    [final] ).

cnf(i_0_3083,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk452_4(X1,X2,X3,X4)),esk453_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1543]),
    [final] ).

cnf(i_0_3084,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk261_4(X1,X2,X3,X4)),esk260_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1540]),
    [final] ).

cnf(i_0_3085,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk189_4(X1,X2,X3,X4)),esk188_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1541]),
    [final] ).

cnf(i_0_3086,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk428_4(X1,X2,X3,X4)),esk429_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1546]),
    [final] ).

cnf(i_0_3087,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk450_4(X1,X2,X3,X4)),esk451_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1547]),
    [final] ).

cnf(i_0_3088,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk263_4(X1,X2,X3,X4)),esk262_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1544]),
    [final] ).

cnf(i_0_3089,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk187_4(X1,X2,X3,X4)),esk186_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1545]),
    [final] ).

cnf(i_0_3090,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk424_4(X1,X2,X3,X4)),esk425_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1549]),
    [final] ).

cnf(i_0_3091,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk259_4(X1,X2,X3,X4)),esk258_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1548]),
    [final] ).

cnf(i_0_3092,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk398_4(X1,X2,X3,X4)),esk399_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1552]),
    [final] ).

cnf(i_0_3093,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk448_4(X1,X2,X3,X4)),esk449_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1553]),
    [final] ).

cnf(i_0_3094,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk233_4(X1,X2,X3,X4)),esk232_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1550]),
    [final] ).

cnf(i_0_3095,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk185_4(X1,X2,X3,X4)),esk184_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1551]),
    [final] ).

cnf(i_0_3096,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk380_4(X1,X2,X3,X4)),esk381_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1556]),
    [final] ).

cnf(i_0_3097,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk454_4(X1,X2,X3,X4)),esk455_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1557]),
    [final] ).

cnf(i_0_3098,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk215_4(X1,X2,X3,X4)),esk214_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1554]),
    [final] ).

cnf(i_0_3099,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk191_4(X1,X2,X3,X4)),esk190_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1555]),
    [final] ).

cnf(i_0_3100,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk402_4(X1,X2,X3,X4)),esk403_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1559]),
    [final] ).

cnf(i_0_3101,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk237_4(X1,X2,X3,X4)),esk236_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1558]),
    [final] ).

cnf(i_0_3102,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk384_4(X1,X2,X3,X4)),esk385_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1562]),
    [final] ).

cnf(i_0_3103,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk458_4(X1,X2,X3,X4)),esk459_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1563]),
    [final] ).

cnf(i_0_3104,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk219_4(X1,X2,X3,X4)),esk218_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1560]),
    [final] ).

cnf(i_0_3105,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk195_4(X1,X2,X3,X4)),esk194_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1561]),
    [final] ).

cnf(i_0_3106,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk414_4(X1,X2,X3,X4)),esk415_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1565]),
    [final] ).

cnf(i_0_3107,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk249_4(X1,X2,X3,X4)),esk248_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1564]),
    [final] ).

cnf(i_0_3108,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk396_4(X1,X2,X3,X4)),esk397_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1568]),
    [final] ).

cnf(i_0_3109,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk470_4(X1,X2,X3,X4)),esk471_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1569]),
    [final] ).

cnf(i_0_3110,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk231_4(X1,X2,X3,X4)),esk230_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1566]),
    [final] ).

cnf(i_0_3111,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk207_4(X1,X2,X3,X4)),esk206_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_3112,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk446_4(X1,X2,X3,X4)),esk447_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1571]),
    [final] ).

cnf(i_0_3113,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk281_4(X1,X2,X3,X4)),esk280_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_3114,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk438_4(X1,X2,X3,X4)),esk439_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1573]),
    [final] ).

cnf(i_0_3115,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk273_4(X1,X2,X3,X4)),esk272_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_3116,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk436_4(X1,X2,X3,X4)),esk437_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1575]),
    [final] ).

cnf(i_0_3117,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk271_4(X1,X2,X3,X4)),esk270_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1574]),
    [final] ).

cnf(i_0_3118,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk434_4(X1,X2,X3,X4)),esk435_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1577]),
    [final] ).

cnf(i_0_3119,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk269_4(X1,X2,X3,X4)),esk268_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1576]),
    [final] ).

cnf(i_0_3120,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk432_4(X1,X2,X3,X4)),esk433_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1579]),
    [final] ).

cnf(i_0_3121,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk267_4(X1,X2,X3,X4)),esk266_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1578]),
    [final] ).

cnf(i_0_3122,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk444_4(X1,X2,X3,X4)),esk445_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1582]),
    [final] ).

cnf(i_0_3123,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk474_4(X1,X2,X3,X4)),esk475_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1583]),
    [final] ).

cnf(i_0_3124,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk279_4(X1,X2,X3,X4)),esk278_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1580]),
    [final] ).

cnf(i_0_3125,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk211_4(X1,X2,X3,X4)),esk210_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1581]),
    [final] ).

cnf(i_0_3126,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk472_4(X1,X2,X3,X4)),esk473_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1585]),
    [final] ).

cnf(i_0_3127,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk209_4(X1,X2,X3,X4)),esk208_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1584]),
    [final] ).

cnf(i_0_3128,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk440_4(X1,X2,X3,X4)),esk441_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1587]),
    [final] ).

cnf(i_0_3129,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk275_4(X1,X2,X3,X4)),esk274_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1586]),
    [final] ).

cnf(i_0_3130,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk442_4(X1,X2,X3,X4)),esk443_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1590]),
    [final] ).

cnf(i_0_3131,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk476_4(X1,X2,X3,X4)),esk477_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1591]),
    [final] ).

cnf(i_0_3132,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk277_4(X1,X2,X3,X4)),esk276_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1588]),
    [final] ).

cnf(i_0_3133,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk213_4(X1,X2,X3,X4)),esk212_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1589]),
    [final] ).

cnf(i_0_3134,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk412_4(X1,X2,X3,X4)),esk413_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1593]),
    [final] ).

cnf(i_0_3135,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk247_4(X1,X2,X3,X4)),esk246_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1592]),
    [final] ).

cnf(i_0_3136,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk394_4(X1,X2,X3,X4)),esk395_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1596]),
    [final] ).

cnf(i_0_3137,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk468_4(X1,X2,X3,X4)),esk469_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1597]),
    [final] ).

cnf(i_0_3138,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk229_4(X1,X2,X3,X4)),esk228_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1594]),
    [final] ).

cnf(i_0_3139,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk205_4(X1,X2,X3,X4)),esk204_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1595]),
    [final] ).

cnf(i_0_3140,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3141,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk479_3(X2,X3,X1))),hAPP_nat_nat(X1,esk480_3(X2,X3,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1703]),
    [final] ).

cnf(i_0_3142,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk139_4(X1,X2,X3,X4)),esk138_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),hAPP_f899613158t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),hAPP_f899613158t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1598]),
    [final] ).

cnf(i_0_3143,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk121_4(X1,X2,X3,X4)),esk120_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),hAPP_n588788980t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),hAPP_n588788980t_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1599]),
    [final] ).

cnf(i_0_3144,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk97_4(X1,X2,X3,X4)),esk96_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),hAPP_n588788980t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),hAPP_n588788980t_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1600]),
    [final] ).

cnf(i_0_3145,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk342_4(X1,X2,X3,X4)),esk343_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_f899613158t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_f899613158t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1601]),
    [final] ).

cnf(i_0_3146,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk324_4(X1,X2,X3,X4)),esk325_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_n588788980t_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_n588788980t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_3147,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk300_4(X1,X2,X3,X4)),esk301_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),hAPP_n588788980t_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),hAPP_n588788980t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1603]),
    [final] ).

cnf(i_0_3148,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk133_4(X1,X2,X3,X4)),esk132_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),hAPP_f769545506l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),hAPP_f769545506l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1604]),
    [final] ).

cnf(i_0_3149,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk115_4(X1,X2,X3,X4)),esk114_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),hAPP_n1674354836l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),hAPP_n1674354836l_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1605]),
    [final] ).

cnf(i_0_3150,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk91_4(X1,X2,X3,X4)),esk90_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),hAPP_n1674354836l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),hAPP_n1674354836l_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1606]),
    [final] ).

cnf(i_0_3151,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk336_4(X1,X2,X3,X4)),esk337_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_f769545506l_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_f769545506l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1607]),
    [final] ).

cnf(i_0_3152,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk318_4(X1,X2,X3,X4)),esk319_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_n1674354836l_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_n1674354836l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1608]),
    [final] ).

cnf(i_0_3153,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk294_4(X1,X2,X3,X4)),esk295_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),hAPP_n1674354836l_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),hAPP_n1674354836l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1609]),
    [final] ).

cnf(i_0_3154,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk135_4(X1,X2,X3,X4)),esk134_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),hAPP_f1449238989l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),hAPP_f1449238989l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1610]),
    [final] ).

cnf(i_0_3155,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk117_4(X1,X2,X3,X4)),esk116_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),hAPP_n295497947l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),hAPP_n295497947l_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1611]),
    [final] ).

cnf(i_0_3156,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk93_4(X1,X2,X3,X4)),esk92_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),hAPP_n295497947l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),hAPP_n295497947l_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1612]),
    [final] ).

cnf(i_0_3157,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk338_4(X1,X2,X3,X4)),esk339_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_f1449238989l_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_f1449238989l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1613]),
    [final] ).

cnf(i_0_3158,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk320_4(X1,X2,X3,X4)),esk321_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_n295497947l_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_n295497947l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1614]),
    [final] ).

cnf(i_0_3159,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk296_4(X1,X2,X3,X4)),esk297_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),hAPP_n295497947l_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),hAPP_n295497947l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_3160,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk137_4(X1,X2,X3,X4)),esk136_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),hAPP_f226010187l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),hAPP_f226010187l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_3161,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk119_4(X1,X2,X3,X4)),esk118_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),hAPP_n2095207769l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),hAPP_n2095207769l_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_3162,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk95_4(X1,X2,X3,X4)),esk94_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),hAPP_n2095207769l_bool(X2,X4)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),hAPP_n2095207769l_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1618]),
    [final] ).

cnf(i_0_3163,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk340_4(X1,X2,X3,X4)),esk341_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_f226010187l_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_f226010187l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1619]),
    [final] ).

cnf(i_0_3164,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk322_4(X1,X2,X3,X4)),esk323_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_n2095207769l_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_n2095207769l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1620]),
    [final] ).

cnf(i_0_3165,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk298_4(X1,X2,X3,X4)),esk299_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),hAPP_n2095207769l_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),hAPP_n2095207769l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1621]),
    [final] ).

cnf(i_0_3166,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk129_4(X1,X2,X3,X4)),esk128_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),hAPP_f1061584978t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),hAPP_f1061584978t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1622]),
    [final] ).

cnf(i_0_3167,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk111_4(X1,X2,X3,X4)),esk110_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),hAPP_n454528608t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),hAPP_n454528608t_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1623]),
    [final] ).

cnf(i_0_3168,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk87_4(X1,X2,X3,X4)),esk86_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),hAPP_n454528608t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),hAPP_n454528608t_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1624]),
    [final] ).

cnf(i_0_3169,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk332_4(X1,X2,X3,X4)),esk333_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_f1061584978t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_f1061584978t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1625]),
    [final] ).

cnf(i_0_3170,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk314_4(X1,X2,X3,X4)),esk315_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_n454528608t_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_n454528608t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1626]),
    [final] ).

cnf(i_0_3171,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk290_4(X1,X2,X3,X4)),esk291_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),hAPP_n454528608t_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),hAPP_n454528608t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1627]),
    [final] ).

cnf(i_0_3172,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk159_4(X1,X2,X3,X4)),esk158_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f1363542492t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f1363542492t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1628]),
    [final] ).

cnf(i_0_3173,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk151_4(X1,X2,X3,X4)),esk150_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f856106132t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f856106132t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1629]),
    [final] ).

cnf(i_0_3174,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk149_4(X1,X2,X3,X4)),esk148_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f985923321t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f985923321t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1630]),
    [final] ).

cnf(i_0_3175,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk147_4(X1,X2,X3,X4)),esk146_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f839525755t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f839525755t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1631]),
    [final] ).

cnf(i_0_3176,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk145_4(X1,X2,X3,X4)),esk144_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f464145314t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f464145314t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1632]),
    [final] ).

cnf(i_0_3177,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk155_4(X1,X2,X3,X4)),esk154_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1633]),
    [final] ).

cnf(i_0_3178,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk83_4(X1,X2,X3,X4)),esk82_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f2026336507t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1634]),
    [final] ).

cnf(i_0_3179,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk157_4(X1,X2,X3,X4)),esk156_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1635]),
    [final] ).

cnf(i_0_3180,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk81_4(X1,X2,X3,X4)),esk80_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f543204480t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1636]),
    [final] ).

cnf(i_0_3181,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk153_4(X1,X2,X3,X4)),esk152_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_b1013836512t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_b1013836512t_bool(X2,X3)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1637]),
    [final] ).

cnf(i_0_3182,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk127_4(X1,X2,X3,X4)),esk126_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f800510211t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f800510211t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1638]),
    [final] ).

cnf(i_0_3183,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk79_4(X1,X2,X3,X4)),esk78_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f800510211t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1639]),
    [final] ).

cnf(i_0_3184,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk109_4(X1,X2,X3,X4)),esk108_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_n1699378549t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_n1699378549t_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1640]),
    [final] ).

cnf(i_0_3185,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk85_4(X1,X2,X3,X4)),esk84_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_n1699378549t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_n1699378549t_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1641]),
    [final] ).

cnf(i_0_3186,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk362_4(X1,X2,X3,X4)),esk363_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f1363542492t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f1363542492t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1642]),
    [final] ).

cnf(i_0_3187,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk354_4(X1,X2,X3,X4)),esk355_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f856106132t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f856106132t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1643]),
    [final] ).

cnf(i_0_3188,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk352_4(X1,X2,X3,X4)),esk353_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f985923321t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f985923321t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1644]),
    [final] ).

cnf(i_0_3189,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk350_4(X1,X2,X3,X4)),esk351_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f839525755t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f839525755t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1645]),
    [final] ).

cnf(i_0_3190,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk348_4(X1,X2,X3,X4)),esk349_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f464145314t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f464145314t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1646]),
    [final] ).

cnf(i_0_3191,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk358_4(X1,X2,X3,X4)),esk359_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1647]),
    [final] ).

cnf(i_0_3192,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk286_4(X1,X2,X3,X4)),esk287_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f2026336507t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1648]),
    [final] ).

cnf(i_0_3193,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk360_4(X1,X2,X3,X4)),esk361_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_3194,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk284_4(X1,X2,X3,X4)),esk285_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f543204480t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_3195,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk356_4(X1,X2,X3,X4)),esk357_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_b1013836512t_bool(X3,X1)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_b1013836512t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1651]),
    [final] ).

cnf(i_0_3196,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk330_4(X1,X2,X3,X4)),esk331_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f800510211t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f800510211t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1652]),
    [final] ).

cnf(i_0_3197,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk282_4(X1,X2,X3,X4)),esk283_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f800510211t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1653]),
    [final] ).

cnf(i_0_3198,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk312_4(X1,X2,X3,X4)),esk313_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_n1699378549t_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_n1699378549t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1654]),
    [final] ).

cnf(i_0_3199,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk288_4(X1,X2,X3,X4)),esk289_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_n1699378549t_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_n1699378549t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1655]),
    [final] ).

cnf(i_0_3200,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk131_4(X1,X2,X3,X4)),esk130_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),hAPP_f632777549i_bool(X2,X4)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),hAPP_f632777549i_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1656]),
    [final] ).

cnf(i_0_3201,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk113_4(X1,X2,X3,X4)),esk112_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),hAPP_n821919323i_bool(X2,X4)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),hAPP_n821919323i_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1657]),
    [final] ).

cnf(i_0_3202,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk89_4(X1,X2,X3,X4)),esk88_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),hAPP_n821919323i_bool(X2,X4)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),hAPP_n821919323i_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1658]),
    [final] ).

cnf(i_0_3203,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk334_4(X1,X2,X3,X4)),esk335_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_f632777549i_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_f632777549i_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1659]),
    [final] ).

cnf(i_0_3204,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk316_4(X1,X2,X3,X4)),esk317_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_n821919323i_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_n821919323i_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1660]),
    [final] ).

cnf(i_0_3205,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk292_4(X1,X2,X3,X4)),esk293_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),hAPP_n821919323i_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),hAPP_n821919323i_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1661]),
    [final] ).

cnf(i_0_3206,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk143_4(X1,X2,X3,X4)),esk142_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),hAPP_f861874780t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),hAPP_f861874780t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1662]),
    [final] ).

cnf(i_0_3207,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk125_4(X1,X2,X3,X4)),esk124_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),hAPP_n539120590t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),hAPP_n539120590t_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1663]),
    [final] ).

cnf(i_0_3208,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk101_4(X1,X2,X3,X4)),esk100_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),hAPP_n539120590t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),hAPP_n539120590t_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_3209,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk346_4(X1,X2,X3,X4)),esk347_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_f861874780t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_f861874780t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1665]),
    [final] ).

cnf(i_0_3210,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk328_4(X1,X2,X3,X4)),esk329_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_n539120590t_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_n539120590t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1666]),
    [final] ).

cnf(i_0_3211,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk304_4(X1,X2,X3,X4)),esk305_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),hAPP_n539120590t_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),hAPP_n539120590t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1667]),
    [final] ).

cnf(i_0_3212,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk175_4(X1,X2,X3,X4)),esk174_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1358350510ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1358350510ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1668]),
    [final] ).

cnf(i_0_3213,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk167_4(X1,X2,X3,X4)),esk166_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f816335862ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f816335862ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1669]),
    [final] ).

cnf(i_0_3214,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk165_4(X1,X2,X3,X4)),esk164_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f897066961ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f897066961ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1670]),
    [final] ).

cnf(i_0_3215,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk163_4(X1,X2,X3,X4)),esk162_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1695077327ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1695077327ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1671]),
    [final] ).

cnf(i_0_3216,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk161_4(X1,X2,X3,X4)),esk160_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1313392232ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1313392232ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1672]),
    [final] ).

cnf(i_0_3217,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk173_4(X1,X2,X3,X4)),esk172_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1673]),
    [final] ).

cnf(i_0_3218,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk105_4(X1,X2,X3,X4)),esk104_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2030293770ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1674]),
    [final] ).

cnf(i_0_3219,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk103_4(X1,X2,X3,X4)),esk102_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f22106695ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f22106695ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1675]),
    [final] ).

cnf(i_0_3220,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk169_4(X1,X2,X3,X4)),esk168_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_bool_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_bool_nat(X2,X3)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1676]),
    [final] ).

cnf(i_0_3221,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk171_4(X1,X2,X3,X4)),esk170_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_3222,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk107_4(X1,X2,X3,X4)),esk106_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2120083535ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1678]),
    [final] ).

cnf(i_0_3223,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,esk378_4(X1,X2,X3,X4)),esk379_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1358350510ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1358350510ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1679]),
    [final] ).

cnf(i_0_3224,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,esk370_4(X1,X2,X3,X4)),esk371_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f816335862ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f816335862ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1680]),
    [final] ).

cnf(i_0_3225,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,esk368_4(X1,X2,X3,X4)),esk369_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f897066961ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f897066961ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1681]),
    [final] ).

cnf(i_0_3226,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,esk366_4(X1,X2,X3,X4)),esk367_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1695077327ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1695077327ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1682]),
    [final] ).

cnf(i_0_3227,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,esk364_4(X1,X2,X3,X4)),esk365_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1313392232ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1313392232ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1683]),
    [final] ).

cnf(i_0_3228,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,esk376_4(X1,X2,X3,X4)),esk377_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1684]),
    [final] ).

cnf(i_0_3229,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,esk308_4(X1,X2,X3,X4)),esk309_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2030293770ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1685]),
    [final] ).

cnf(i_0_3230,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,esk306_4(X1,X2,X3,X4)),esk307_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f22106695ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f22106695ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1686]),
    [final] ).

cnf(i_0_3231,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,esk372_4(X1,X2,X3,X4)),esk373_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_bool_nat(X3,X1)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_bool_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1687]),
    [final] ).

cnf(i_0_3232,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,esk374_4(X1,X2,X3,X4)),esk375_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1688]),
    [final] ).

cnf(i_0_3233,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,esk310_4(X1,X2,X3,X4)),esk311_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2120083535ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1689]),
    [final] ).

cnf(i_0_3234,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk141_4(X1,X2,X3,X4)),esk140_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),hAPP_f54304608l_bool(X2,X4)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),hAPP_f54304608l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1690]),
    [final] ).

cnf(i_0_3235,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk123_4(X1,X2,X3,X4)),esk122_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),hAPP_nat_bool(X2,X4)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),hAPP_nat_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1691]),
    [final] ).

cnf(i_0_3236,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk99_4(X1,X2,X3,X4)),esk98_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),hAPP_nat_bool(X2,X4)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),hAPP_nat_bool(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1692]),
    [final] ).

cnf(i_0_3237,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk344_4(X1,X2,X3,X4)),esk345_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_f54304608l_bool(X3,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X1))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_f54304608l_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1693]),
    [final] ).

cnf(i_0_3238,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk326_4(X1,X2,X3,X4)),esk327_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_nat_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_nat_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1694]),
    [final] ).

cnf(i_0_3239,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk302_4(X1,X2,X3,X4)),esk303_4(X1,X2,X3,X4)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),hAPP_nat_bool(X3,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X1))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),hAPP_nat_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1695]),
    [final] ).

cnf(i_0_3240,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3241,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3242,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3243,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3244,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3245,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3246,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk21_2(X1,X2)),esk22_2(X1,X2))),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk21_2(X1,X2)),esk22_2(X1,X2))),X1))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1704]),
    [final] ).

cnf(i_0_3247,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(cn,[status(thm)],[i_0_1705]),
    [final] ).

cnf(i_0_3248,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1))
    | hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X1))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,X2))))) != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_1706]),
    [final] ).

cnf(i_0_3249,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1)))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3250,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hAPP_A1637648121di_nat(h,X1) = n
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3251,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk481_3(X2,X3,X1))),hAPP_nat_nat(X1,esk482_3(X2,X3,X1))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1707]),
    [final] ).

cnf(i_0_3252,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hAPP_A1637648121di_nat(h,X1) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3253,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | hAPP_A1637648121di_nat(h,X1) = n
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3254,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X3),X4),X5)))
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X2)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3255,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3256,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hAPP_A1637648121di_nat(h,X1) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3257,plain,
    ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X1),pi_Pro1122146355t_unit(X3,X2)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X1,esk42_3(X1,X2,X3))),hAPP_P332578347t_bool(X2,esk42_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1709]),
    [final] ).

cnf(i_0_3258,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),pi_Pro666468413t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X1,esk69_3(X1,X2,X3))),hAPP_P324742453l_bool(X2,esk69_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1710]),
    [final] ).

cnf(i_0_3259,plain,
    ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X1),pi_Pro1270767662e_indi(X3,X2)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X1,esk41_3(X1,X2,X3))),hAPP_P1875867302i_bool(X2,esk41_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1711]),
    [final] ).

cnf(i_0_3260,plain,
    ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X1),pi_fun308431217t_unit(X3,X2)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X1,esk51_3(X1,X2,X3))),hAPP_f1710744577t_bool(X2,esk51_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1712]),
    [final] ).

cnf(i_0_3261,plain,
    ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X1),pi_fun1575168891l_bool(X3,X2)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X1,esk50_3(X1,X2,X3))),hAPP_f210572555l_bool(X2,esk50_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1713]),
    [final] ).

cnf(i_0_3262,plain,
    ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X1),pi_fun896360044e_indi(X3,X2)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X1,esk49_3(X1,X2,X3))),hAPP_f244157820i_bool(X2,esk49_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1714]),
    [final] ).

cnf(i_0_3263,plain,
    ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X1),pi_fun321364250t_unit(X3,X2)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X1,esk48_3(X1,X2,X3))),hAPP_f1866147972t_bool(X2,esk48_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1715]),
    [final] ).

cnf(i_0_3264,plain,
    ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X1),pi_fun52649508l_bool(X3,X2)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X1,esk47_3(X1,X2,X3))),hAPP_f1624277646l_bool(X2,esk47_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1716]),
    [final] ).

cnf(i_0_3265,plain,
    ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X1),pi_fun1002945429e_indi(X3,X2)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X1,esk46_3(X1,X2,X3))),hAPP_f1552576127i_bool(X2,esk46_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1717]),
    [final] ).

cnf(i_0_3266,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),pi_fun150026276t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X1,esk70_3(X1,X2,X3))),hAPP_f1277514478l_bool(X2,esk70_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1718]),
    [final] ).

cnf(i_0_3267,plain,
    ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X1),pi_fun1877263000t_unit(X3,X2)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X1,esk45_3(X1,X2,X3))),hAPP_f1891021702t_bool(X2,esk45_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3268,plain,
    ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X1),pi_fun823343522l_bool(X3,X2)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X1,esk44_3(X1,X2,X3))),hAPP_f839832464l_bool(X2,esk44_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1720]),
    [final] ).

cnf(i_0_3269,plain,
    ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X1),pi_fun753830419e_indi(X3,X2)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X1,esk43_3(X1,X2,X3))),hAPP_f1948454017i_bool(X2,esk43_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1721]),
    [final] ).

cnf(i_0_3270,plain,
    ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X1),pi_Pro1928973619le_alt(X3,X2)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X1,esk57_3(X1,X2,X3))),hAPP_P1341894483t_bool(X2,esk57_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1722]),
    [final] ).

cnf(i_0_3271,plain,
    ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X1),pi_Pro718203741t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X1,esk65_3(X1,X2,X3))),hAPP_P1294997365l_bool(X2,esk65_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1723]),
    [final] ).

cnf(i_0_3272,plain,
    ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X1),pi_Pro1880661658t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X1,esk63_3(X1,X2,X3))),hAPP_P1171466554l_bool(X2,esk63_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1724]),
    [final] ).

cnf(i_0_3273,plain,
    ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X1),pi_Pro610293528t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X1,esk60_3(X1,X2,X3))),hAPP_P254387896l_bool(X2,esk60_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1725]),
    [final] ).

cnf(i_0_3274,plain,
    ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X1),pi_Product_unit_nat(X3,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X1,esk68_3(X1,X2,X3))),hAPP_P32877782t_bool(X2,esk68_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1726]),
    [final] ).

cnf(i_0_3275,plain,
    ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X1),pi_nat_Product_unit(X3,X2)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X1,esk54_3(X1,X2,X3))),hAPP_n454528608t_bool(X2,esk54_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1727]),
    [final] ).

cnf(i_0_3276,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),pi_nat_bool(X3,X2)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X1,esk53_3(X1,X2,X3))),hAPP_n1006566506l_bool(X2,esk53_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1728]),
    [final] ).

cnf(i_0_3277,plain,
    ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X1),pi_nat660525389e_indi(X3,X2)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X1,esk52_3(X1,X2,X3))),hAPP_n821919323i_bool(X2,esk52_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1729]),
    [final] ).

cnf(i_0_3278,plain,
    ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X1),pi_boo115158845le_alt(X3,X2)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X1,esk56_3(X1,X2,X3))),hAPP_b1703662281t_bool(X2,esk56_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1730]),
    [final] ).

cnf(i_0_3279,plain,
    ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X1),pi_boo538701011t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X1,esk64_3(X1,X2,X3))),hAPP_b1812770943l_bool(X2,esk64_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1731]),
    [final] ).

cnf(i_0_3280,plain,
    ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X1),pi_boo1117000868t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X1,esk62_3(X1,X2,X3))),hAPP_b517355696l_bool(X2,esk62_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1732]),
    [final] ).

cnf(i_0_3281,plain,
    ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X1),pi_boo175444770t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X1,esk59_3(X1,X2,X3))),hAPP_b1048178734l_bool(X2,esk59_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1733]),
    [final] ).

cnf(i_0_3282,plain,
    ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X1),pi_bool_nat(X3,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X1,esk67_3(X1,X2,X3))),hAPP_b1013836512t_bool(X2,esk67_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1734]),
    [final] ).

cnf(i_0_3283,plain,
    ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X1),pi_Arr1199386158le_alt(X3,X2)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X1,esk55_3(X1,X2,X3))),hAPP_A1677245848t_bool(X2,esk55_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1735]),
    [final] ).

cnf(i_0_3284,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),pi_Arr990697634t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X1,esk71_3(X1,X2,X3))),hAPP_A60074736l_bool(X2,esk71_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1736]),
    [final] ).

cnf(i_0_3285,plain,
    ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X1),pi_Arr1936979349t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X1,esk61_3(X1,X2,X3))),hAPP_A1112981887l_bool(X2,esk61_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1737]),
    [final] ).

cnf(i_0_3286,plain,
    ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X1),pi_Arr2020412179t_bool(X3,X2)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X1,esk58_3(X1,X2,X3))),hAPP_A1952883197l_bool(X2,esk58_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1738]),
    [final] ).

cnf(i_0_3287,plain,
    ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X1),pi_Arr346900227di_nat(X3,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X1,esk66_3(X1,X2,X3))),hAPP_A2046586321t_bool(X2,esk66_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_3288,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),arrow_1539419881_below(X3,X5,X4)))
    | X5 = X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X2)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3289,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3290,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3291,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3292,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3293,plain,
    ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X2),X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk24_2(X1,X2)),esk25_2(X1,X2))),hAPP_f412050202t_bool(X2,esk23_2(X1,X2))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X2),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1741]),
    [final] ).

cnf(i_0_3294,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3295,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1)))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3296,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e))) ),
    inference(cn,[status(thm)],[i_0_1742]),
    [final] ).

cnf(i_0_3297,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3298,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3299,plain,
    ( X3 = X1
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X5),X4),X2)))
    | X4 = X2
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X1)),X5))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3300,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X3),X4),X5)))
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | X1 != X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X2)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3301,plain,
    ( X1 = X5
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X3),X4),X5)))
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3302,plain,
    ( X2 = X4
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X3),X5),X4)))
    | X5 = X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X5),X2)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3303,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk21_2(X1,X2)),esk22_2(X1,X2))),X2))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk21_2(X1,X2)),esk22_2(X1,X2))),X1))
    | X2 = X1
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1704]),
    [final] ).

cnf(i_0_3304,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3305,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3306,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3307,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3308,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3309,plain,
    ( X1 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),arrow_1539419881_below(X5,X2,X3)))
    | X2 = X3
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),X5))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3310,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),arrow_1539419881_below(X3,X5,X4)))
    | X5 = X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | X2 != X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3311,plain,
    ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X1)),esk13_1(X1))),hAPP_f412050202t_bool(X1,esk10_1(X1))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X1)),esk13_1(X1))),hAPP_f412050202t_bool(X1,esk11_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_3312,plain,
    ( X1 = X4
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),arrow_1539419881_below(X3,X4,X5)))
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X5)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3313,plain,
    ( X2 = X5
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),arrow_1539419881_below(X3,X5,X4)))
    | X5 = X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X2)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3314,plain,
    is_fun158382675l_bool(undefi1466315554l_bool(fun(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel]),
    [final] ).

cnf(i_0_3315,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_3316,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3317,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk479_3(X1,X2,X3)),esk480_3(X1,X2,X3)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X3,X1)),X2)),hAPP_nat_nat(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1703]),
    [final] ).

cnf(i_0_3318,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3319,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_f412050202t_bool(f,X4)))
    | is_Arr43961803e_indi(esk5_4(X3,X4,X2,X1))
    | X2 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1697]),
    [final] ).

cnf(i_0_3320,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),hAPP_f412050202t_bool(f,X4)))
    | is_Arr43961803e_indi(esk5_4(X4,X3,X1,X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_f412050202t_bool(f,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1697]),
    [final] ).

cnf(i_0_3321,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3322,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3323,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3324,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,X1)),c),e)))
    | hAPP_A1637648121di_nat(h,X1) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ),
    inference(cn,[status(thm)],[i_0_1743]),
    [final] ).

cnf(i_0_3325,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3326,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3327,plain,
    ( X3 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | X3 = X2
    | X4 = X2
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X5),X4),X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3328,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),X4))
    | X3 = X2
    | X5 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X5),X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3329,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | X3 = X2
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X5),X3),X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3330,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(cn,[status(thm)],[i_0_1744]),
    [final] ).

cnf(i_0_3331,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3332,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X1)),esk13_1(X1))),hAPP_A1677245848t_bool(esk11_1(X1),X2)))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X1)),esk13_1(X1))),hAPP_A1677245848t_bool(esk10_1(X1),X2)))
    | ~ is_Arr43961803e_indi(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_3333,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X1)),esk13_1(X1))),hAPP_A1677245848t_bool(esk10_1(X1),X2)))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X1)),esk13_1(X1))),hAPP_A1677245848t_bool(esk11_1(X1),X2)))
    | ~ is_Arr43961803e_indi(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_3334,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk24_2(X1,X2)),esk25_2(X1,X2))),hAPP_A1677245848t_bool(esk23_2(X1,X2),X1)))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X2),X1))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X2),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1741]),
    [final] ).

cnf(i_0_3335,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e))) ),
    inference(cn,[status(thm)],[i_0_1745]),
    [final] ).

cnf(i_0_3336,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3337,plain,
    ( X3 = X1
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X5),X4),X2)))
    | X4 = X2
    | X1 != X2
    | X3 != X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X1)),X5))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3338,plain,
    ( X3 = X2
    | X3 = X1
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X5),X4),X2)))
    | X4 = X2
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3339,plain,
    ( X1 = X5
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X3),X4),X5)))
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | X1 != X4
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3340,plain,
    ( X2 = X4
    | X1 = X4
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X3),X5),X4)))
    | X5 = X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3341,plain,
    ( X1 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X5),X3),X2)))
    | X3 = X2
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3342,plain,
    ( X3 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X3)),X5))
    | X3 = X2
    | X2 = X4
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),arrow_1539419881_below(X5,X2,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3343,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),X4))
    | X3 = X2
    | X2 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),arrow_1539419881_below(X4,X2,X5)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3344,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | X2 = X4
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),arrow_1539419881_below(X5,X2,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3345,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1746]),
    [final] ).

cnf(i_0_3346,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1747]),
    [final] ).

cnf(i_0_3347,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ),
    inference(cn,[status(thm)],[i_0_1748]),
    [final] ).

cnf(i_0_3348,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3349,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),X2)),X1))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk488_2(X1,X2)),hAPP_nat_nat(X2,esk488_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1749]),
    [final] ).

cnf(i_0_3350,plain,
    ( hAPP_A1637648121di_nat(h,X1) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,X1)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,X1)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ),
    inference(cn,[status(thm)],[i_0_1750]),
    [final] ).

cnf(i_0_3351,plain,
    ( X1 = X3
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),arrow_1539419881_below(X5,X2,X4)))
    | X2 = X4
    | X1 != X2
    | X3 != X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),X5))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3352,plain,
    ( X4 = X2
    | X1 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X4)),arrow_1539419881_below(X5,X2,X3)))
    | X2 = X3
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3353,plain,
    ( X2 = X5
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),arrow_1539419881_below(X3,X5,X4)))
    | X5 = X4
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | X2 != X4
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X5)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3354,plain,
    ( X1 = X4
    | X2 = X4
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),arrow_1539419881_below(X3,X4,X5)))
    | X4 = X5
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3355,plain,
    ( X3 = X1
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),arrow_1539419881_below(X5,X2,X4)))
    | X2 = X4
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),X5))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3356,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1751]),
    [final] ).

cnf(i_0_3357,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),X1)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X2))))),
    inference(split_conjunct,[status(thm)],[i_0_1752]),
    [final] ).

cnf(i_0_3358,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X3)),X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1753]),
    [final] ).

cnf(i_0_3359,plain,
    ( X4 = X5
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X3),X4),X5)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3360,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X1)),esk13_1(X1))),hAPP_f412050202t_bool(X1,esk10_1(X1))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk12_1(X1)),esk13_1(X1))),hAPP_f412050202t_bool(X1,esk11_1(X1))))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_3361,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4),X2)))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1754]),
    [final] ).

cnf(i_0_3362,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4),X2)))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_3363,plain,
    ( X1 = hAPP_n1699378549t_bool(ord_at4362885an_nat(X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_f22106695ol_nat(finite_card_nat,X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_n1699378549t_bool(ord_at4362885an_nat(X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_f22106695ol_nat(finite_card_nat,X1))))) ),
    inference(split_conjunct,[status(thm)],[i_0_1756]),
    [final] ).

cnf(i_0_3364,plain,
    ( X1 = X2
    | X1 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X3),X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_3365,plain,
    ( X1 = X2
    | X2 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X3),X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1754]),
    [final] ).

cnf(i_0_3366,plain,
    ( X2 = X4
    | X1 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X3),X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_3367,plain,
    ( X1 = X4
    | X2 = X4
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X3),X4)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1754]),
    [final] ).

cnf(i_0_3368,plain,
    ( is_Arr43961803e_indi(esk14_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X4)),hAPP_f412050202t_bool(X1,X2)))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X2),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1701]),
    [final] ).

cnf(i_0_3369,plain,
    ( is_fun1568535512t_bool(esk475_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1583]),
    [final] ).

cnf(i_0_3370,plain,
    ( is_fun1568535512t_bool(esk474_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1583]),
    [final] ).

cnf(i_0_3371,plain,
    ( is_fun1568535512t_bool(esk451_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1547]),
    [final] ).

cnf(i_0_3372,plain,
    ( is_fun1568535512t_bool(esk450_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1547]),
    [final] ).

cnf(i_0_3373,plain,
    ( is_fun1568535512t_bool(esk445_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1582]),
    [final] ).

cnf(i_0_3374,plain,
    ( is_fun1568535512t_bool(esk444_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1582]),
    [final] ).

cnf(i_0_3375,plain,
    ( is_fun1568535512t_bool(esk429_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1546]),
    [final] ).

cnf(i_0_3376,plain,
    ( is_fun1568535512t_bool(esk428_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1546]),
    [final] ).

cnf(i_0_3377,plain,
    ( is_fun1568535512t_bool(esk279_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1580]),
    [final] ).

cnf(i_0_3378,plain,
    ( is_fun1568535512t_bool(esk278_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1580]),
    [final] ).

cnf(i_0_3379,plain,
    ( is_fun1568535512t_bool(esk263_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1544]),
    [final] ).

cnf(i_0_3380,plain,
    ( is_fun1568535512t_bool(esk262_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1544]),
    [final] ).

cnf(i_0_3381,plain,
    ( is_fun1568535512t_bool(esk211_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1581]),
    [final] ).

cnf(i_0_3382,plain,
    ( is_fun1568535512t_bool(esk210_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1581]),
    [final] ).

cnf(i_0_3383,plain,
    ( is_fun1568535512t_bool(esk187_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1545]),
    [final] ).

cnf(i_0_3384,plain,
    ( is_fun1568535512t_bool(esk186_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1545]),
    [final] ).

cnf(i_0_3385,plain,
    ( is_fun2093718614t_bool(esk447_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1571]),
    [final] ).

cnf(i_0_3386,plain,
    ( is_fun2093718614t_bool(esk446_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1571]),
    [final] ).

cnf(i_0_3387,plain,
    ( is_fun2093718614t_bool(esk431_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1531]),
    [final] ).

cnf(i_0_3388,plain,
    ( is_fun2093718614t_bool(esk430_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1531]),
    [final] ).

cnf(i_0_3389,plain,
    ( is_fun2093718614t_bool(esk281_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_3390,plain,
    ( is_fun2093718614t_bool(esk280_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_3391,plain,
    ( is_fun2093718614t_bool(esk265_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1530]),
    [final] ).

cnf(i_0_3392,plain,
    ( is_fun2093718614t_bool(esk264_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1530]),
    [final] ).

cnf(i_0_3393,plain,
    ( is_bool(esk441_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1587]),
    [final] ).

cnf(i_0_3394,plain,
    ( is_bool(esk440_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1587]),
    [final] ).

cnf(i_0_3395,plain,
    ( is_bool(esk425_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1549]),
    [final] ).

cnf(i_0_3396,plain,
    ( is_bool(esk424_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1549]),
    [final] ).

cnf(i_0_3397,plain,
    ( is_bool(esk275_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1586]),
    [final] ).

cnf(i_0_3398,plain,
    ( is_bool(esk274_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1586]),
    [final] ).

cnf(i_0_3399,plain,
    ( is_bool(esk259_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1548]),
    [final] ).

cnf(i_0_3400,plain,
    ( is_bool(esk258_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1548]),
    [final] ).

cnf(i_0_3401,plain,
    ( is_fun1236654035i_bool(esk477_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1591]),
    [final] ).

cnf(i_0_3402,plain,
    ( is_fun1236654035i_bool(esk476_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1591]),
    [final] ).

cnf(i_0_3403,plain,
    ( is_fun1236654035i_bool(esk453_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1543]),
    [final] ).

cnf(i_0_3404,plain,
    ( is_fun1236654035i_bool(esk452_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1543]),
    [final] ).

cnf(i_0_3405,plain,
    ( is_fun1236654035i_bool(esk443_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1590]),
    [final] ).

cnf(i_0_3406,plain,
    ( is_fun1236654035i_bool(esk442_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1590]),
    [final] ).

cnf(i_0_3407,plain,
    ( is_fun1236654035i_bool(esk427_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1542]),
    [final] ).

cnf(i_0_3408,plain,
    ( is_fun1236654035i_bool(esk426_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1542]),
    [final] ).

cnf(i_0_3409,plain,
    ( is_fun1236654035i_bool(esk277_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1588]),
    [final] ).

cnf(i_0_3410,plain,
    ( is_fun1236654035i_bool(esk276_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1588]),
    [final] ).

cnf(i_0_3411,plain,
    ( is_fun1236654035i_bool(esk261_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1540]),
    [final] ).

cnf(i_0_3412,plain,
    ( is_fun1236654035i_bool(esk260_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1540]),
    [final] ).

cnf(i_0_3413,plain,
    ( is_fun1236654035i_bool(esk213_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1589]),
    [final] ).

cnf(i_0_3414,plain,
    ( is_fun1236654035i_bool(esk212_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1589]),
    [final] ).

cnf(i_0_3415,plain,
    ( is_fun1236654035i_bool(esk189_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1541]),
    [final] ).

cnf(i_0_3416,plain,
    ( is_fun1236654035i_bool(esk188_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1541]),
    [final] ).

cnf(i_0_3417,plain,
    ( is_fun961089132t_bool(esk439_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1573]),
    [final] ).

cnf(i_0_3418,plain,
    ( is_fun961089132t_bool(esk438_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1573]),
    [final] ).

cnf(i_0_3419,plain,
    ( is_fun961089132t_bool(esk423_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1533]),
    [final] ).

cnf(i_0_3420,plain,
    ( is_fun961089132t_bool(esk422_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1533]),
    [final] ).

cnf(i_0_3421,plain,
    ( is_fun961089132t_bool(esk273_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_3422,plain,
    ( is_fun961089132t_bool(esk272_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_3423,plain,
    ( is_fun961089132t_bool(esk257_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1532]),
    [final] ).

cnf(i_0_3424,plain,
    ( is_fun961089132t_bool(esk256_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1532]),
    [final] ).

cnf(i_0_3425,plain,
    ( is_fun288122577l_bool(esk437_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1575]),
    [final] ).

cnf(i_0_3426,plain,
    ( is_fun288122577l_bool(esk436_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1575]),
    [final] ).

cnf(i_0_3427,plain,
    ( is_fun288122577l_bool(esk421_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1535]),
    [final] ).

cnf(i_0_3428,plain,
    ( is_fun288122577l_bool(esk420_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1535]),
    [final] ).

cnf(i_0_3429,plain,
    ( is_fun288122577l_bool(esk271_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1574]),
    [final] ).

cnf(i_0_3430,plain,
    ( is_fun288122577l_bool(esk270_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1574]),
    [final] ).

cnf(i_0_3431,plain,
    ( is_fun288122577l_bool(esk255_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1534]),
    [final] ).

cnf(i_0_3432,plain,
    ( is_fun288122577l_bool(esk254_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1534]),
    [final] ).

cnf(i_0_3433,plain,
    ( is_fun279392540l_bool(esk433_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1579]),
    [final] ).

cnf(i_0_3434,plain,
    ( is_fun279392540l_bool(esk432_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1579]),
    [final] ).

cnf(i_0_3435,plain,
    ( is_fun279392540l_bool(esk417_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1539]),
    [final] ).

cnf(i_0_3436,plain,
    ( is_fun279392540l_bool(esk416_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1539]),
    [final] ).

cnf(i_0_3437,plain,
    ( is_fun279392540l_bool(esk267_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1578]),
    [final] ).

cnf(i_0_3438,plain,
    ( is_fun279392540l_bool(esk266_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1578]),
    [final] ).

cnf(i_0_3439,plain,
    ( is_fun279392540l_bool(esk251_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1538]),
    [final] ).

cnf(i_0_3440,plain,
    ( is_fun279392540l_bool(esk250_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1538]),
    [final] ).

cnf(i_0_3441,plain,
    ( is_fun158382675l_bool(esk435_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1577]),
    [final] ).

cnf(i_0_3442,plain,
    ( is_fun158382675l_bool(esk434_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X3)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X1,X4)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1577]),
    [final] ).

cnf(i_0_3443,plain,
    ( is_fun158382675l_bool(esk419_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1537]),
    [final] ).

cnf(i_0_3444,plain,
    ( is_fun158382675l_bool(esk418_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X3)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X1,X4)),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1537]),
    [final] ).

cnf(i_0_3445,plain,
    ( is_fun158382675l_bool(esk269_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1576]),
    [final] ).

cnf(i_0_3446,plain,
    ( is_fun158382675l_bool(esk268_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X2,X1)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1576]),
    [final] ).

cnf(i_0_3447,plain,
    ( is_fun158382675l_bool(esk253_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1536]),
    [final] ).

cnf(i_0_3448,plain,
    ( is_fun158382675l_bool(esk252_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X2,X1)),X4))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1536]),
    [final] ).

cnf(i_0_3449,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk481_3(X1,X2,X3)),esk482_3(X1,X2,X3)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X3,X1)),hAPP_nat_nat(X3,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1707]),
    [final] ).

cnf(i_0_3450,plain,
    ( X4 = X5
    | X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),arrow_1539419881_below(X3,X4,X5)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3451,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X3),X2)),X4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),X2)),X4),
    inference(split_conjunct,[status(thm)],[i_0_1757]),
    [final] ).

cnf(i_0_3452,plain,
    ( hAPP_nat_nat(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk512_1(X1)),X2)) = hAPP_nat_nat(X1,esk512_1(X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,hAPP_nat_nat(suc,esk511_1(X1)))),hAPP_nat_nat(X1,esk511_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1758]),
    [final] ).

cnf(i_0_3453,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X3)),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X3)),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1746]),
    [final] ).

cnf(i_0_3454,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X3)),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X3)),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1747]),
    [final] ).

cnf(i_0_3455,plain,
    ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk16_1(X1)),esk17_1(X1))),hAPP_f412050202t_bool(X1,esk15_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1701]),
    [final] ).

cnf(i_0_3456,plain,
    ( is_fun1568535512t_bool(esk377_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1684]),
    [final] ).

cnf(i_0_3457,plain,
    ( is_fun1568535512t_bool(esk376_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1684]),
    [final] ).

cnf(i_0_3458,plain,
    ( is_fun1568535512t_bool(esk361_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_3459,plain,
    ( is_fun1568535512t_bool(esk360_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_3460,plain,
    ( is_fun1568535512t_bool(esk309_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2030293770ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1685]),
    [final] ).

cnf(i_0_3461,plain,
    ( is_fun1568535512t_bool(esk308_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2030293770ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2030293770ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1685]),
    [final] ).

cnf(i_0_3462,plain,
    ( is_fun1568535512t_bool(esk285_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f543204480t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_3463,plain,
    ( is_fun1568535512t_bool(esk284_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f543204480t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f543204480t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_3464,plain,
    ( is_fun1568535512t_bool(esk173_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1673]),
    [final] ).

cnf(i_0_3465,plain,
    ( is_fun1568535512t_bool(esk172_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1673]),
    [final] ).

cnf(i_0_3466,plain,
    ( is_fun1568535512t_bool(esk157_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1635]),
    [final] ).

cnf(i_0_3467,plain,
    ( is_fun1568535512t_bool(esk156_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1635]),
    [final] ).

cnf(i_0_3468,plain,
    ( is_fun1568535512t_bool(esk105_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2030293770ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1674]),
    [final] ).

cnf(i_0_3469,plain,
    ( is_fun1568535512t_bool(esk104_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2030293770ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2030293770ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1674]),
    [final] ).

cnf(i_0_3470,plain,
    ( is_fun1568535512t_bool(esk81_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f543204480t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1636]),
    [final] ).

cnf(i_0_3471,plain,
    ( is_fun1568535512t_bool(esk80_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f543204480t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f543204480t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1636]),
    [final] ).

cnf(i_0_3472,plain,
    ( is_fun2093718614t_bool(esk379_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1358350510ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1358350510ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1679]),
    [final] ).

cnf(i_0_3473,plain,
    ( is_fun2093718614t_bool(esk378_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1358350510ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1358350510ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1679]),
    [final] ).

cnf(i_0_3474,plain,
    ( is_fun2093718614t_bool(esk363_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f1363542492t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f1363542492t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1642]),
    [final] ).

cnf(i_0_3475,plain,
    ( is_fun2093718614t_bool(esk362_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f1363542492t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f1363542492t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1642]),
    [final] ).

cnf(i_0_3476,plain,
    ( is_fun2093718614t_bool(esk175_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1358350510ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1358350510ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1668]),
    [final] ).

cnf(i_0_3477,plain,
    ( is_fun2093718614t_bool(esk174_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1358350510ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1358350510ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1668]),
    [final] ).

cnf(i_0_3478,plain,
    ( is_fun2093718614t_bool(esk159_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f1363542492t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f1363542492t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1628]),
    [final] ).

cnf(i_0_3479,plain,
    ( is_fun2093718614t_bool(esk158_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f1363542492t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f1363542492t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1628]),
    [final] ).

cnf(i_0_3480,plain,
    ( is_bool(esk373_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_bool_nat(X3,X1)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_bool_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1687]),
    [final] ).

cnf(i_0_3481,plain,
    ( is_bool(esk372_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_bool_nat(X3,X1)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_bool_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1687]),
    [final] ).

cnf(i_0_3482,plain,
    ( is_bool(esk357_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_b1013836512t_bool(X3,X1)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_b1013836512t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1651]),
    [final] ).

cnf(i_0_3483,plain,
    ( is_bool(esk356_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_b1013836512t_bool(X3,X1)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_b1013836512t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1651]),
    [final] ).

cnf(i_0_3484,plain,
    ( is_bool(esk169_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_bool_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_bool_nat(X2,X3)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1676]),
    [final] ).

cnf(i_0_3485,plain,
    ( is_bool(esk168_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_bool_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_bool_nat(X2,X3)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1676]),
    [final] ).

cnf(i_0_3486,plain,
    ( is_bool(esk153_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_b1013836512t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_b1013836512t_bool(X2,X3)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1637]),
    [final] ).

cnf(i_0_3487,plain,
    ( is_bool(esk152_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_b1013836512t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_b1013836512t_bool(X2,X3)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1637]),
    [final] ).

cnf(i_0_3488,plain,
    ( is_fun1236654035i_bool(esk375_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1688]),
    [final] ).

cnf(i_0_3489,plain,
    ( is_fun1236654035i_bool(esk374_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1688]),
    [final] ).

cnf(i_0_3490,plain,
    ( is_fun1236654035i_bool(esk359_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1647]),
    [final] ).

cnf(i_0_3491,plain,
    ( is_fun1236654035i_bool(esk358_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1647]),
    [final] ).

cnf(i_0_3492,plain,
    ( is_fun1236654035i_bool(esk311_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2120083535ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1689]),
    [final] ).

cnf(i_0_3493,plain,
    ( is_fun1236654035i_bool(esk310_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f2120083535ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2120083535ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1689]),
    [final] ).

cnf(i_0_3494,plain,
    ( is_fun1236654035i_bool(esk287_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f2026336507t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1648]),
    [final] ).

cnf(i_0_3495,plain,
    ( is_fun1236654035i_bool(esk286_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f2026336507t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f2026336507t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1648]),
    [final] ).

cnf(i_0_3496,plain,
    ( is_fun1236654035i_bool(esk171_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_3497,plain,
    ( is_fun1236654035i_bool(esk170_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_3498,plain,
    ( is_fun1236654035i_bool(esk155_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1633]),
    [final] ).

cnf(i_0_3499,plain,
    ( is_fun1236654035i_bool(esk154_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1633]),
    [final] ).

cnf(i_0_3500,plain,
    ( is_fun1236654035i_bool(esk107_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2120083535ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1678]),
    [final] ).

cnf(i_0_3501,plain,
    ( is_fun1236654035i_bool(esk106_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f2120083535ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2120083535ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1678]),
    [final] ).

cnf(i_0_3502,plain,
    ( is_fun1236654035i_bool(esk83_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f2026336507t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1634]),
    [final] ).

cnf(i_0_3503,plain,
    ( is_fun1236654035i_bool(esk82_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f2026336507t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f2026336507t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1634]),
    [final] ).

cnf(i_0_3504,plain,
    ( is_fun961089132t_bool(esk371_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f816335862ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f816335862ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1680]),
    [final] ).

cnf(i_0_3505,plain,
    ( is_fun961089132t_bool(esk370_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f816335862ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f816335862ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1680]),
    [final] ).

cnf(i_0_3506,plain,
    ( is_fun961089132t_bool(esk355_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f856106132t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f856106132t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1643]),
    [final] ).

cnf(i_0_3507,plain,
    ( is_fun961089132t_bool(esk354_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f856106132t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f856106132t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1643]),
    [final] ).

cnf(i_0_3508,plain,
    ( is_fun961089132t_bool(esk167_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f816335862ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f816335862ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1669]),
    [final] ).

cnf(i_0_3509,plain,
    ( is_fun961089132t_bool(esk166_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f816335862ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f816335862ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1669]),
    [final] ).

cnf(i_0_3510,plain,
    ( is_fun961089132t_bool(esk151_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f856106132t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f856106132t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1629]),
    [final] ).

cnf(i_0_3511,plain,
    ( is_fun961089132t_bool(esk150_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f856106132t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f856106132t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1629]),
    [final] ).

cnf(i_0_3512,plain,
    ( is_fun288122577l_bool(esk369_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f897066961ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f897066961ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1681]),
    [final] ).

cnf(i_0_3513,plain,
    ( is_fun288122577l_bool(esk368_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f897066961ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f897066961ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1681]),
    [final] ).

cnf(i_0_3514,plain,
    ( is_fun288122577l_bool(esk353_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f985923321t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f985923321t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1644]),
    [final] ).

cnf(i_0_3515,plain,
    ( is_fun288122577l_bool(esk352_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f985923321t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f985923321t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1644]),
    [final] ).

cnf(i_0_3516,plain,
    ( is_fun288122577l_bool(esk165_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f897066961ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f897066961ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1670]),
    [final] ).

cnf(i_0_3517,plain,
    ( is_fun288122577l_bool(esk164_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f897066961ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f897066961ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1670]),
    [final] ).

cnf(i_0_3518,plain,
    ( is_fun288122577l_bool(esk149_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f985923321t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f985923321t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1630]),
    [final] ).

cnf(i_0_3519,plain,
    ( is_fun288122577l_bool(esk148_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f985923321t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f985923321t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1630]),
    [final] ).

cnf(i_0_3520,plain,
    ( is_fun279392540l_bool(esk365_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1313392232ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1313392232ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1683]),
    [final] ).

cnf(i_0_3521,plain,
    ( is_fun279392540l_bool(esk364_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1313392232ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1313392232ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1683]),
    [final] ).

cnf(i_0_3522,plain,
    ( is_fun279392540l_bool(esk349_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f464145314t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f464145314t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1646]),
    [final] ).

cnf(i_0_3523,plain,
    ( is_fun279392540l_bool(esk348_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f464145314t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f464145314t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1646]),
    [final] ).

cnf(i_0_3524,plain,
    ( is_fun279392540l_bool(esk161_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1313392232ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1313392232ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1672]),
    [final] ).

cnf(i_0_3525,plain,
    ( is_fun279392540l_bool(esk160_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1313392232ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1313392232ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1672]),
    [final] ).

cnf(i_0_3526,plain,
    ( is_fun279392540l_bool(esk145_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f464145314t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f464145314t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1632]),
    [final] ).

cnf(i_0_3527,plain,
    ( is_fun279392540l_bool(esk144_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f464145314t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f464145314t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1632]),
    [final] ).

cnf(i_0_3528,plain,
    ( is_fun158382675l_bool(esk367_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1695077327ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1695077327ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1682]),
    [final] ).

cnf(i_0_3529,plain,
    ( is_fun158382675l_bool(esk366_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1695077327ol_nat(X3,X1)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_f1695077327ol_nat(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1682]),
    [final] ).

cnf(i_0_3530,plain,
    ( is_fun158382675l_bool(esk351_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f839525755t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f839525755t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1645]),
    [final] ).

cnf(i_0_3531,plain,
    ( is_fun158382675l_bool(esk350_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f839525755t_bool(X3,X1)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X4),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),hAPP_f839525755t_bool(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1645]),
    [final] ).

cnf(i_0_3532,plain,
    ( is_fun158382675l_bool(esk163_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1695077327ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1695077327ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1671]),
    [final] ).

cnf(i_0_3533,plain,
    ( is_fun158382675l_bool(esk162_4(X1,X2,X3,X4))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1695077327ol_nat(X2,X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_f1695077327ol_nat(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1671]),
    [final] ).

cnf(i_0_3534,plain,
    ( is_fun158382675l_bool(esk147_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f839525755t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f839525755t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1631]),
    [final] ).

cnf(i_0_3535,plain,
    ( is_fun158382675l_bool(esk146_4(X1,X2,X3,X4))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f839525755t_bool(X2,X4)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),hAPP_f839525755t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1631]),
    [final] ).

cnf(i_0_3536,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X1,esk179_2(X1,X2))),hAPP_P606313927t_bool(X2,esk179_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1759]),
    [final] ).

cnf(i_0_3537,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X1,esk32_2(X1,X2))),hAPP_P606313927t_bool(X2,esk32_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1760]),
    [final] ).

cnf(i_0_3538,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X1,esk176_2(X1,X2))),hAPP_f592646513l_bool(X2,esk176_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1761]),
    [final] ).

cnf(i_0_3539,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X1,esk29_2(X1,X2))),hAPP_f592646513l_bool(X2,esk29_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1762]),
    [final] ).

cnf(i_0_3540,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X1,esk177_2(X1,X2))),hAPP_f312250286l_bool(X2,esk177_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1763]),
    [final] ).

cnf(i_0_3541,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X1,esk30_2(X1,X2))),hAPP_f312250286l_bool(X2,esk30_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1764]),
    [final] ).

cnf(i_0_3542,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X1,esk178_2(X1,X2))),hAPP_f965095724l_bool(X2,esk178_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1765]),
    [final] ).

cnf(i_0_3543,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X1,esk31_2(X1,X2))),hAPP_f965095724l_bool(X2,esk31_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1766]),
    [final] ).

cnf(i_0_3544,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X1,esk181_2(X1,X2))),hAPP_P1676879539t_bool(X2,esk181_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1767]),
    [final] ).

cnf(i_0_3545,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X1,esk34_2(X1,X2))),hAPP_P1676879539t_bool(X2,esk34_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1768]),
    [final] ).

cnf(i_0_3546,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk183_2(X1,X2))),hAPP_nat_bool(X2,esk183_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1769]),
    [final] ).

cnf(i_0_3547,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk36_2(X1,X2))),hAPP_nat_bool(X2,esk36_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1770]),
    [final] ).

cnf(i_0_3548,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X1,esk180_2(X1,X2))),hAPP_A1785763630i_bool(X2,esk180_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1771]),
    [final] ).

cnf(i_0_3549,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X1,esk33_2(X1,X2))),hAPP_A1785763630i_bool(X2,esk33_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1772]),
    [final] ).

cnf(i_0_3550,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X1,esk182_2(X1,X2))),hAPP_A1664620203t_bool(X2,esk182_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1773]),
    [final] ).

cnf(i_0_3551,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X1,esk35_2(X1,X2))),hAPP_A1664620203t_bool(X2,esk35_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1774]),
    [final] ).

cnf(i_0_3552,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X3),X1),X2)),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1775]),
    [final] ).

cnf(i_0_3553,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1776]),
    [final] ).

cnf(i_0_3554,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_3555,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1778]),
    [final] ).

cnf(i_0_3556,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1779]),
    [final] ).

cnf(i_0_3557,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_3558,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1781]),
    [final] ).

cnf(i_0_3559,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1782]),
    [final] ).

cnf(i_0_3560,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1783]),
    [final] ).

cnf(i_0_3561,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1784]),
    [final] ).

cnf(i_0_3562,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1785]),
    [final] ).

cnf(i_0_3563,plain,
    ( X3 = X2
    | X3 = X1
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X5),X4),X2)))
    | X4 = X2
    | X1 != X2
    | X3 != X4
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3564,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X3))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X1)),X3))
    | X1 = X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1751]),
    [final] ).

cnf(i_0_3565,plain,
    ( X1 != X2
    | X1 != X3
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4),X2)))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1754]),
    [final] ).

cnf(i_0_3566,plain,
    ( X1 != X2
    | X3 != X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4),X2)))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_3567,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4),X2)))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_3568,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4),X2)))
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1754]),
    [final] ).

cnf(i_0_3569,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X1)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1786]),
    [final] ).

cnf(i_0_3570,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X1)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1787]),
    [final] ).

cnf(i_0_3571,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X1)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1788]),
    [final] ).

cnf(i_0_3572,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X1)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1789]),
    [final] ).

cnf(i_0_3573,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1790]),
    [final] ).

cnf(i_0_3574,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1791]),
    [final] ).

cnf(i_0_3575,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1792]),
    [final] ).

cnf(i_0_3576,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1793]),
    [final] ).

cnf(i_0_3577,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1794]),
    [final] ).

cnf(i_0_3578,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1795]),
    [final] ).

cnf(i_0_3579,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1796]),
    [final] ).

cnf(i_0_3580,plain,
    ( X3 = X2
    | X1 = X3
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),arrow_1539419881_below(X5,X2,X4)))
    | X2 = X4
    | X1 != X2
    | X3 != X4
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X5),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3581,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X1),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1797]),
    [final] ).

cnf(i_0_3582,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X2),X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1798]),
    [final] ).

cnf(i_0_3583,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk496_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_nat_bool(X1,X2))
    | ~ hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1799]),
    [final] ).

cnf(i_0_3584,plain,
    ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk496_3(X1,X2,X3))))
    | hBOOL(hAPP_nat_bool(X1,X2))
    | ~ hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1799]),
    [final] ).

cnf(i_0_3585,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(times_times_nat(X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1800]),
    [final] ).

cnf(i_0_3586,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(times_times_nat(X1),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1801]),
    [final] ).

cnf(i_0_3587,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(times_times_nat(X1),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1802]),
    [final] ).

cnf(i_0_3588,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(times_times_nat(X1),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1803]),
    [final] ).

cnf(i_0_3589,plain,
    is_fun288122577l_bool(undefi203294880l_bool(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn]),
    [final] ).

cnf(i_0_3590,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1804]),
    [final] ).

cnf(i_0_3591,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1804]),
    [final] ).

cnf(i_0_3592,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1805]),
    [final] ).

cnf(i_0_3593,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1806]),
    [final] ).

cnf(i_0_3594,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1807]),
    [final] ).

cnf(i_0_3595,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X1,X4)),X3))
    | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X1),pi_Pro1928973619le_alt(X2,hAPP_f1066247963t_bool(cOMBK_812212462t_unit,X3))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1808]),
    [final] ).

cnf(i_0_3596,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X1),pi_boo115158845le_alt(X2,hAPP_f340261009t_bool(cOMBK_545135096l_bool,X3))))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1809]),
    [final] ).

cnf(i_0_3597,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X1),pi_Arr1199386158le_alt(X2,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X3))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1810]),
    [final] ).

cnf(i_0_3598,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),pi_fun150026276t_bool(X2,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,X3))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1811]),
    [final] ).

cnf(i_0_3599,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X1),pi_Pro718203741t_bool(X2,hAPP_f2028504885l_bool(cOMBK_384545070t_unit,X3))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1812]),
    [final] ).

cnf(i_0_3600,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X1),pi_boo538701011t_bool(X2,hAPP_f256804927l_bool(cOMBK_69806648l_bool,X3))))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1813]),
    [final] ).

cnf(i_0_3601,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),pi_Arr990697634t_bool(X2,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,X3))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1814]),
    [final] ).

cnf(i_0_3602,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X1),pi_Pro1880661658t_bool(X2,hAPP_f1028353513l_bool(cOMBK_731023445t_unit,X3))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1815]),
    [final] ).

cnf(i_0_3603,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X1),pi_boo1117000868t_bool(X2,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,X3))))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1816]),
    [final] ).

cnf(i_0_3604,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X1),pi_Arr1936979349t_bool(X2,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,X3))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3605,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X1),pi_Pro610293528t_bool(X2,hAPP_f512628453l_bool(cOMBK_295807955t_unit,X3))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1818]),
    [final] ).

cnf(i_0_3606,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X1),pi_boo175444770t_bool(X2,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,X3))))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1819]),
    [final] ).

cnf(i_0_3607,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X1),pi_Arr2020412179t_bool(X2,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,X3))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1820]),
    [final] ).

cnf(i_0_3608,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X1,X4)),X3))
    | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X1),pi_nat_Product_unit(X2,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,X3))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1821]),
    [final] ).

cnf(i_0_3609,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X1,X4)),X3))
    | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X1),pi_fun308431217t_unit(X2,hAPP_f478658281t_bool(cOMBK_1589894370t_bool,X3))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1822]),
    [final] ).

cnf(i_0_3610,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X1),pi_fun321364250t_unit(X2,hAPP_f894574520t_bool(cOMBK_1733280085t_bool,X3))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1823]),
    [final] ).

cnf(i_0_3611,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X1,X4)),X3))
    | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X1),pi_fun1877263000t_unit(X2,hAPP_f587035834t_bool(cOMBK_1048254163t_bool,X3))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1824]),
    [final] ).

cnf(i_0_3612,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X1,X4)),X3))
    | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X1),pi_Pro1122146355t_unit(X2,hAPP_f1165814111t_bool(cOMBK_859929070le_alt,X3))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1825]),
    [final] ).

cnf(i_0_3613,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X1,X4)),X3))
    | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X1),pi_Product_unit_nat(X2,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,X3))))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1826]),
    [final] ).

cnf(i_0_3614,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X1,X4)),X3))
    | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X1),pi_bool_nat(X2,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,X3))))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1827]),
    [final] ).

cnf(i_0_3615,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X1),pi_Arr346900227di_nat(X2,hAPP_f1491725936t_bool(cOMBK_847149194e_indi,X3))))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1828]),
    [final] ).

cnf(i_0_3616,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),pi_Pro666468413t_bool(X2,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,X3))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1829]),
    [final] ).

cnf(i_0_3617,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X1),pi_fun1575168891l_bool(X2,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,X3))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1830]),
    [final] ).

cnf(i_0_3618,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X1),pi_fun52649508l_bool(X2,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,X3))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1831]),
    [final] ).

cnf(i_0_3619,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X1),pi_fun823343522l_bool(X2,hAPP_f746617550l_bool(cOMBK_370033373t_bool,X3))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1832]),
    [final] ).

cnf(i_0_3620,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),pi_nat_bool(X2,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,X3))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1833]),
    [final] ).

cnf(i_0_3621,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X1),pi_Pro1270767662e_indi(X2,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,X3))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1834]),
    [final] ).

cnf(i_0_3622,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X1,X4)),X3))
    | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X1),pi_fun896360044e_indi(X2,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,X3))))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1835]),
    [final] ).

cnf(i_0_3623,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X1,X4)),X3))
    | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X1),pi_fun1002945429e_indi(X2,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,X3))))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1836]),
    [final] ).

cnf(i_0_3624,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X1,X4)),X3))
    | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X1),pi_fun753830419e_indi(X2,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,X3))))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1837]),
    [final] ).

cnf(i_0_3625,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X1,X4)),X3))
    | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X1),pi_nat660525389e_indi(X2,hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,X3))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1838]),
    [final] ).

cnf(i_0_3626,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(times_times_nat(X1),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1839]),
    [final] ).

cnf(i_0_3627,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(times_times_nat(X2),X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1840]),
    [final] ).

cnf(i_0_3628,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,arrow_1539419881_below(X3,X1,X2)),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),arrow_1681063817le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1841]),
    [final] ).

cnf(i_0_3629,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,esk42_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X1),pi_Pro1122146355t_unit(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1709]),
    [final] ).

cnf(i_0_3630,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,esk69_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),pi_Pro666468413t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1710]),
    [final] ).

cnf(i_0_3631,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,esk41_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X1),pi_Pro1270767662e_indi(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1711]),
    [final] ).

cnf(i_0_3632,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk51_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X1),pi_fun308431217t_unit(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1712]),
    [final] ).

cnf(i_0_3633,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk50_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X1),pi_fun1575168891l_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1713]),
    [final] ).

cnf(i_0_3634,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk49_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X1),pi_fun896360044e_indi(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1714]),
    [final] ).

cnf(i_0_3635,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,esk48_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X1),pi_fun321364250t_unit(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1715]),
    [final] ).

cnf(i_0_3636,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,esk47_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X1),pi_fun52649508l_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1716]),
    [final] ).

cnf(i_0_3637,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,esk46_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X1),pi_fun1002945429e_indi(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1717]),
    [final] ).

cnf(i_0_3638,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk70_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),pi_fun150026276t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1718]),
    [final] ).

cnf(i_0_3639,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk45_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X1),pi_fun1877263000t_unit(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3640,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk44_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X1),pi_fun823343522l_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1720]),
    [final] ).

cnf(i_0_3641,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk43_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X1),pi_fun753830419e_indi(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1721]),
    [final] ).

cnf(i_0_3642,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk57_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X1),pi_Pro1928973619le_alt(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1722]),
    [final] ).

cnf(i_0_3643,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk65_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X1),pi_Pro718203741t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1723]),
    [final] ).

cnf(i_0_3644,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk63_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X1),pi_Pro1880661658t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1724]),
    [final] ).

cnf(i_0_3645,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk60_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X1),pi_Pro610293528t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1725]),
    [final] ).

cnf(i_0_3646,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,esk68_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X1),pi_Product_unit_nat(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1726]),
    [final] ).

cnf(i_0_3647,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk54_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X1),pi_nat_Product_unit(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1727]),
    [final] ).

cnf(i_0_3648,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk53_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),pi_nat_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1728]),
    [final] ).

cnf(i_0_3649,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk52_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X1),pi_nat660525389e_indi(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1729]),
    [final] ).

cnf(i_0_3650,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk56_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X1),pi_boo115158845le_alt(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1730]),
    [final] ).

cnf(i_0_3651,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk64_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X1),pi_boo538701011t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1731]),
    [final] ).

cnf(i_0_3652,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk62_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X1),pi_boo1117000868t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1732]),
    [final] ).

cnf(i_0_3653,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk59_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X1),pi_boo175444770t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1733]),
    [final] ).

cnf(i_0_3654,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,esk67_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X1),pi_bool_nat(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1734]),
    [final] ).

cnf(i_0_3655,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk55_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X1),pi_Arr1199386158le_alt(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1735]),
    [final] ).

cnf(i_0_3656,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk71_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),pi_Arr990697634t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1736]),
    [final] ).

cnf(i_0_3657,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk61_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X1),pi_Arr1936979349t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1737]),
    [final] ).

cnf(i_0_3658,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk58_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X1),pi_Arr2020412179t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1738]),
    [final] ).

cnf(i_0_3659,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk66_3(X1,X2,X3)),X3))
    | hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X1),pi_Arr346900227di_nat(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_3660,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1842]),
    [final] ).

cnf(i_0_3661,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1776]),
    [final] ).

cnf(i_0_3662,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1843]),
    [final] ).

cnf(i_0_3663,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1778]),
    [final] ).

cnf(i_0_3664,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1779]),
    [final] ).

cnf(i_0_3665,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1844]),
    [final] ).

cnf(i_0_3666,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1845]),
    [final] ).

cnf(i_0_3667,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1781]),
    [final] ).

cnf(i_0_3668,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1846]),
    [final] ).

cnf(i_0_3669,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1783]),
    [final] ).

cnf(i_0_3670,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1784]),
    [final] ).

cnf(i_0_3671,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1847]),
    [final] ).

cnf(i_0_3672,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,h),n)))),
    inference(split_conjunct,[status(thm)],[fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0]),
    [final] ).

cnf(i_0_3673,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk16_1(X2)),esk17_1(X2))),hAPP_A1677245848t_bool(esk15_1(X2),X1)))
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X2))
    | ~ is_Arr43961803e_indi(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1701]),
    [final] ).

cnf(i_0_3674,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X1)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),X2)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1786]),
    [final] ).

cnf(i_0_3675,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X1)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1787]),
    [final] ).

cnf(i_0_3676,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X1)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),X2)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1788]),
    [final] ).

cnf(i_0_3677,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X1)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),X2)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1789]),
    [final] ).

cnf(i_0_3678,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1790]),
    [final] ).

cnf(i_0_3679,plain,
    ( hBOOL(hAPP_nat_bool(X1,X2))
    | ~ hBOOL(hAPP_nat_bool(X1,esk496_3(X1,X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1799]),
    [final] ).

cnf(i_0_3680,negated_conjecture,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
    inference(split_conjunct,[status(thm)],[i_0_1848]),
    [final] ).

cnf(i_0_3681,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1849]),
    [final] ).

cnf(i_0_3682,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1850]),
    [final] ).

cnf(i_0_3683,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk23_2(X1,X2)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X2),X1))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X2),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1741]),
    [final] ).

cnf(i_0_3684,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),X3)),hAPP_nat_nat(times_times_nat(X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1851]),
    [final] ).

cnf(i_0_3685,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X3),X1)),hAPP_nat_nat(times_times_nat(X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3686,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X1,X4)),hAPP_P1341894483t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X1),pi_Pro1928973619le_alt(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1853]),
    [final] ).

cnf(i_0_3687,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(X1,X4)),hAPP_P1341894483t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,X1),pi_Pro1928973619le_alt(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1854]),
    [final] ).

cnf(i_0_3688,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X1,X4)),hAPP_b1703662281t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X1),pi_boo115158845le_alt(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1855]),
    [final] ).

cnf(i_0_3689,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(X1,X4)),hAPP_b1703662281t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X1),pi_boo115158845le_alt(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1856]),
    [final] ).

cnf(i_0_3690,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X1,X4)),hAPP_A1677245848t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X1),pi_Arr1199386158le_alt(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1857]),
    [final] ).

cnf(i_0_3691,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(X1,X4)),hAPP_A1677245848t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X1),pi_Arr1199386158le_alt(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1858]),
    [final] ).

cnf(i_0_3692,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X1,X4)),hAPP_f1277514478l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),pi_fun150026276t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1859]),
    [final] ).

cnf(i_0_3693,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(X1,X4)),hAPP_f1277514478l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),pi_fun150026276t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1860]),
    [final] ).

cnf(i_0_3694,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X1,X4)),hAPP_P1294997365l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X1),pi_Pro718203741t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1861]),
    [final] ).

cnf(i_0_3695,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(X1,X4)),hAPP_P1294997365l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,X1),pi_Pro718203741t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1862]),
    [final] ).

cnf(i_0_3696,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X1,X4)),hAPP_b1812770943l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X1),pi_boo538701011t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1863]),
    [final] ).

cnf(i_0_3697,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(X1,X4)),hAPP_b1812770943l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X1),pi_boo538701011t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1864]),
    [final] ).

cnf(i_0_3698,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X1,X4)),hAPP_A60074736l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),pi_Arr990697634t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1865]),
    [final] ).

cnf(i_0_3699,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(X1,X4)),hAPP_A60074736l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),pi_Arr990697634t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1866]),
    [final] ).

cnf(i_0_3700,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X1,X4)),hAPP_P1171466554l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X1),pi_Pro1880661658t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1867]),
    [final] ).

cnf(i_0_3701,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(X1,X4)),hAPP_P1171466554l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,X1),pi_Pro1880661658t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1868]),
    [final] ).

cnf(i_0_3702,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X1,X4)),hAPP_b517355696l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X1),pi_boo1117000868t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1869]),
    [final] ).

cnf(i_0_3703,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(X1,X4)),hAPP_b517355696l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X1),pi_boo1117000868t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1870]),
    [final] ).

cnf(i_0_3704,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X1,X4)),hAPP_A1112981887l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X1),pi_Arr1936979349t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1871]),
    [final] ).

cnf(i_0_3705,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(X1,X4)),hAPP_A1112981887l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X1),pi_Arr1936979349t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1872]),
    [final] ).

cnf(i_0_3706,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X1,X4)),hAPP_P254387896l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X1),pi_Pro610293528t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1873]),
    [final] ).

cnf(i_0_3707,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(X1,X4)),hAPP_P254387896l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,X1),pi_Pro610293528t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1874]),
    [final] ).

cnf(i_0_3708,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X1,X4)),hAPP_b1048178734l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X1),pi_boo175444770t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1875]),
    [final] ).

cnf(i_0_3709,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(X1,X4)),hAPP_b1048178734l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X1),pi_boo175444770t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1876]),
    [final] ).

cnf(i_0_3710,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X1,X4)),hAPP_A1952883197l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X1),pi_Arr2020412179t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1877]),
    [final] ).

cnf(i_0_3711,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(X1,X4)),hAPP_A1952883197l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X1),pi_Arr2020412179t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1878]),
    [final] ).

cnf(i_0_3712,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X1,X4)),hAPP_n454528608t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X1),pi_nat_Product_unit(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1879]),
    [final] ).

cnf(i_0_3713,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(X1,X4)),hAPP_n454528608t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,X1),pi_nat_Product_unit(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1880]),
    [final] ).

cnf(i_0_3714,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X1,X4)),hAPP_f1710744577t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X1),pi_fun308431217t_unit(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1881]),
    [final] ).

cnf(i_0_3715,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(X1,X4)),hAPP_f1710744577t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X1),pi_fun308431217t_unit(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1882]),
    [final] ).

cnf(i_0_3716,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X1,X4)),hAPP_f1866147972t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X1),pi_fun321364250t_unit(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1883]),
    [final] ).

cnf(i_0_3717,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(X1,X4)),hAPP_f1866147972t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,X1),pi_fun321364250t_unit(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1884]),
    [final] ).

cnf(i_0_3718,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X1,X4)),hAPP_f1891021702t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X1),pi_fun1877263000t_unit(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1885]),
    [final] ).

cnf(i_0_3719,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(X1,X4)),hAPP_f1891021702t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,X1),pi_fun1877263000t_unit(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1886]),
    [final] ).

cnf(i_0_3720,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X1,X4)),hAPP_P332578347t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X1),pi_Pro1122146355t_unit(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1887]),
    [final] ).

cnf(i_0_3721,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(X1,X4)),hAPP_P332578347t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,X1),pi_Pro1122146355t_unit(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1888]),
    [final] ).

cnf(i_0_3722,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X1,X4)),hAPP_P32877782t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X1),pi_Product_unit_nat(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1889]),
    [final] ).

cnf(i_0_3723,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(X1,X4)),hAPP_P32877782t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,X1),pi_Product_unit_nat(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1890]),
    [final] ).

cnf(i_0_3724,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X1,X4)),hAPP_b1013836512t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X1),pi_bool_nat(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1891]),
    [final] ).

cnf(i_0_3725,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(X1,X4)),hAPP_b1013836512t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X1),pi_bool_nat(X2,X3)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1892]),
    [final] ).

cnf(i_0_3726,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X1,X4)),hAPP_A2046586321t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X1),pi_Arr346900227di_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1893]),
    [final] ).

cnf(i_0_3727,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(X1,X4)),hAPP_A2046586321t_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X1),pi_Arr346900227di_nat(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1894]),
    [final] ).

cnf(i_0_3728,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X1,X4)),hAPP_P324742453l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),pi_Pro666468413t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1895]),
    [final] ).

cnf(i_0_3729,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(X1,X4)),hAPP_P324742453l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),pi_Pro666468413t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1896]),
    [final] ).

cnf(i_0_3730,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X1,X4)),hAPP_f210572555l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X1),pi_fun1575168891l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1897]),
    [final] ).

cnf(i_0_3731,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(X1,X4)),hAPP_f210572555l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X1),pi_fun1575168891l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1898]),
    [final] ).

cnf(i_0_3732,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X1,X4)),hAPP_f1624277646l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X1),pi_fun52649508l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1899]),
    [final] ).

cnf(i_0_3733,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(X1,X4)),hAPP_f1624277646l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,X1),pi_fun52649508l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1900]),
    [final] ).

cnf(i_0_3734,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X1,X4)),hAPP_f839832464l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X1),pi_fun823343522l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1901]),
    [final] ).

cnf(i_0_3735,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(X1,X4)),hAPP_f839832464l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,X1),pi_fun823343522l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1902]),
    [final] ).

cnf(i_0_3736,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X1,X4)),hAPP_n1006566506l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),pi_nat_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1903]),
    [final] ).

cnf(i_0_3737,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(X1,X4)),hAPP_n1006566506l_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),pi_nat_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1904]),
    [final] ).

cnf(i_0_3738,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X1,X4)),hAPP_P1875867302i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X1),pi_Pro1270767662e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1905]),
    [final] ).

cnf(i_0_3739,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(X1,X4)),hAPP_P1875867302i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,X1),pi_Pro1270767662e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1906]),
    [final] ).

cnf(i_0_3740,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X1,X4)),hAPP_f244157820i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X1),pi_fun896360044e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1907]),
    [final] ).

cnf(i_0_3741,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(X1,X4)),hAPP_f244157820i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X1),pi_fun896360044e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1908]),
    [final] ).

cnf(i_0_3742,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X1,X4)),hAPP_f1552576127i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X1),pi_fun1002945429e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1909]),
    [final] ).

cnf(i_0_3743,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(X1,X4)),hAPP_f1552576127i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,X1),pi_fun1002945429e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1910]),
    [final] ).

cnf(i_0_3744,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X1,X4)),hAPP_f1948454017i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X1),pi_fun753830419e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1911]),
    [final] ).

cnf(i_0_3745,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(X1,X4)),hAPP_f1948454017i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,X1),pi_fun753830419e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1912]),
    [final] ).

cnf(i_0_3746,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X1,X4)),hAPP_n821919323i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X1),pi_nat660525389e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1913]),
    [final] ).

cnf(i_0_3747,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(X1,X4)),hAPP_n821919323i_bool(X3,X4)))
    | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,X1),pi_nat660525389e_indi(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1914]),
    [final] ).

cnf(i_0_3748,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(times_times_nat(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3749,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1851]),
    [final] ).

cnf(i_0_3750,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X3)),hAPP_nat_nat(times_times_nat(X2),X4)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1915]),
    [final] ).

cnf(i_0_3751,plain,
    ( X1 = X3
    | X3 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X4),X2)))
    | X1 != X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1754]),
    [final] ).

cnf(i_0_3752,plain,
    ( X3 = X1
    | X3 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X4),X2)))
    | X1 != X2
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_3753,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X3),X1)),hAPP_nat_nat(times_times_nat(X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1801]),
    [final] ).

cnf(i_0_3754,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(times_times_nat(X1),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3755,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),X3)),hAPP_nat_nat(times_times_nat(X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1916]),
    [final] ).

cnf(i_0_3756,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1851]),
    [final] ).

cnf(i_0_3757,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X3),X1)),hAPP_nat_nat(times_times_nat(X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1803]),
    [final] ).

cnf(i_0_3758,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X3),X1)),hAPP_nat_nat(times_times_nat(X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1917]),
    [final] ).

cnf(i_0_3759,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1797]),
    [final] ).

cnf(i_0_3760,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1797]),
    [final] ).

cnf(i_0_3761,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)),
    inference(split_conjunct,[status(thm)],[i_0_1918]),
    [final] ).

cnf(i_0_3762,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)),
    inference(split_conjunct,[status(thm)],[i_0_1919]),
    [final] ).

cnf(i_0_3763,plain,
    ( hAPP_n1699378549t_bool(ord_at4362885an_nat(X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(X1),X2)),hAPP_n1699378549t_bool(ord_at4362885an_nat(X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1920]),
    [final] ).

cnf(i_0_3764,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1921]),
    [final] ).

cnf(i_0_3765,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X1),X2)),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),arrow_1681063817le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1922]),
    [final] ).

cnf(i_0_3766,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X1),X2)),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),arrow_1681063817le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1923]),
    [final] ).

cnf(i_0_3767,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1924]),
    [final] ).

cnf(i_0_3768,plain,
    ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk490_2(X2,X1)),one_one_nat)))
    | hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1925]),
    [final] ).

cnf(i_0_3769,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,X1)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1924]),
    [final] ).

cnf(i_0_3770,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk514_2(X1,X2)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X2)))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1926]),
    [final] ).

cnf(i_0_3771,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk510_2(X1,X2)),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X2)))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1927]),
    [final] ).

cnf(i_0_3772,plain,
    ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X2),X1))
    | esk24_2(X1,X2) != esk25_2(X1,X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X2),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1741]),
    [final] ).

cnf(i_0_3773,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),esk26_2(X1,X2)))
    | X1 = X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1928]),
    [final] ).

cnf(i_0_3774,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk515_2(X1,X2)),X2))
    | hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1929]),
    [final] ).

cnf(i_0_3775,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk507_2(X1,X2)),X2))
    | hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1930]),
    [final] ).

cnf(i_0_3776,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X3)),hAPP_nat_nat(times_times_nat(X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1800]),
    [final] ).

cnf(i_0_3777,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X3)),hAPP_nat_nat(times_times_nat(X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1931]),
    [final] ).

cnf(i_0_3778,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X3),X1)),hAPP_nat_nat(times_times_nat(X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1802]),
    [final] ).

cnf(i_0_3779,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X3),X1)),hAPP_nat_nat(times_times_nat(X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1932]),
    [final] ).

cnf(i_0_3780,plain,
    hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X1)),hAPP_n1699378549t_bool(ord_at238088361st_nat(X2),X3)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1933]),
    [final] ).

cnf(i_0_3781,plain,
    hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X1)),hAPP_n1699378549t_bool(ord_at4362885an_nat(X2),X3)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1934]),
    [final] ).

cnf(i_0_3782,plain,
    ( is_Arr1861959080le_alt(esk25_2(X1,X2))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X2),X1))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X2),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1741]),
    [final] ).

cnf(i_0_3783,plain,
    ( is_Arr1861959080le_alt(esk24_2(X1,X2))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X2),X1))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X2),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1741]),
    [final] ).

cnf(i_0_3784,plain,
    ( hBOOL(hAPP_P606313927t_bool(X1,X2))
    | ~ hBOOL(hAPP_P606313927t_bool(X1,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,esk7_1(X1)),esk8_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1935]),
    [final] ).

cnf(i_0_3785,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk513_2(X1,X2)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1926]),
    [final] ).

cnf(i_0_3786,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk509_2(X1,X2)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1927]),
    [final] ).

cnf(i_0_3787,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1936]),
    [final] ).

cnf(i_0_3788,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1937]),
    [final] ).

cnf(i_0_3789,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1938]),
    [final] ).

cnf(i_0_3790,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_1939]),
    [final] ).

cnf(i_0_3791,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_1940]),
    [final] ).

cnf(i_0_3792,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1941]),
    [final] ).

cnf(i_0_3793,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk516_2(X1,X2)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X2)))
    | hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1929]),
    [final] ).

cnf(i_0_3794,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk508_2(X1,X2)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X2)))
    | hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1930]),
    [final] ).

cnf(i_0_3795,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk501_2(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1942]),
    [final] ).

cnf(i_0_3796,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1943]),
    [final] ).

cnf(i_0_3797,plain,
    ( hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(X1,esk515_2(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1929]),
    [final] ).

cnf(i_0_3798,plain,
    ( hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(X1,esk507_2(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1930]),
    [final] ).

cnf(i_0_3799,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(times_times_nat(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1802]),
    [final] ).

cnf(i_0_3800,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1800]),
    [final] ).

cnf(i_0_3801,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk494_2(X1,X2)),X2))
    | X1 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_3802,plain,
    ( X1 = X2
    | ~ is_Arr43961803e_indi(X1)
    | ~ is_Arr43961803e_indi(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X3),X4))
    | hAPP_A1637648121di_nat(X3,X1) != hAPP_A1637648121di_nat(X3,X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1945]),
    [final] ).

cnf(i_0_3803,plain,
    ( X1 = X2
    | ~ is_Arr43961803e_indi(X1)
    | ~ is_Arr43961803e_indi(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X3),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X2),X4))
    | hAPP_A1637648121di_nat(X3,X1) != hAPP_A1637648121di_nat(X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1946]),
    [final] ).

cnf(i_0_3804,plain,
    ( X2 = X3
    | hAPP_A1637648121di_nat(X1,X2) != hAPP_A1637648121di_nat(X1,X3)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X3),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X2),X4))
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X4))
    | ~ is_Arr43961803e_indi(X3)
    | ~ is_Arr43961803e_indi(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1947]),
    [final] ).

cnf(i_0_3805,plain,
    ( X3 = X4
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X2))
    | ~ is_Arr43961803e_indi(X3)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X3),X2))
    | ~ is_Arr43961803e_indi(X4)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X4),X2))
    | hAPP_A1637648121di_nat(X1,X3) != hAPP_A1637648121di_nat(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_3806,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X1),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1949]),
    [final] ).

cnf(i_0_3807,plain,
    ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X1,X3)),hAPP_A1664620203t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ is_Arr1861959080le_alt(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1774]),
    [final] ).

cnf(i_0_3808,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X1,X3)),hAPP_f592646513l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ is_fun961089132t_bool(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1762]),
    [final] ).

cnf(i_0_3809,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X1,X3)),hAPP_A1785763630i_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ is_Arr43961803e_indi(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1772]),
    [final] ).

cnf(i_0_3810,plain,
    ( hBOOL(hAPP_nat_bool(X1,X2))
    | ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk505_2(X2,X1))))
    | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1950]),
    [final] ).

cnf(i_0_3811,plain,
    ( X2 = X3
    | hAPP_nat_nat(X1,X2) != hAPP_nat_nat(X1,X3)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X4))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1951]),
    [final] ).

cnf(i_0_3812,plain,
    ( X3 = X4
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2))
    | hAPP_nat_nat(X1,X3) != hAPP_nat_nat(X1,X4)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1952]),
    [final] ).

cnf(i_0_3813,plain,
    ( X3 = X4
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2))
    | hAPP_nat_nat(X1,X3) != hAPP_nat_nat(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1953]),
    [final] ).

cnf(i_0_3814,plain,
    ( X3 = X4
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2))
    | hAPP_nat_nat(X1,X3) != hAPP_nat_nat(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_3815,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(X2,X3)),pi_Pro666468413t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1955]),
    [final] ).

cnf(i_0_3816,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(X2,X3)),pi_fun150026276t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1956]),
    [final] ).

cnf(i_0_3817,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(X2,X3)),pi_Arr990697634t_bool(X1,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1957]),
    [final] ).

cnf(i_0_3818,plain,
    ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X1,X3)),hAPP_A1664620203t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1958]),
    [final] ).

cnf(i_0_3819,plain,
    ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(X1,X3)),hAPP_A1664620203t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1959]),
    [final] ).

cnf(i_0_3820,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X1,X3)),hAPP_P606313927t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1760]),
    [final] ).

cnf(i_0_3821,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X1,X3)),hAPP_P606313927t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1960]),
    [final] ).

cnf(i_0_3822,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(X1,X3)),hAPP_P606313927t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1961]),
    [final] ).

cnf(i_0_3823,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X1,X3)),hAPP_f592646513l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1962]),
    [final] ).

cnf(i_0_3824,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(X1,X3)),hAPP_f592646513l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1963]),
    [final] ).

cnf(i_0_3825,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X1,X3)),hAPP_f312250286l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1764]),
    [final] ).

cnf(i_0_3826,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X1,X3)),hAPP_f312250286l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1964]),
    [final] ).

cnf(i_0_3827,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(X1,X3)),hAPP_f312250286l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1965]),
    [final] ).

cnf(i_0_3828,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X1,X3)),hAPP_f965095724l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1766]),
    [final] ).

cnf(i_0_3829,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X1,X3)),hAPP_f965095724l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1966]),
    [final] ).

cnf(i_0_3830,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(X1,X3)),hAPP_f965095724l_bool(X2,X3)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1967]),
    [final] ).

cnf(i_0_3831,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X1,X3)),hAPP_P1676879539t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1768]),
    [final] ).

cnf(i_0_3832,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X1,X3)),hAPP_P1676879539t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1968]),
    [final] ).

cnf(i_0_3833,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(X1,X3)),hAPP_P1676879539t_bool(X2,X3)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1969]),
    [final] ).

cnf(i_0_3834,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X3)),hAPP_nat_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1770]),
    [final] ).

cnf(i_0_3835,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X3)),hAPP_nat_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1970]),
    [final] ).

cnf(i_0_3836,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X3)),hAPP_nat_bool(X2,X3)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1971]),
    [final] ).

cnf(i_0_3837,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X1,X3)),hAPP_A1785763630i_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1972]),
    [final] ).

cnf(i_0_3838,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(X1,X3)),hAPP_A1785763630i_bool(X2,X3)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1973]),
    [final] ).

cnf(i_0_3839,plain,
    ( hBOOL(hAPP_nat_bool(X1,esk514_2(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X2)))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1926]),
    [final] ).

cnf(i_0_3840,plain,
    ( hBOOL(hAPP_nat_bool(X1,esk510_2(X1,X2)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),X2)))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1927]),
    [final] ).

cnf(i_0_3841,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1974]),
    [final] ).

cnf(i_0_3842,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1975]),
    [final] ).

cnf(i_0_3843,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1976]),
    [final] ).

cnf(i_0_3844,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1977]),
    [final] ).

cnf(i_0_3845,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1978]),
    [final] ).

cnf(i_0_3846,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1979]),
    [final] ).

cnf(i_0_3847,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1980]),
    [final] ).

cnf(i_0_3848,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1981]),
    [final] ).

cnf(i_0_3849,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1982]),
    [final] ).

cnf(i_0_3850,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1983]),
    [final] ).

cnf(i_0_3851,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1984]),
    [final] ).

cnf(i_0_3852,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1985]),
    [final] ).

cnf(i_0_3853,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1986]),
    [final] ).

cnf(i_0_3854,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_1987]),
    [final] ).

cnf(i_0_3855,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_1988]),
    [final] ).

cnf(i_0_3856,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1936]),
    [final] ).

cnf(i_0_3857,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1937]),
    [final] ).

cnf(i_0_3858,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1989]),
    [final] ).

cnf(i_0_3859,plain,
    ( hBOOL(hAPP_nat_bool(X3,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk490_2(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(X3,X1))
    | ~ hBOOL(hAPP_nat_bool(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1925]),
    [final] ).

cnf(i_0_3860,plain,
    ( hBOOL(hAPP_nat_bool(X3,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk491_2(X2,X3)))
    | ~ hBOOL(hAPP_nat_bool(X3,X1))
    | ~ hBOOL(hAPP_nat_bool(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1990]),
    [final] ).

cnf(i_0_3861,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1921]),
    [final] ).

cnf(i_0_3862,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1921]),
    [final] ).

cnf(i_0_3863,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),esk20_0)),
    inference(split_conjunct,[status(thm)],[i_0_1991]),
    [final] ).

cnf(i_0_3864,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)),
    inference(split_conjunct,[status(thm)],[fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]),
    [final] ).

cnf(i_0_3865,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),esk19_0)),
    inference(split_conjunct,[status(thm)],[i_0_1992]),
    [final] ).

cnf(i_0_3866,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)),
    inference(split_conjunct,[status(thm)],[fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]),
    [final] ).

cnf(i_0_3867,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1993]),
    [final] ).

cnf(i_0_3868,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X3),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1994]),
    [final] ).

cnf(i_0_3869,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X3),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1995]),
    [final] ).

cnf(i_0_3870,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X3),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1996]),
    [final] ).

cnf(i_0_3871,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1997]),
    [final] ).

cnf(i_0_3872,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1998]),
    [final] ).

cnf(i_0_3873,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1999]),
    [final] ).

cnf(i_0_3874,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2000]),
    [final] ).

cnf(i_0_3875,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2001]),
    [final] ).

cnf(i_0_3876,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X3))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2002]),
    [final] ).

cnf(i_0_3877,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X3),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2003]),
    [final] ).

cnf(i_0_3878,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X3),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2004]),
    [final] ).

cnf(i_0_3879,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2005]),
    [final] ).

cnf(i_0_3880,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2006]),
    [final] ).

cnf(i_0_3881,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2007]),
    [final] ).

cnf(i_0_3882,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2008]),
    [final] ).

cnf(i_0_3883,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2009]),
    [final] ).

cnf(i_0_3884,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2010]),
    [final] ).

cnf(i_0_3885,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X3),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2011]),
    [final] ).

cnf(i_0_3886,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X3),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2012]),
    [final] ).

cnf(i_0_3887,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),X3))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2013]),
    [final] ).

cnf(i_0_3888,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2014]),
    [final] ).

cnf(i_0_3889,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2015]),
    [final] ).

cnf(i_0_3890,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2016]),
    [final] ).

cnf(i_0_3891,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2017]),
    [final] ).

cnf(i_0_3892,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2018]),
    [final] ).

cnf(i_0_3893,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2019]),
    [final] ).

cnf(i_0_3894,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2020]),
    [final] ).

cnf(i_0_3895,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2021]),
    [final] ).

cnf(i_0_3896,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2022]),
    [final] ).

cnf(i_0_3897,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X3),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2023]),
    [final] ).

cnf(i_0_3898,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X3),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2024]),
    [final] ).

cnf(i_0_3899,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),X3))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2025]),
    [final] ).

cnf(i_0_3900,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X3),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2026]),
    [final] ).

cnf(i_0_3901,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X3),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2027]),
    [final] ).

cnf(i_0_3902,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X3),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2028]),
    [final] ).

cnf(i_0_3903,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2029]),
    [final] ).

cnf(i_0_3904,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2030]),
    [final] ).

cnf(i_0_3905,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2031]),
    [final] ).

cnf(i_0_3906,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2032]),
    [final] ).

cnf(i_0_3907,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2033]),
    [final] ).

cnf(i_0_3908,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2034]),
    [final] ).

cnf(i_0_3909,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X3),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2035]),
    [final] ).

cnf(i_0_3910,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X3),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2036]),
    [final] ).

cnf(i_0_3911,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),X3))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2037]),
    [final] ).

cnf(i_0_3912,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2038]),
    [final] ).

cnf(i_0_3913,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2039]),
    [final] ).

cnf(i_0_3914,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2040]),
    [final] ).

cnf(i_0_3915,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2041]),
    [final] ).

cnf(i_0_3916,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2042]),
    [final] ).

cnf(i_0_3917,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2043]),
    [final] ).

cnf(i_0_3918,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2044]),
    [final] ).

cnf(i_0_3919,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2045]),
    [final] ).

cnf(i_0_3920,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X3))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2046]),
    [final] ).

cnf(i_0_3921,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2047]),
    [final] ).

cnf(i_0_3922,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2048]),
    [final] ).

cnf(i_0_3923,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2049]),
    [final] ).

cnf(i_0_3924,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X3),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2050]),
    [final] ).

cnf(i_0_3925,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2051]),
    [final] ).

cnf(i_0_3926,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2052]),
    [final] ).

cnf(i_0_3927,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2053]),
    [final] ).

cnf(i_0_3928,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2054]),
    [final] ).

cnf(i_0_3929,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2055]),
    [final] ).

cnf(i_0_3930,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2056]),
    [final] ).

cnf(i_0_3931,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2057]),
    [final] ).

cnf(i_0_3932,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2058]),
    [final] ).

cnf(i_0_3933,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3934,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2060]),
    [final] ).

cnf(i_0_3935,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2061]),
    [final] ).

cnf(i_0_3936,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2062]),
    [final] ).

cnf(i_0_3937,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2063]),
    [final] ).

cnf(i_0_3938,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2064]),
    [final] ).

cnf(i_0_3939,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2065]),
    [final] ).

cnf(i_0_3940,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X3),X2))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,X1),X2))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2066]),
    [final] ).

cnf(i_0_3941,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2067]),
    [final] ).

cnf(i_0_3942,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2068]),
    [final] ).

cnf(i_0_3943,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2069]),
    [final] ).

cnf(i_0_3944,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2070]),
    [final] ).

cnf(i_0_3945,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2071]),
    [final] ).

cnf(i_0_3946,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2072]),
    [final] ).

cnf(i_0_3947,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2073]),
    [final] ).

cnf(i_0_3948,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2074]),
    [final] ).

cnf(i_0_3949,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2075]),
    [final] ).

cnf(i_0_3950,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X3),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2076]),
    [final] ).

cnf(i_0_3951,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2077]),
    [final] ).

cnf(i_0_3952,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2078]),
    [final] ).

cnf(i_0_3953,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X3),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2079]),
    [final] ).

cnf(i_0_3954,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X3),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2080]),
    [final] ).

cnf(i_0_3955,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X3))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2081]),
    [final] ).

cnf(i_0_3956,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2082]),
    [final] ).

cnf(i_0_3957,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2083]),
    [final] ).

cnf(i_0_3958,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2084]),
    [final] ).

cnf(i_0_3959,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2085]),
    [final] ).

cnf(i_0_3960,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2086]),
    [final] ).

cnf(i_0_3961,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2087]),
    [final] ).

cnf(i_0_3962,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2088]),
    [final] ).

cnf(i_0_3963,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2089]),
    [final] ).

cnf(i_0_3964,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2090]),
    [final] ).

cnf(i_0_3965,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2091]),
    [final] ).

cnf(i_0_3966,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2092]),
    [final] ).

cnf(i_0_3967,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2093]),
    [final] ).

cnf(i_0_3968,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2094]),
    [final] ).

cnf(i_0_3969,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2095]),
    [final] ).

cnf(i_0_3970,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X3),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2096]),
    [final] ).

cnf(i_0_3971,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X3),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2097]),
    [final] ).

cnf(i_0_3972,plain,
    hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X1),X3)),hAPP_nat_nat(times_times_nat(X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2098]),
    [final] ).

cnf(i_0_3973,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2099]),
    [final] ).

cnf(i_0_3974,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_2100]),
    [final] ).

cnf(i_0_3975,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2101]),
    [final] ).

cnf(i_0_3976,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk485_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2102]),
    [final] ).

cnf(i_0_3977,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk487_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2103]),
    [final] ).

cnf(i_0_3978,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk489_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2104]),
    [final] ).

cnf(i_0_3979,plain,
    is_fun279392540l_bool(undefi871250829l_bool(fun(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool),bool))),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe]),
    [final] ).

cnf(i_0_3980,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X1),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_2105]),
    [final] ).

cnf(i_0_3981,plain,
    hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2106]),
    [final] ).

cnf(i_0_3982,plain,
    ( X1 = hAPP_nat_nat(suc,esk501_2(X2,X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1942]),
    [final] ).

cnf(i_0_3983,plain,
    ( X2 = hAPP_nat_nat(suc,esk499_2(X1,X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2107]),
    [final] ).

cnf(i_0_3984,plain,
    ( hAPP_nat_nat(suc,X1) = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2108]),
    [final] ).

cnf(i_0_3985,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1949]),
    [final] ).

cnf(i_0_3986,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1949]),
    [final] ).

cnf(i_0_3987,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2109]),
    [final] ).

cnf(i_0_3988,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2110]),
    [final] ).

cnf(i_0_3989,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2111]),
    [final] ).

cnf(i_0_3990,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1976]),
    [final] ).

cnf(i_0_3991,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1977]),
    [final] ).

cnf(i_0_3992,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X1 = hAPP_nat_nat(suc,X2)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2112]),
    [final] ).

cnf(i_0_3993,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X1 = hAPP_nat_nat(suc,X2)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2113]),
    [final] ).

cnf(i_0_3994,plain,
    ( hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(X1,esk516_2(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1929]),
    [final] ).

cnf(i_0_3995,plain,
    ( hBOOL(hAPP_nat_bool(X1,X3))
    | ~ hBOOL(hAPP_nat_bool(X1,esk508_2(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1930]),
    [final] ).

cnf(i_0_3996,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X1)),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),arrow_1681063817le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_2114]),
    [final] ).

cnf(i_0_3997,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X1))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2115]),
    [final] ).

cnf(i_0_3998,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X1))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2116]),
    [final] ).

cnf(i_0_3999,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X1))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2117]),
    [final] ).

cnf(i_0_4000,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X1))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2118]),
    [final] ).

cnf(i_0_4001,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X1))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2119]),
    [final] ).

cnf(i_0_4002,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X1))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2120]),
    [final] ).

cnf(i_0_4003,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X1))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2121]),
    [final] ).

cnf(i_0_4004,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X1))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2122]),
    [final] ).

cnf(i_0_4005,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X1))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2123]),
    [final] ).

cnf(i_0_4006,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X1))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2124]),
    [final] ).

cnf(i_0_4007,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2125]),
    [final] ).

cnf(i_0_4008,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2126]),
    [final] ).

cnf(i_0_4009,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X1))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2127]),
    [final] ).

cnf(i_0_4010,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X1))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2128]),
    [final] ).

cnf(i_0_4011,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X1))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2129]),
    [final] ).

cnf(i_0_4012,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X1))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2130]),
    [final] ).

cnf(i_0_4013,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2131]),
    [final] ).

cnf(i_0_4014,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2132]),
    [final] ).

cnf(i_0_4015,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2133]),
    [final] ).

cnf(i_0_4016,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2134]),
    [final] ).

cnf(i_0_4017,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X2 = X1
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2135]),
    [final] ).

cnf(i_0_4018,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2136]),
    [final] ).

cnf(i_0_4019,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2137]),
    [final] ).

cnf(i_0_4020,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2138]),
    [final] ).

cnf(i_0_4021,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X3)))
    | X1 != hAPP_nat_nat(suc,X2)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_4022,plain,
    ( hAPP_f412050202t_bool(X1,X3) = hAPP_A1677245848t_bool(X3,X2)
    | ~ hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X3),arrow_1721807329e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_2139]),
    [final] ).

cnf(i_0_4023,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk500_2(X1,X2)))
    | X2 = hAPP_nat_nat(suc,X1)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2140]),
    [final] ).

cnf(i_0_4024,plain,
    ( hAPP_n1951273283e_indi(hilber693666498di_nat(X3,X2),hAPP_A1637648121di_nat(X2,X1)) = X1
    | ~ is_Arr43961803e_indi(X1)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X2),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2141]),
    [final] ).

cnf(i_0_4025,plain,
    ( hAPP_n1951273283e_indi(hilber693666498di_nat(X3,X2),X4) = X1
    | ~ is_Arr43961803e_indi(X1)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X2),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),X3))
    | hAPP_A1637648121di_nat(X2,X1) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_2142]),
    [final] ).

cnf(i_0_4026,plain,
    ( X2 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk497_2(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2143]),
    [final] ).

cnf(i_0_4027,plain,
    ( X2 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk495_2(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2144]),
    [final] ).

cnf(i_0_4028,plain,
    ( X1 = X2
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2145]),
    [final] ).

cnf(i_0_4029,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X1))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2146]),
    [final] ).

cnf(i_0_4030,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X1))
    | ~ is_fun1568535512t_bool(X2)
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2147]),
    [final] ).

cnf(i_0_4031,plain,
    ( X1 = X2
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2148]),
    [final] ).

cnf(i_0_4032,plain,
    ( X2 = X1
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2149]),
    [final] ).

cnf(i_0_4033,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X1))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2150]),
    [final] ).

cnf(i_0_4034,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X1))
    | ~ is_fun2093718614t_bool(X2)
    | ~ is_fun2093718614t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2151]),
    [final] ).

cnf(i_0_4035,plain,
    ( X1 = X2
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2152]),
    [final] ).

cnf(i_0_4036,plain,
    ( X2 = X1
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2153]),
    [final] ).

cnf(i_0_4037,plain,
    ( X1 = X2
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2154]),
    [final] ).

cnf(i_0_4038,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X1))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2155]),
    [final] ).

cnf(i_0_4039,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X1))
    | ~ is_fun1236654035i_bool(X2)
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2156]),
    [final] ).

cnf(i_0_4040,plain,
    ( X1 = X2
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2157]),
    [final] ).

cnf(i_0_4041,plain,
    ( X2 = X1
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2158]),
    [final] ).

cnf(i_0_4042,plain,
    ( X1 = X2
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2159]),
    [final] ).

cnf(i_0_4043,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X1))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2160]),
    [final] ).

cnf(i_0_4044,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X1))
    | ~ is_fun961089132t_bool(X2)
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2161]),
    [final] ).

cnf(i_0_4045,plain,
    ( X1 = X2
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2162]),
    [final] ).

cnf(i_0_4046,plain,
    ( X2 = X1
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2163]),
    [final] ).

cnf(i_0_4047,plain,
    ( X1 = X2
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2164]),
    [final] ).

cnf(i_0_4048,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X1))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2165]),
    [final] ).

cnf(i_0_4049,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X1))
    | ~ is_fun288122577l_bool(X2)
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2166]),
    [final] ).

cnf(i_0_4050,plain,
    ( X1 = X2
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2167]),
    [final] ).

cnf(i_0_4051,plain,
    ( X2 = X1
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2168]),
    [final] ).

cnf(i_0_4052,plain,
    ( X1 = X2
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2169]),
    [final] ).

cnf(i_0_4053,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X1))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2170]),
    [final] ).

cnf(i_0_4054,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X1))
    | ~ is_fun279392540l_bool(X2)
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2171]),
    [final] ).

cnf(i_0_4055,plain,
    ( X1 = X2
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2172]),
    [final] ).

cnf(i_0_4056,plain,
    ( X2 = X1
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2173]),
    [final] ).

cnf(i_0_4057,plain,
    ( X1 = X2
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2174]),
    [final] ).

cnf(i_0_4058,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X1))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2175]),
    [final] ).

cnf(i_0_4059,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X1))
    | ~ is_fun158382675l_bool(X2)
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2176]),
    [final] ).

cnf(i_0_4060,plain,
    ( X1 = X2
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2177]),
    [final] ).

cnf(i_0_4061,plain,
    ( X2 = X1
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2178]),
    [final] ).

cnf(i_0_4062,plain,
    ( hBOOL(hAPP_P606313927t_bool(X1,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X3)))
    | ~ hBOOL(hAPP_P606313927t_bool(X1,esk6_1(X1)))
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1935]),
    [final] ).

cnf(i_0_4063,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk491_2(X1,X2)),X1))
    | hBOOL(hAPP_nat_bool(X2,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1990]),
    [final] ).

cnf(i_0_4064,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk490_2(X1,X2)),X1))
    | hBOOL(hAPP_nat_bool(X2,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1925]),
    [final] ).

cnf(i_0_4065,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(X2,X1),hAPP_nat_nat(X1,X3)) = X3
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2179]),
    [final] ).

cnf(i_0_4066,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk18_2(X1,X2)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2139]),
    [final] ).

cnf(i_0_4067,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(X2,X1),X4) = X3
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
    | hAPP_nat_nat(X1,X3) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_2180]),
    [final] ).

cnf(i_0_4068,plain,
    ( hBOOL(X2)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2181]),
    [final] ).

cnf(i_0_4069,plain,
    ( hBOOL(X2)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2181]),
    [final] ).

cnf(i_0_4070,plain,
    ( hBOOL(X2)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2182]),
    [final] ).

cnf(i_0_4071,plain,
    ( hBOOL(X2)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2182]),
    [final] ).

cnf(i_0_4072,plain,
    ( hBOOL(X2)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2183]),
    [final] ).

cnf(i_0_4073,plain,
    ( hBOOL(X2)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2183]),
    [final] ).

cnf(i_0_4074,plain,
    ( hBOOL(X2)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2184]),
    [final] ).

cnf(i_0_4075,plain,
    ( hBOOL(X2)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2184]),
    [final] ).

cnf(i_0_4076,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),esk484_1(X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2102]),
    [final] ).

cnf(i_0_4077,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),esk486_1(X1)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2103]),
    [final] ).

cnf(i_0_4078,plain,
    ( hBOOL(hAPP_nat_bool(X1,esk513_2(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1926]),
    [final] ).

cnf(i_0_4079,plain,
    ( hBOOL(hAPP_nat_bool(X1,esk509_2(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1927]),
    [final] ).

cnf(i_0_4080,plain,
    ( hilber693666498di_nat(top_to1576102282i_bool,X2) = X1
    | ~ is_fun1217980910e_indi(X1)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X2),top_to1576102282i_bool))
    | hAPP_A1637648121di_nat(X2,hAPP_n1951273283e_indi(X1,esk72_2(X1,X2))) != esk72_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2185]),
    [final] ).

cnf(i_0_4081,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | X1 != X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2099]),
    [final] ).

cnf(i_0_4082,plain,
    ( hBOOL(X3)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2186]),
    [final] ).

cnf(i_0_4083,plain,
    ( hBOOL(X3)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2187]),
    [final] ).

cnf(i_0_4084,plain,
    ( hBOOL(X3)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2188]),
    [final] ).

cnf(i_0_4085,plain,
    ( hBOOL(X3)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2189]),
    [final] ).

cnf(i_0_4086,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1943]),
    [final] ).

cnf(i_0_4087,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2190]),
    [final] ).

cnf(i_0_4088,plain,
    hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_nat_nat(times_times_nat(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2191]),
    [final] ).

cnf(i_0_4089,plain,
    ( hilber195283148at_nat(top_top_fun_nat_bool,X1) = X2
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),top_top_fun_nat_bool))
    | hAPP_nat_nat(X1,hAPP_nat_nat(X2,esk73_2(X2,X1))) != esk73_2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2192]),
    [final] ).

cnf(i_0_4090,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2193]),
    [final] ).

cnf(i_0_4091,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2194]),
    [final] ).

cnf(i_0_4092,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2195]),
    [final] ).

cnf(i_0_4093,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2196]),
    [final] ).

cnf(i_0_4094,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2197]),
    [final] ).

cnf(i_0_4095,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2198]),
    [final] ).

cnf(i_0_4096,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2199]),
    [final] ).

cnf(i_0_4097,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2200]),
    [final] ).

cnf(i_0_4098,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2201]),
    [final] ).

cnf(i_0_4099,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2202]),
    [final] ).

cnf(i_0_4100,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2203]),
    [final] ).

cnf(i_0_4101,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk492_2(X1,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2204]),
    [final] ).

cnf(i_0_4102,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2112]),
    [final] ).

cnf(i_0_4103,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2205]),
    [final] ).

cnf(i_0_4104,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2206]),
    [final] ).

cnf(i_0_4105,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2137]),
    [final] ).

cnf(i_0_4106,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2133]),
    [final] ).

cnf(i_0_4107,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2207]),
    [final] ).

cnf(i_0_4108,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2115]),
    [final] ).

cnf(i_0_4109,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2116]),
    [final] ).

cnf(i_0_4110,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2117]),
    [final] ).

cnf(i_0_4111,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2118]),
    [final] ).

cnf(i_0_4112,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2119]),
    [final] ).

cnf(i_0_4113,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2120]),
    [final] ).

cnf(i_0_4114,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2121]),
    [final] ).

cnf(i_0_4115,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2122]),
    [final] ).

cnf(i_0_4116,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2123]),
    [final] ).

cnf(i_0_4117,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2124]),
    [final] ).

cnf(i_0_4118,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2208]),
    [final] ).

cnf(i_0_4119,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2209]),
    [final] ).

cnf(i_0_4120,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2210]),
    [final] ).

cnf(i_0_4121,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2211]),
    [final] ).

cnf(i_0_4122,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2212]),
    [final] ).

cnf(i_0_4123,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2125]),
    [final] ).

cnf(i_0_4124,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2126]),
    [final] ).

cnf(i_0_4125,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2213]),
    [final] ).

cnf(i_0_4126,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2214]),
    [final] ).

cnf(i_0_4127,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2215]),
    [final] ).

cnf(i_0_4128,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2216]),
    [final] ).

cnf(i_0_4129,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2217]),
    [final] ).

cnf(i_0_4130,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2127]),
    [final] ).

cnf(i_0_4131,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2128]),
    [final] ).

cnf(i_0_4132,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2218]),
    [final] ).

cnf(i_0_4133,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2219]),
    [final] ).

cnf(i_0_4134,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2220]),
    [final] ).

cnf(i_0_4135,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2221]),
    [final] ).

cnf(i_0_4136,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2222]),
    [final] ).

cnf(i_0_4137,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2129]),
    [final] ).

cnf(i_0_4138,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2130]),
    [final] ).

cnf(i_0_4139,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2223]),
    [final] ).

cnf(i_0_4140,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2224]),
    [final] ).

cnf(i_0_4141,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2131]),
    [final] ).

cnf(i_0_4142,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2225]),
    [final] ).

cnf(i_0_4143,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2226]),
    [final] ).

cnf(i_0_4144,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2227]),
    [final] ).

cnf(i_0_4145,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2228]),
    [final] ).

cnf(i_0_4146,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2229]),
    [final] ).

cnf(i_0_4147,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2230]),
    [final] ).

cnf(i_0_4148,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2231]),
    [final] ).

cnf(i_0_4149,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2132]),
    [final] ).

cnf(i_0_4150,plain,
    ( is_bool(esk67_3(X1,X2,X3))
    | hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,X1),pi_bool_nat(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1734]),
    [final] ).

cnf(i_0_4151,plain,
    ( is_bool(esk64_3(X1,X2,X3))
    | hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,X1),pi_boo538701011t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1731]),
    [final] ).

cnf(i_0_4152,plain,
    ( is_bool(esk62_3(X1,X2,X3))
    | hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,X1),pi_boo1117000868t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1732]),
    [final] ).

cnf(i_0_4153,plain,
    ( is_bool(esk59_3(X1,X2,X3))
    | hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,X1),pi_boo175444770t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1733]),
    [final] ).

cnf(i_0_4154,plain,
    ( is_bool(esk56_3(X1,X2,X3))
    | hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,X1),pi_boo115158845le_alt(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1730]),
    [final] ).

cnf(i_0_4155,plain,
    ( is_Arr43961803e_indi(esk71_3(X1,X2,X3))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),pi_Arr990697634t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1736]),
    [final] ).

cnf(i_0_4156,plain,
    ( is_Arr43961803e_indi(esk66_3(X1,X2,X3))
    | hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,X1),pi_Arr346900227di_nat(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_4157,plain,
    ( is_Arr43961803e_indi(esk61_3(X1,X2,X3))
    | hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,X1),pi_Arr1936979349t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1737]),
    [final] ).

cnf(i_0_4158,plain,
    ( is_Arr43961803e_indi(esk58_3(X1,X2,X3))
    | hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,X1),pi_Arr2020412179t_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1738]),
    [final] ).

cnf(i_0_4159,plain,
    ( is_Arr43961803e_indi(esk55_3(X1,X2,X3))
    | hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,X1),pi_Arr1199386158le_alt(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1735]),
    [final] ).

cnf(i_0_4160,plain,
    ( is_fun961089132t_bool(esk51_3(X1,X2,X3))
    | hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,X1),pi_fun308431217t_unit(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1712]),
    [final] ).

cnf(i_0_4161,plain,
    ( is_fun961089132t_bool(esk50_3(X1,X2,X3))
    | hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,X1),pi_fun1575168891l_bool(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1713]),
    [final] ).

cnf(i_0_4162,plain,
    ( is_fun961089132t_bool(esk49_3(X1,X2,X3))
    | hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,X1),pi_fun896360044e_indi(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1714]),
    [final] ).

cnf(i_0_4163,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X1),X2))
    | X2 = X1
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2232]),
    [final] ).

cnf(i_0_4164,plain,
    ( X1 = hAPP_nat_nat(suc,esk494_2(X1,X2))
    | X1 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_4165,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2233]),
    [final] ).

cnf(i_0_4166,plain,
    ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2234]),
    [final] ).

cnf(i_0_4167,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk40_2(X1,X2)),X2))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_4168,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk39_2(X1,X2)),X2))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_4169,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk38_2(X1,X2)),X2))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_4170,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,esk37_2(X1,X2)),X2))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_4171,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2235]),
    [final] ).

cnf(i_0_4172,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))),
    inference(split_conjunct,[status(thm)],[i_0_2236]),
    [final] ).

cnf(i_0_4173,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2237]),
    [final] ).

cnf(i_0_4174,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),one_one_nat))),
    inference(split_conjunct,[status(thm)],[i_0_2238]),
    [final] ).

cnf(i_0_4175,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2239]),
    [final] ).

cnf(i_0_4176,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2240]),
    [final] ).

cnf(i_0_4177,plain,
    ( X2 = X1
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2241]),
    [final] ).

cnf(i_0_4178,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2242]),
    [final] ).

cnf(i_0_4179,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | X1 = X2
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2243]),
    [final] ).

cnf(i_0_4180,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2244]),
    [final] ).

cnf(i_0_4181,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2245]),
    [final] ).

cnf(i_0_4182,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2246]),
    [final] ).

cnf(i_0_4183,plain,
    ( X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X2),X1))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2247]),
    [final] ).

cnf(i_0_4184,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2248]),
    [final] ).

cnf(i_0_4185,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2249]),
    [final] ).

cnf(i_0_4186,plain,
    ( X2 = X1
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2250]),
    [final] ).

cnf(i_0_4187,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2251]),
    [final] ).

cnf(i_0_4188,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | X1 = X2
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2252]),
    [final] ).

cnf(i_0_4189,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2253]),
    [final] ).

cnf(i_0_4190,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2254]),
    [final] ).

cnf(i_0_4191,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2255]),
    [final] ).

cnf(i_0_4192,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X2),X1))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2256]),
    [final] ).

cnf(i_0_4193,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2257]),
    [final] ).

cnf(i_0_4194,plain,
    ( X1 = X2
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2258]),
    [final] ).

cnf(i_0_4195,plain,
    ( X2 = X1
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2259]),
    [final] ).

cnf(i_0_4196,plain,
    ( X1 = X2
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2260]),
    [final] ).

cnf(i_0_4197,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | X1 = X2
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2261]),
    [final] ).

cnf(i_0_4198,plain,
    ( X1 = X2
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2262]),
    [final] ).

cnf(i_0_4199,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2263]),
    [final] ).

cnf(i_0_4200,plain,
    ( X1 = X2
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2264]),
    [final] ).

cnf(i_0_4201,plain,
    ( X1 = X2
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X2),X1))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2265]),
    [final] ).

cnf(i_0_4202,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2266]),
    [final] ).

cnf(i_0_4203,plain,
    ( X1 = X2
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2267]),
    [final] ).

cnf(i_0_4204,plain,
    ( X2 = X1
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2268]),
    [final] ).

cnf(i_0_4205,plain,
    ( X1 = X2
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2269]),
    [final] ).

cnf(i_0_4206,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | X1 = X2
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2270]),
    [final] ).

cnf(i_0_4207,plain,
    ( X1 = X2
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2271]),
    [final] ).

cnf(i_0_4208,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2272]),
    [final] ).

cnf(i_0_4209,plain,
    ( X1 = X2
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2273]),
    [final] ).

cnf(i_0_4210,plain,
    ( X1 = X2
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X2),X1))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2274]),
    [final] ).

cnf(i_0_4211,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2275]),
    [final] ).

cnf(i_0_4212,plain,
    ( X1 = X2
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2276]),
    [final] ).

cnf(i_0_4213,plain,
    ( X2 = X1
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2277]),
    [final] ).

cnf(i_0_4214,plain,
    ( X1 = X2
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2278]),
    [final] ).

cnf(i_0_4215,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | X1 = X2
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2279]),
    [final] ).

cnf(i_0_4216,plain,
    ( X1 = X2
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2280]),
    [final] ).

cnf(i_0_4217,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2281]),
    [final] ).

cnf(i_0_4218,plain,
    ( X1 = X2
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2282]),
    [final] ).

cnf(i_0_4219,plain,
    ( X1 = X2
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X2),X1))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2283]),
    [final] ).

cnf(i_0_4220,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2284]),
    [final] ).

cnf(i_0_4221,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2285]),
    [final] ).

cnf(i_0_4222,plain,
    ( X2 = X1
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2286]),
    [final] ).

cnf(i_0_4223,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2287]),
    [final] ).

cnf(i_0_4224,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | X1 = X2
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2288]),
    [final] ).

cnf(i_0_4225,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2289]),
    [final] ).

cnf(i_0_4226,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2290]),
    [final] ).

cnf(i_0_4227,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2291]),
    [final] ).

cnf(i_0_4228,plain,
    ( X1 = X2
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X2),X1))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2292]),
    [final] ).

cnf(i_0_4229,plain,
    ( X2 = X1
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2293]),
    [final] ).

cnf(i_0_4230,plain,
    ( X1 = X2
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2294]),
    [final] ).

cnf(i_0_4231,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | X1 = X2
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2295]),
    [final] ).

cnf(i_0_4232,plain,
    ( X1 = X2
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2296]),
    [final] ).

cnf(i_0_4233,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2297]),
    [final] ).

cnf(i_0_4234,plain,
    ( X1 = X2
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2298]),
    [final] ).

cnf(i_0_4235,plain,
    ( X1 = X2
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X2),X1))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2299]),
    [final] ).

cnf(i_0_4236,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2239]),
    [final] ).

cnf(i_0_4237,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2240]),
    [final] ).

cnf(i_0_4238,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2245]),
    [final] ).

cnf(i_0_4239,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2246]),
    [final] ).

cnf(i_0_4240,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2248]),
    [final] ).

cnf(i_0_4241,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2249]),
    [final] ).

cnf(i_0_4242,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2254]),
    [final] ).

cnf(i_0_4243,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2255]),
    [final] ).

cnf(i_0_4244,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2257]),
    [final] ).

cnf(i_0_4245,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2258]),
    [final] ).

cnf(i_0_4246,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2263]),
    [final] ).

cnf(i_0_4247,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2264]),
    [final] ).

cnf(i_0_4248,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2266]),
    [final] ).

cnf(i_0_4249,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2267]),
    [final] ).

cnf(i_0_4250,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2272]),
    [final] ).

cnf(i_0_4251,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2273]),
    [final] ).

cnf(i_0_4252,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2275]),
    [final] ).

cnf(i_0_4253,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2276]),
    [final] ).

cnf(i_0_4254,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2281]),
    [final] ).

cnf(i_0_4255,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2282]),
    [final] ).

cnf(i_0_4256,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2284]),
    [final] ).

cnf(i_0_4257,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2285]),
    [final] ).

cnf(i_0_4258,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2290]),
    [final] ).

cnf(i_0_4259,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2291]),
    [final] ).

cnf(i_0_4260,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2297]),
    [final] ).

cnf(i_0_4261,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2298]),
    [final] ).

cnf(i_0_4262,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2182]),
    [final] ).

cnf(i_0_4263,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2300]),
    [final] ).

cnf(i_0_4264,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2301]),
    [final] ).

cnf(i_0_4265,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2302]),
    [final] ).

cnf(i_0_4266,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2303]),
    [final] ).

cnf(i_0_4267,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
    | X1 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2144]),
    [final] ).

cnf(i_0_4268,plain,
    ( hAPP_f22106695ol_nat(big_co387207925at_nat(X1),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),X2)) = hAPP_f22106695ol_nat(big_co387207925at_nat(X1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),X2))
    | hAPP_nat_nat(X1,zero_zero_nat) != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2304]),
    [final] ).

cnf(i_0_4269,plain,
    ( X2 = X3
    | hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X1)),X2) != hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2305]),
    [final] ).

cnf(i_0_4270,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2306]),
    [final] ).

cnf(i_0_4271,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2307]),
    [final] ).

cnf(i_0_4272,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2308]),
    [final] ).

cnf(i_0_4273,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2309]),
    [final] ).

cnf(i_0_4274,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2310]),
    [final] ).

cnf(i_0_4275,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2311]),
    [final] ).

cnf(i_0_4276,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2312]),
    [final] ).

cnf(i_0_4277,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2306]),
    [final] ).

cnf(i_0_4278,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2307]),
    [final] ).

cnf(i_0_4279,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2308]),
    [final] ).

cnf(i_0_4280,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2309]),
    [final] ).

cnf(i_0_4281,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2310]),
    [final] ).

cnf(i_0_4282,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2311]),
    [final] ).

cnf(i_0_4283,plain,
    ( hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X2),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2312]),
    [final] ).

cnf(i_0_4284,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk487_2(X1,X2)),X1))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2103]),
    [final] ).

cnf(i_0_4285,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk485_2(X1,X2)),X1))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2102]),
    [final] ).

cnf(i_0_4286,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk489_2(X1,X2)),X2))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2104]),
    [final] ).

cnf(i_0_4287,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2182]),
    [final] ).

cnf(i_0_4288,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2300]),
    [final] ).

cnf(i_0_4289,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2301]),
    [final] ).

cnf(i_0_4290,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2302]),
    [final] ).

cnf(i_0_4291,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2303]),
    [final] ).

cnf(i_0_4292,plain,
    ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,X1),X2))
    | hAPP_f412050202t_bool(X1,esk18_2(X1,X2)) != hAPP_A1677245848t_bool(esk18_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2139]),
    [final] ).

cnf(i_0_4293,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2134]),
    [final] ).

cnf(i_0_4294,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2313]),
    [final] ).

cnf(i_0_4295,plain,
    ( X1 = X2
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2314]),
    [final] ).

cnf(i_0_4296,plain,
    ( X2 = X1
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2315]),
    [final] ).

cnf(i_0_4297,plain,
    ( X1 = X2
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2316]),
    [final] ).

cnf(i_0_4298,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2317]),
    [final] ).

cnf(i_0_4299,plain,
    ( X1 = X2
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2318]),
    [final] ).

cnf(i_0_4300,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2319]),
    [final] ).

cnf(i_0_4301,plain,
    ( X1 = X2
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2320]),
    [final] ).

cnf(i_0_4302,plain,
    ( X1 = X2
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2321]),
    [final] ).

cnf(i_0_4303,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2322]),
    [final] ).

cnf(i_0_4304,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2323]),
    [final] ).

cnf(i_0_4305,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2324]),
    [final] ).

cnf(i_0_4306,plain,
    ( X2 = X1
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2325]),
    [final] ).

cnf(i_0_4307,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2326]),
    [final] ).

cnf(i_0_4308,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2327]),
    [final] ).

cnf(i_0_4309,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2190]),
    [final] ).

cnf(i_0_4310,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2328]),
    [final] ).

cnf(i_0_4311,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2329]),
    [final] ).

cnf(i_0_4312,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2330]),
    [final] ).

cnf(i_0_4313,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2331]),
    [final] ).

cnf(i_0_4314,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2332]),
    [final] ).

cnf(i_0_4315,plain,
    ( hBOOL(hAPP_nat_bool(X2,X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2333]),
    [final] ).

cnf(i_0_4316,plain,
    ( hBOOL(hAPP_nat_bool(X3,X2))
    | ~ hBOOL(hAPP_nat_bool(X1,X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2334]),
    [final] ).

cnf(i_0_4317,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_nat_nat(suc,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_2101]),
    [final] ).

cnf(i_0_4318,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2335]),
    [final] ).

cnf(i_0_4319,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2115]),
    [final] ).

cnf(i_0_4320,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2336]),
    [final] ).

cnf(i_0_4321,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2116]),
    [final] ).

cnf(i_0_4322,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2337]),
    [final] ).

cnf(i_0_4323,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2117]),
    [final] ).

cnf(i_0_4324,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2338]),
    [final] ).

cnf(i_0_4325,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2118]),
    [final] ).

cnf(i_0_4326,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2339]),
    [final] ).

cnf(i_0_4327,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2119]),
    [final] ).

cnf(i_0_4328,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2340]),
    [final] ).

cnf(i_0_4329,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2120]),
    [final] ).

cnf(i_0_4330,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2341]),
    [final] ).

cnf(i_0_4331,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2121]),
    [final] ).

cnf(i_0_4332,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2342]),
    [final] ).

cnf(i_0_4333,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2122]),
    [final] ).

cnf(i_0_4334,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2343]),
    [final] ).

cnf(i_0_4335,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2123]),
    [final] ).

cnf(i_0_4336,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2344]),
    [final] ).

cnf(i_0_4337,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2124]),
    [final] ).

cnf(i_0_4338,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2345]),
    [final] ).

cnf(i_0_4339,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2313]),
    [final] ).

cnf(i_0_4340,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2314]),
    [final] ).

cnf(i_0_4341,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2125]),
    [final] ).

cnf(i_0_4342,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2346]),
    [final] ).

cnf(i_0_4343,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2319]),
    [final] ).

cnf(i_0_4344,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2126]),
    [final] ).

cnf(i_0_4345,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2320]),
    [final] ).

cnf(i_0_4346,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2347]),
    [final] ).

cnf(i_0_4347,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2127]),
    [final] ).

cnf(i_0_4348,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2348]),
    [final] ).

cnf(i_0_4349,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2128]),
    [final] ).

cnf(i_0_4350,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2129]),
    [final] ).

cnf(i_0_4351,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2349]),
    [final] ).

cnf(i_0_4352,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2130]),
    [final] ).

cnf(i_0_4353,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2350]),
    [final] ).

cnf(i_0_4354,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2351]),
    [final] ).

cnf(i_0_4355,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2352]),
    [final] ).

cnf(i_0_4356,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2323]),
    [final] ).

cnf(i_0_4357,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2324]),
    [final] ).

cnf(i_0_4358,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2353]),
    [final] ).

cnf(i_0_4359,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2330]),
    [final] ).

cnf(i_0_4360,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2131]),
    [final] ).

cnf(i_0_4361,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2331]),
    [final] ).

cnf(i_0_4362,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2354]),
    [final] ).

cnf(i_0_4363,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2311]),
    [final] ).

cnf(i_0_4364,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2132]),
    [final] ).

cnf(i_0_4365,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2312]),
    [final] ).

cnf(i_0_4366,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,f),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))),
    inference(split_conjunct,[status(thm)],[fact_71_assms_I1_J]),
    [final] ).

cnf(i_0_4367,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk26_2(X1,X2)),arrow_1681063817le_Lin))
    | X1 = X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1928]),
    [final] ).

cnf(i_0_4368,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk492_2(X1,X2)) = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2204]),
    [final] ).

cnf(i_0_4369,plain,
    ( X2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk478_2(X1,X2))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2355]),
    [final] ).

cnf(i_0_4370,plain,
    ( X1 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,zero_zero_nat))) ),
    inference(split_conjunct,[status(thm)],[i_0_2356]),
    [final] ).

cnf(i_0_4371,plain,
    hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),X1))) = hAPP_nat_nat(suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2357]),
    [final] ).

cnf(i_0_4372,plain,
    ( X2 = X3
    | hAPP_nat_nat(times_times_nat(X1),X2) != hAPP_nat_nat(times_times_nat(X1),X3)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2358]),
    [final] ).

cnf(i_0_4373,plain,
    ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk504_1(X1))))
    | hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2359]),
    [final] ).

cnf(i_0_4374,plain,
    ( X1 = hAPP_nat_nat(suc,esk500_2(X2,X1))
    | X1 = hAPP_nat_nat(suc,X2)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2140]),
    [final] ).

cnf(i_0_4375,plain,
    hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X1))) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2360]),
    [final] ).

cnf(i_0_4376,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2361]),
    [final] ).

cnf(i_0_4377,plain,
    ( hBOOL(hAPP_nat_bool(X1,esk491_2(X2,X1)))
    | hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1990]),
    [final] ).

cnf(i_0_4378,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2329]),
    [final] ).

cnf(i_0_4379,plain,
    ( hBOOL(hAPP_nat_bool(X1,esk505_2(X2,X1)))
    | hBOOL(hAPP_nat_bool(X1,X2))
    | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1950]),
    [final] ).

cnf(i_0_4380,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2362]),
    [final] ).

cnf(i_0_4381,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2363]),
    [final] ).

cnf(i_0_4382,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2364]),
    [final] ).

cnf(i_0_4383,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2226]),
    [final] ).

cnf(i_0_4384,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2365]),
    [final] ).

cnf(i_0_4385,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2366]),
    [final] ).

cnf(i_0_4386,plain,
    ( X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2367]),
    [final] ).

cnf(i_0_4387,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 = X2
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2368]),
    [final] ).

cnf(i_0_4388,plain,
    hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2369]),
    [final] ).

cnf(i_0_4389,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2370]),
    [final] ).

cnf(i_0_4390,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2371]),
    [final] ).

cnf(i_0_4391,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2372]),
    [final] ).

cnf(i_0_4392,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2373]),
    [final] ).

cnf(i_0_4393,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2225]),
    [final] ).

cnf(i_0_4394,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2374]),
    [final] ).

cnf(i_0_4395,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2375]),
    [final] ).

cnf(i_0_4396,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2223]),
    [final] ).

cnf(i_0_4397,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(times_times_nat(X1),X1))),
    inference(split_conjunct,[status(thm)],[i_0_2376]),
    [final] ).

cnf(i_0_4398,plain,
    ( hBOOL(hAPP_P606313927t_bool(X2,X1))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2377]),
    [final] ).

cnf(i_0_4399,plain,
    ( hBOOL(hAPP_f592646513l_bool(X2,X1))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2378]),
    [final] ).

cnf(i_0_4400,plain,
    ( hBOOL(hAPP_f312250286l_bool(X2,X1))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2379]),
    [final] ).

cnf(i_0_4401,plain,
    ( hBOOL(hAPP_f965095724l_bool(X2,X1))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2380]),
    [final] ).

cnf(i_0_4402,plain,
    ( hBOOL(hAPP_P1676879539t_bool(X2,X1))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2381]),
    [final] ).

cnf(i_0_4403,plain,
    ( hBOOL(hAPP_nat_bool(X2,X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2382]),
    [final] ).

cnf(i_0_4404,plain,
    ( hBOOL(hAPP_bool_bool(X2,X1))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2383]),
    [final] ).

cnf(i_0_4405,plain,
    ( hBOOL(hAPP_A1785763630i_bool(X2,X1))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2384]),
    [final] ).

cnf(i_0_4406,plain,
    ( X1 = X2
    | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X4)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_2385]),
    [final] ).

cnf(i_0_4407,plain,
    ( X1 = X2
    | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X4)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_2386]),
    [final] ).

cnf(i_0_4408,plain,
    ( X1 = X2
    | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X2)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2385]),
    [final] ).

cnf(i_0_4409,plain,
    ( X1 = X2
    | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X4),X2)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X4)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2386]),
    [final] ).

cnf(i_0_4410,plain,
    hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(X1),X2)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2387]),
    [final] ).

cnf(i_0_4411,plain,
    hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(X1),X2)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2388]),
    [final] ).

cnf(i_0_4412,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2389]),
    [final] ).

cnf(i_0_4413,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
    | X1 != hAPP_nat_nat(suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2112]),
    [final] ).

cnf(i_0_4414,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(suc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2390]),
    [final] ).

cnf(i_0_4415,plain,
    ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(X1,esk504_1(X1)))
    | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2359]),
    [final] ).

cnf(i_0_4416,plain,
    hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2391]),
    [final] ).

cnf(i_0_4417,plain,
    hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,X1)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(split_conjunct,[status(thm)],[i_0_2392]),
    [final] ).

cnf(i_0_4418,plain,
    hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,X1)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(split_conjunct,[status(thm)],[i_0_2393]),
    [final] ).

cnf(i_0_4419,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2276]),
    [final] ).

cnf(i_0_4420,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2282]),
    [final] ).

cnf(i_0_4421,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X2))
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2298]),
    [final] ).

cnf(i_0_4422,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2285]),
    [final] ).

cnf(i_0_4423,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2291]),
    [final] ).

cnf(i_0_4424,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2240]),
    [final] ).

cnf(i_0_4425,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X2))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2246]),
    [final] ).

cnf(i_0_4426,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2267]),
    [final] ).

cnf(i_0_4427,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X2))
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2273]),
    [final] ).

cnf(i_0_4428,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2249]),
    [final] ).

cnf(i_0_4429,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2255]),
    [final] ).

cnf(i_0_4430,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2258]),
    [final] ).

cnf(i_0_4431,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X2))
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2264]),
    [final] ).

cnf(i_0_4432,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
    | X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2355]),
    [final] ).

cnf(i_0_4433,plain,
    is_fun961089132t_bool(undefi1481304379t_bool(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool))),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp]),
    [final] ).

cnf(i_0_4434,plain,
    is_fun2093718614t_bool(undefi1931156935t_bool(fun(arrow_107136085le_alt,fun(arrow_107136085le_alt,bool)))),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__]),
    [final] ).

cnf(i_0_4435,plain,
    ( ~ hBOOL(X1)
    | ~ hBOOL(X2)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2312]),
    [final] ).

cnf(i_0_4436,plain,
    ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,X2),hAPP_A1637648121di_nat(X2,X1)) = X1
    | ~ is_Arr43961803e_indi(X1)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X2),top_to1576102282i_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2394]),
    [final] ).

cnf(i_0_4437,plain,
    ( is_fun961089132t_bool(arrow_1539419881_below(X1,X2,X3))
    | ~ is_fun961089132t_bool(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2395]),
    [final] ).

cnf(i_0_4438,plain,
    ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,X2),X3) = X1
    | ~ is_Arr43961803e_indi(X1)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X2),top_to1576102282i_bool))
    | hAPP_A1637648121di_nat(X2,X1) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_2396]),
    [final] ).

cnf(i_0_4439,plain,
    ( X1 = hAPP_nat_nat(suc,esk498_1(X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2397]),
    [final] ).

cnf(i_0_4440,plain,
    ( X1 = hAPP_nat_nat(suc,esk493_1(X1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2398]),
    [final] ).

cnf(i_0_4441,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2312]),
    [final] ).

cnf(i_0_4442,plain,
    ( ~ hBOOL(X1)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),top_top_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2399]),
    [final] ).

cnf(i_0_4443,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,X1),hAPP_nat_nat(X1,X2)) = X2
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),top_top_fun_nat_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2400]),
    [final] ).

cnf(i_0_4444,plain,
    hAPP_A1102281708t_bool(hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,X1),X2),X3) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2401]),
    [final] ).

cnf(i_0_4445,plain,
    hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,X1),X2),X3) = hAPP_A1941004017t_bool(hAPP_A621939144t_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2402]),
    [final] ).

cnf(i_0_4446,plain,
    hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,X1),X2),X3) = hAPP_f1663053423t_bool(hAPP_A572596845t_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2403]),
    [final] ).

cnf(i_0_4447,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,X1),X2),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2404]),
    [final] ).

cnf(i_0_4448,plain,
    hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,X1),X2),X3) = hAPP_f592646513l_bool(hAPP_P229966473l_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2405]),
    [final] ).

cnf(i_0_4449,plain,
    hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,X1),X2),X3) = hAPP_f1749234559l_bool(hAPP_f566237389l_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2406]),
    [final] ).

cnf(i_0_4450,plain,
    hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,X1),X2),X3) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2407]),
    [final] ).

cnf(i_0_4451,plain,
    hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,X1),X2),X3) = hAPP_f777333846l_bool(hAPP_f461621971l_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2408]),
    [final] ).

cnf(i_0_4452,plain,
    hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,X1),X2),X3) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2409]),
    [final] ).

cnf(i_0_4453,plain,
    hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,X1),X2),X3) = hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2410]),
    [final] ).

cnf(i_0_4454,plain,
    hAPP_A1677245848t_bool(hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,X1),X2),X3) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2411]),
    [final] ).

cnf(i_0_4455,plain,
    hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,X1),X2),X3) = hAPP_A568203993t_bool(hAPP_A1625428400t_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2412]),
    [final] ).

cnf(i_0_4456,plain,
    hAPP_A1785763630i_bool(hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,X1),X2),X3) = hAPP_nat_bool(hAPP_A2046586321t_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2413]),
    [final] ).

cnf(i_0_4457,plain,
    hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,X1),X2),X3) = hAPP_f592646513l_bool(hAPP_A187815023l_bool(X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2414]),
    [final] ).

cnf(i_0_4458,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2133]),
    [final] ).

cnf(i_0_4459,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk15_1(X1)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1701]),
    [final] ).

cnf(i_0_4460,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk11_1(X1)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_4461,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,esk10_1(X1)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_4462,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),top_to565915683t_bool))
    | X1 != top_to565915683t_bool
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2415]),
    [final] ).

cnf(i_0_4463,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),top_to1853035173l_bool))
    | X1 != top_to1853035173l_bool
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2416]),
    [final] ).

cnf(i_0_4464,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),top_to1714702858l_bool))
    | X1 != top_to1714702858l_bool
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2417]),
    [final] ).

cnf(i_0_4465,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),top_to522745736l_bool))
    | X1 != top_to522745736l_bool
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2418]),
    [final] ).

cnf(i_0_4466,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),top_to1257323279t_bool))
    | X1 != top_to1257323279t_bool
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2419]),
    [final] ).

cnf(i_0_4467,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),top_to1576102282i_bool))
    | X1 != top_to1576102282i_bool
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2420]),
    [final] ).

cnf(i_0_4468,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,X1),X3) = X2
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),top_top_fun_nat_bool))
    | hAPP_nat_nat(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_2421]),
    [final] ).

cnf(i_0_4469,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_4470,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2422]),
    [final] ).

cnf(i_0_4471,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2423]),
    [final] ).

cnf(i_0_4472,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X2),X1))
    | ~ hBOOL(hAPP_P606313927t_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2377]),
    [final] ).

cnf(i_0_4473,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X2),X1))
    | ~ hBOOL(hAPP_f592646513l_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2378]),
    [final] ).

cnf(i_0_4474,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X2),X1))
    | ~ hBOOL(hAPP_f312250286l_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2379]),
    [final] ).

cnf(i_0_4475,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X2),X1))
    | ~ hBOOL(hAPP_f965095724l_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2380]),
    [final] ).

cnf(i_0_4476,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X2),X1))
    | ~ hBOOL(hAPP_P1676879539t_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2381]),
    [final] ).

cnf(i_0_4477,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
    | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2382]),
    [final] ).

cnf(i_0_4478,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X2),X1))
    | ~ hBOOL(hAPP_bool_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2383]),
    [final] ).

cnf(i_0_4479,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X2),X1))
    | ~ hBOOL(hAPP_A1785763630i_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2384]),
    [final] ).

cnf(i_0_4480,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2424]),
    [final] ).

cnf(i_0_4481,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2425]),
    [final] ).

cnf(i_0_4482,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2426]),
    [final] ).

cnf(i_0_4483,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2314]),
    [final] ).

cnf(i_0_4484,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2320]),
    [final] ).

cnf(i_0_4485,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2427]),
    [final] ).

cnf(i_0_4486,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2428]),
    [final] ).

cnf(i_0_4487,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2429]),
    [final] ).

cnf(i_0_4488,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2430]),
    [final] ).

cnf(i_0_4489,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2431]),
    [final] ).

cnf(i_0_4490,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2432]),
    [final] ).

cnf(i_0_4491,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2324]),
    [final] ).

cnf(i_0_4492,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2433]),
    [final] ).

cnf(i_0_4493,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2434]),
    [final] ).

cnf(i_0_4494,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2363]),
    [final] ).

cnf(i_0_4495,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2363]),
    [final] ).

cnf(i_0_4496,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2331]),
    [final] ).

cnf(i_0_4497,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2364]),
    [final] ).

cnf(i_0_4498,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2364]),
    [final] ).

cnf(i_0_4499,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2226]),
    [final] ).

cnf(i_0_4500,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2435]),
    [final] ).

cnf(i_0_4501,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2436]),
    [final] ).

cnf(i_0_4502,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2437]),
    [final] ).

cnf(i_0_4503,plain,
    ( X1 = X2
    | ~ is_Arr43961803e_indi(X1)
    | ~ is_Arr43961803e_indi(X2)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X3),top_to1576102282i_bool))
    | hAPP_A1637648121di_nat(X3,X1) != hAPP_A1637648121di_nat(X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2438]),
    [final] ).

cnf(i_0_4504,plain,
    ( X2 = X3
    | hAPP_A1637648121di_nat(X1,X2) != hAPP_A1637648121di_nat(X1,X3)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),top_to1576102282i_bool))
    | ~ is_Arr43961803e_indi(X2)
    | ~ is_Arr43961803e_indi(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2439]),
    [final] ).

cnf(i_0_4505,plain,
    ( hAPP_nat_nat(X1,esk39_2(X1,X2)) = hAPP_nat_nat(X1,esk40_2(X1,X2))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_4506,plain,
    ( hAPP_A1637648121di_nat(X1,esk37_2(X1,X2)) = hAPP_A1637648121di_nat(X1,esk38_2(X1,X2))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_4507,plain,
    ( hBOOL(X1)
    | hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),top_top_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2399]),
    [final] ).

cnf(i_0_4508,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | X2 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2440]),
    [final] ).

cnf(i_0_4509,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2441]),
    [final] ).

cnf(i_0_4510,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_2442]),
    [final] ).

cnf(i_0_4511,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2443]),
    [final] ).

cnf(i_0_4512,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(X1)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2444]),
    [final] ).

cnf(i_0_4513,plain,
    ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2445]),
    [final] ).

cnf(i_0_4514,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2446]),
    [final] ).

cnf(i_0_4515,plain,
    ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2447]),
    [final] ).

cnf(i_0_4516,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2448]),
    [final] ).

cnf(i_0_4517,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2449]),
    [final] ).

cnf(i_0_4518,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2450]),
    [final] ).

cnf(i_0_4519,plain,
    ( hBOOL(X1)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2443]),
    [final] ).

cnf(i_0_4520,plain,
    ( hBOOL(X1)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2444]),
    [final] ).

cnf(i_0_4521,plain,
    ( X1 = top_to565915683t_bool
    | ~ is_fun961089132t_bool(X1)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2451]),
    [final] ).

cnf(i_0_4522,plain,
    ( X1 = top_to565915683t_bool
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),X1))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2452]),
    [final] ).

cnf(i_0_4523,plain,
    ( X1 = top_to1853035173l_bool
    | ~ is_fun279392540l_bool(X1)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2453]),
    [final] ).

cnf(i_0_4524,plain,
    ( X1 = top_to1853035173l_bool
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),X1))
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2454]),
    [final] ).

cnf(i_0_4525,plain,
    ( X1 = top_to1714702858l_bool
    | ~ is_fun158382675l_bool(X1)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2455]),
    [final] ).

cnf(i_0_4526,plain,
    ( X1 = top_to1714702858l_bool
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),X1))
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2456]),
    [final] ).

cnf(i_0_4527,plain,
    ( X1 = top_to522745736l_bool
    | ~ is_fun288122577l_bool(X1)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2457]),
    [final] ).

cnf(i_0_4528,plain,
    ( X1 = top_to522745736l_bool
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),X1))
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2458]),
    [final] ).

cnf(i_0_4529,plain,
    ( X1 = top_to1257323279t_bool
    | ~ is_fun1568535512t_bool(X1)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2459]),
    [final] ).

cnf(i_0_4530,plain,
    ( X1 = top_to1257323279t_bool
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),X1))
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2460]),
    [final] ).

cnf(i_0_4531,plain,
    ( X1 = top_to1576102282i_bool
    | ~ is_fun1236654035i_bool(X1)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2461]),
    [final] ).

cnf(i_0_4532,plain,
    ( X1 = top_to1576102282i_bool
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),X1))
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2462]),
    [final] ).

cnf(i_0_4533,plain,
    ( X1 = top_to178429151t_bool
    | ~ is_fun2093718614t_bool(X1)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2463]),
    [final] ).

cnf(i_0_4534,plain,
    ( X1 = top_to178429151t_bool
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),X1))
    | ~ is_fun2093718614t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2464]),
    [final] ).

cnf(i_0_4535,plain,
    ( X1 = X3
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2465]),
    [final] ).

cnf(i_0_4536,plain,
    ( X1 = X3
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2466]),
    [final] ).

cnf(i_0_4537,plain,
    ( X1 = X3
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2467]),
    [final] ).

cnf(i_0_4538,plain,
    ( X2 = X3
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2468]),
    [final] ).

cnf(i_0_4539,plain,
    ( X2 = X3
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2469]),
    [final] ).

cnf(i_0_4540,plain,
    ( X2 = X3
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2470]),
    [final] ).

cnf(i_0_4541,plain,
    ( X2 = X3
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2471]),
    [final] ).

cnf(i_0_4542,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,zero_zero_nat)))
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2356]),
    [final] ).

cnf(i_0_4543,plain,
    hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2472]),
    [final] ).

cnf(i_0_4544,plain,
    hAPP_A1102281708t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(X1),X2),X3) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(X1,X3),hAPP_A1677245848t_bool(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2473]),
    [final] ).

cnf(i_0_4545,plain,
    hAPP_nat_bool(hAPP_f800510211t_bool(cOMBS_nat_bool_bool(X1),X2),X3) = hAPP_bool_bool(hAPP_n1006566506l_bool(X1,X3),hAPP_nat_bool(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2474]),
    [final] ).

cnf(i_0_4546,plain,
    hAPP_A1677245848t_bool(hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(X1),X2),X3) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(X1,X3),hAPP_A1677245848t_bool(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2475]),
    [final] ).

cnf(i_0_4547,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),top_top_fun_nat_bool))
    | X1 != top_top_fun_nat_bool ),
    inference(split_conjunct,[status(thm)],[i_0_2476]),
    [final] ).

cnf(i_0_4548,plain,
    ( X1 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
    inference(split_conjunct,[status(thm)],[i_0_2477]),
    [final] ).

cnf(i_0_4549,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_2478]),
    [final] ).

cnf(i_0_4550,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
    inference(split_conjunct,[status(thm)],[i_0_2479]),
    [final] ).

cnf(i_0_4551,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
    inference(split_conjunct,[status(thm)],[i_0_2480]),
    [final] ).

cnf(i_0_4552,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
    inference(split_conjunct,[status(thm)],[i_0_2481]),
    [final] ).

cnf(i_0_4553,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2482]),
    [final] ).

cnf(i_0_4554,plain,
    ( X1 = top_top_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2483]),
    [final] ).

cnf(i_0_4555,plain,
    ( X1 = top_top_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2484]),
    [final] ).

cnf(i_0_4556,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2485]),
    [final] ).

cnf(i_0_4557,plain,
    ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2486]),
    [final] ).

cnf(i_0_4558,plain,
    ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2487]),
    [final] ).

cnf(i_0_4559,plain,
    ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2488]),
    [final] ).

cnf(i_0_4560,plain,
    ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2489]),
    [final] ).

cnf(i_0_4561,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2490]),
    [final] ).

cnf(i_0_4562,plain,
    ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2491]),
    [final] ).

cnf(i_0_4563,plain,
    ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2492]),
    [final] ).

cnf(i_0_4564,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk28_0),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    inference(split_conjunct,[status(thm)],[i_0_1494]),
    [final] ).

cnf(i_0_4565,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk27_0),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    inference(split_conjunct,[status(thm)],[i_0_1495]),
    [final] ).

cnf(i_0_4566,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    inference(split_conjunct,[status(thm)],[fact_19_n_I1_J]),
    [final] ).

cnf(i_0_4567,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),top_top_fun_nat_bool))
    | hAPP_nat_nat(X1,X2) != hAPP_nat_nat(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2493]),
    [final] ).

cnf(i_0_4568,plain,
    ( X2 = X3
    | hAPP_nat_nat(X1,X2) != hAPP_nat_nat(X1,X3)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),top_top_fun_nat_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2494]),
    [final] ).

cnf(i_0_4569,plain,
    ( is_Arr43961803e_indi(esk180_2(X1,X2))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1771]),
    [final] ).

cnf(i_0_4570,plain,
    ( is_Arr43961803e_indi(esk33_2(X1,X2))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1772]),
    [final] ).

cnf(i_0_4571,plain,
    ( is_Arr1861959080le_alt(esk182_2(X1,X2))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1773]),
    [final] ).

cnf(i_0_4572,plain,
    ( is_Arr1861959080le_alt(esk35_2(X1,X2))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1774]),
    [final] ).

cnf(i_0_4573,plain,
    ( is_fun961089132t_bool(esk176_2(X1,X2))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1761]),
    [final] ).

cnf(i_0_4574,plain,
    ( is_fun961089132t_bool(esk29_2(X1,X2))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1762]),
    [final] ).

cnf(i_0_4575,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2495]),
    [final] ).

cnf(i_0_4576,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2496]),
    [final] ).

cnf(i_0_4577,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2497]),
    [final] ).

cnf(i_0_4578,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2498]),
    [final] ).

cnf(i_0_4579,plain,
    ( X1 = hAPP_nat_nat(suc,zero_zero_nat)
    | X2 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2499]),
    [final] ).

cnf(i_0_4580,plain,
    ( X1 = hAPP_nat_nat(suc,zero_zero_nat)
    | X2 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_4581,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | X1 != X2
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2239]),
    [final] ).

cnf(i_0_4582,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | X1 != X2
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2245]),
    [final] ).

cnf(i_0_4583,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | X1 != X2
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2160]),
    [final] ).

cnf(i_0_4584,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | X2 != X1
    | ~ is_fun961089132t_bool(X2)
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2160]),
    [final] ).

cnf(i_0_4585,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2248]),
    [final] ).

cnf(i_0_4586,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2254]),
    [final] ).

cnf(i_0_4587,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2170]),
    [final] ).

cnf(i_0_4588,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | X2 != X1
    | ~ is_fun279392540l_bool(X2)
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2170]),
    [final] ).

cnf(i_0_4589,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2257]),
    [final] ).

cnf(i_0_4590,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2263]),
    [final] ).

cnf(i_0_4591,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2175]),
    [final] ).

cnf(i_0_4592,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | X2 != X1
    | ~ is_fun158382675l_bool(X2)
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2175]),
    [final] ).

cnf(i_0_4593,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2266]),
    [final] ).

cnf(i_0_4594,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2272]),
    [final] ).

cnf(i_0_4595,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | X1 != X2
    | ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2165]),
    [final] ).

cnf(i_0_4596,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | X2 != X1
    | ~ is_fun288122577l_bool(X2)
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2165]),
    [final] ).

cnf(i_0_4597,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | X1 != X2
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2275]),
    [final] ).

cnf(i_0_4598,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | X1 != X2
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2281]),
    [final] ).

cnf(i_0_4599,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | X1 != X2
    | ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2146]),
    [final] ).

cnf(i_0_4600,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | X2 != X1
    | ~ is_fun1568535512t_bool(X2)
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2146]),
    [final] ).

cnf(i_0_4601,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | X1 != X2
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2284]),
    [final] ).

cnf(i_0_4602,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | X1 != X2
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2290]),
    [final] ).

cnf(i_0_4603,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | X1 != X2
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2155]),
    [final] ).

cnf(i_0_4604,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | X2 != X1
    | ~ is_fun1236654035i_bool(X2)
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2155]),
    [final] ).

cnf(i_0_4605,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | X1 != X2
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2297]),
    [final] ).

cnf(i_0_4606,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | X1 != X2
    | ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2150]),
    [final] ).

cnf(i_0_4607,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | X2 != X1
    | ~ is_fun2093718614t_bool(X2)
    | ~ is_fun2093718614t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2150]),
    [final] ).

cnf(i_0_4608,plain,
    hAPP_A1455239488t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(X1),X2),X3) = hAPP_b1588041841t_bool(X1,hAPP_A1785763630i_bool(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2501]),
    [final] ).

cnf(i_0_4609,plain,
    hAPP_A1553574765l_bool(hAPP_f156764033l_bool(cOMBB_2112722489le_alt(X1),X2),X3) = hAPP_f1539445765l_bool(X1,hAPP_A1505516597le_alt(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2502]),
    [final] ).

cnf(i_0_4610,plain,
    hAPP_A621939144t_bool(hAPP_f210227915t_bool(cOMBB_1769989562e_indi(X1),X2),X3) = hAPP_f344580165t_bool(X1,hAPP_A1677245848t_bool(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2503]),
    [final] ).

cnf(i_0_4611,plain,
    hAPP_A572596845t_bool(hAPP_f1324249913t_bool(cOMBB_747702273le_alt(X1),X2),X3) = hAPP_f653880381t_bool(X1,hAPP_A1553574765l_bool(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2504]),
    [final] ).

cnf(i_0_4612,plain,
    hAPP_A1625428400t_bool(hAPP_f721938099t_bool(cOMBB_2032668066e_indi(X1),X2),X3) = hAPP_f393984045t_bool(X1,hAPP_A1677245848t_bool(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2505]),
    [final] ).

cnf(i_0_4613,plain,
    hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(X1),X2),X3) = hAPP_b589554111l_bool(X1,hAPP_nat_bool(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2506]),
    [final] ).

cnf(i_0_4614,plain,
    hAPP_A2046586321t_bool(hAPP_f224734595t_bool(cOMBB_1883918730e_indi(X1),X2),X3) = hAPP_n1699378549t_bool(X1,hAPP_A1637648121di_nat(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2507]),
    [final] ).

cnf(i_0_4615,plain,
    hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(X1),X2),X3) = hAPP_n215258509l_bool(X1,hAPP_nat_nat(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2508]),
    [final] ).

cnf(i_0_4616,plain,
    hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(X1),X2),X3) = hAPP_n1699378549t_bool(X1,hAPP_nat_nat(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2509]),
    [final] ).

cnf(i_0_4617,plain,
    hAPP_A187815023l_bool(hAPP_f1539445765l_bool(cOMBB_84213429le_alt(X1),X2),X3) = hAPP_P229966473l_bool(X1,hAPP_A702847159le_alt(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_2510]),
    [final] ).

cnf(i_0_4618,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
    | X1 != hAPP_nat_nat(suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2398]),
    [final] ).

cnf(i_0_4619,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2511]),
    [final] ).

cnf(i_0_4620,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2311]),
    [final] ).

cnf(i_0_4621,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2181]),
    [final] ).

cnf(i_0_4622,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(X2)
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2181]),
    [final] ).

cnf(i_0_4623,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2512]),
    [final] ).

cnf(i_0_4624,plain,
    ( X1 = zero_zero_nat
    | X1 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2499]),
    [final] ).

cnf(i_0_4625,plain,
    ( X1 = hAPP_nat_nat(suc,zero_zero_nat)
    | X1 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2499]),
    [final] ).

cnf(i_0_4626,plain,
    ( X1 = zero_zero_nat
    | X1 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_4627,plain,
    ( X1 = hAPP_nat_nat(suc,zero_zero_nat)
    | X1 = zero_zero_nat
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_4628,plain,
    ( hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),X1),X2) = X1
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2513]),
    [final] ).

cnf(i_0_4629,plain,
    ( hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fFalse),X2),X1) = X1
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2514]),
    [final] ).

cnf(i_0_4630,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),X2))
    | esk39_2(X1,X2) != esk40_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_4631,plain,
    ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X2))
    | esk37_2(X1,X2) != esk38_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_4632,plain,
    hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_2515]),
    [final] ).

cnf(i_0_4633,plain,
    hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_2516]),
    [final] ).

cnf(i_0_4634,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2311]),
    [final] ).

cnf(i_0_4635,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | hBOOL(X1)
    | hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2181]),
    [final] ).

cnf(i_0_4636,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
    | hBOOL(X2)
    | hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2181]),
    [final] ).

cnf(i_0_4637,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2512]),
    [final] ).

cnf(i_0_4638,plain,
    ( hBOOL(top_top_bool)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),top_top_bool))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2399]),
    [final] ).

cnf(i_0_4639,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X1),top_top_bool))
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2399]),
    [final] ).

cnf(i_0_4640,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X1))
    | ~ hBOOL(X1)
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2444]),
    [final] ).

cnf(i_0_4641,plain,
    ( X1 = top_to565915683t_bool
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),top_to565915683t_bool))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2415]),
    [final] ).

cnf(i_0_4642,plain,
    ( X1 = top_to1853035173l_bool
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),top_to1853035173l_bool))
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2416]),
    [final] ).

cnf(i_0_4643,plain,
    ( X1 = top_to1714702858l_bool
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),top_to1714702858l_bool))
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2417]),
    [final] ).

cnf(i_0_4644,plain,
    ( X1 = top_to522745736l_bool
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),top_to522745736l_bool))
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2418]),
    [final] ).

cnf(i_0_4645,plain,
    ( X1 = top_to1257323279t_bool
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),top_to1257323279t_bool))
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2419]),
    [final] ).

cnf(i_0_4646,plain,
    ( X1 = top_to1576102282i_bool
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),top_to1576102282i_bool))
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2420]),
    [final] ).

cnf(i_0_4647,plain,
    ( hAPP_nat_nat(X1,esk76_1(X1)) = hAPP_nat_nat(X1,esk77_1(X1))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),top_top_fun_nat_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2517]),
    [final] ).

cnf(i_0_4648,plain,
    ( hAPP_A1637648121di_nat(X1,esk74_1(X1)) = hAPP_A1637648121di_nat(X1,esk75_1(X1))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),top_to1576102282i_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2518]),
    [final] ).

cnf(i_0_4649,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2519]),
    [final] ).

cnf(i_0_4650,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2520]),
    [final] ).

cnf(i_0_4651,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2521]),
    [final] ).

cnf(i_0_4652,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2522]),
    [final] ).

cnf(i_0_4653,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2523]),
    [final] ).

cnf(i_0_4654,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2193]),
    [final] ).

cnf(i_0_4655,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2193]),
    [final] ).

cnf(i_0_4656,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2524]),
    [final] ).

cnf(i_0_4657,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2525]),
    [final] ).

cnf(i_0_4658,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2525]),
    [final] ).

cnf(i_0_4659,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2313]),
    [final] ).

cnf(i_0_4660,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2319]),
    [final] ).

cnf(i_0_4661,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2195]),
    [final] ).

cnf(i_0_4662,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2195]),
    [final] ).

cnf(i_0_4663,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2526]),
    [final] ).

cnf(i_0_4664,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2527]),
    [final] ).

cnf(i_0_4665,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2528]),
    [final] ).

cnf(i_0_4666,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2529]),
    [final] ).

cnf(i_0_4667,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2351]),
    [final] ).

cnf(i_0_4668,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2323]),
    [final] ).

cnf(i_0_4669,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2530]),
    [final] ).

cnf(i_0_4670,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2330]),
    [final] ).

cnf(i_0_4671,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2200]),
    [final] ).

cnf(i_0_4672,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2200]),
    [final] ).

cnf(i_0_4673,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2531]),
    [final] ).

cnf(i_0_4674,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2532]),
    [final] ).

cnf(i_0_4675,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),X1))
    | X1 != top_to565915683t_bool
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2452]),
    [final] ).

cnf(i_0_4676,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),X1))
    | X1 != top_to1853035173l_bool
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2454]),
    [final] ).

cnf(i_0_4677,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),X1))
    | X1 != top_to1714702858l_bool
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2456]),
    [final] ).

cnf(i_0_4678,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),X1))
    | X1 != top_to522745736l_bool
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2458]),
    [final] ).

cnf(i_0_4679,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),X1))
    | X1 != top_to1257323279t_bool
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2460]),
    [final] ).

cnf(i_0_4680,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),X1))
    | X1 != top_to1576102282i_bool
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2462]),
    [final] ).

cnf(i_0_4681,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),X1))
    | X1 != top_to178429151t_bool
    | ~ is_fun2093718614t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2464]),
    [final] ).

cnf(i_0_4682,plain,
    ( X1 = zero_zero_nat
    | X2 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2499]),
    [final] ).

cnf(i_0_4683,plain,
    ( X1 = zero_zero_nat
    | X2 = zero_zero_nat
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_4684,plain,
    ( hBOOL(X1)
    | hBOOL(top_top_bool)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2444]),
    [final] ).

cnf(i_0_4685,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2533]),
    [final] ).

cnf(i_0_4686,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2534]),
    [final] ).

cnf(i_0_4687,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2535]),
    [final] ).

cnf(i_0_4688,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2536]),
    [final] ).

cnf(i_0_4689,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2537]),
    [final] ).

cnf(i_0_4690,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2538]),
    [final] ).

cnf(i_0_4691,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2539]),
    [final] ).

cnf(i_0_4692,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2540]),
    [final] ).

cnf(i_0_4693,plain,
    hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2541]),
    [final] ).

cnf(i_0_4694,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2542]),
    [final] ).

cnf(i_0_4695,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2543]),
    [final] ).

cnf(i_0_4696,plain,
    hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2544]),
    [final] ).

cnf(i_0_4697,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2477]),
    [final] ).

cnf(i_0_4698,plain,
    ( X1 = top_top_fun_nat_bool
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),top_top_fun_nat_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2476]),
    [final] ).

cnf(i_0_4699,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_2545]),
    [final] ).

cnf(i_0_4700,plain,
    ( is_Arr43961803e_indi(esk38_2(X1,X2))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_4701,plain,
    ( is_Arr43961803e_indi(esk37_2(X1,X2))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_4702,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X1),top_to565915683t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2546]),
    [final] ).

cnf(i_0_4703,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X1),top_to565915683t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2547]),
    [final] ).

cnf(i_0_4704,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),top_to565915683t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2548]),
    [final] ).

cnf(i_0_4705,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),top_to565915683t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2549]),
    [final] ).

cnf(i_0_4706,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),top_to1853035173l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2550]),
    [final] ).

cnf(i_0_4707,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),top_to1853035173l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2551]),
    [final] ).

cnf(i_0_4708,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),top_to1853035173l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2552]),
    [final] ).

cnf(i_0_4709,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X1),top_to1853035173l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2553]),
    [final] ).

cnf(i_0_4710,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),top_to1714702858l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2554]),
    [final] ).

cnf(i_0_4711,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),top_to1714702858l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2555]),
    [final] ).

cnf(i_0_4712,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),top_to1714702858l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2556]),
    [final] ).

cnf(i_0_4713,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X1),top_to1714702858l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2557]),
    [final] ).

cnf(i_0_4714,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),top_to522745736l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2558]),
    [final] ).

cnf(i_0_4715,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),top_to522745736l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2559]),
    [final] ).

cnf(i_0_4716,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),top_to522745736l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2560]),
    [final] ).

cnf(i_0_4717,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X1),top_to522745736l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2561]),
    [final] ).

cnf(i_0_4718,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),top_to1257323279t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2562]),
    [final] ).

cnf(i_0_4719,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),top_to1257323279t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2563]),
    [final] ).

cnf(i_0_4720,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X1),top_to1257323279t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2564]),
    [final] ).

cnf(i_0_4721,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X1),top_to1257323279t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2565]),
    [final] ).

cnf(i_0_4722,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),top_top_fun_nat_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2566]),
    [final] ).

cnf(i_0_4723,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),top_top_fun_nat_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2567]),
    [final] ).

cnf(i_0_4724,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),top_top_fun_nat_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2568]),
    [final] ).

cnf(i_0_4725,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),top_top_fun_nat_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2569]),
    [final] ).

cnf(i_0_4726,plain,
    hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X1),top_to1647826457l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2570]),
    [final] ).

cnf(i_0_4727,plain,
    hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X1),top_to1647826457l_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2571]),
    [final] ).

cnf(i_0_4728,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2572]),
    [final] ).

cnf(i_0_4729,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2573]),
    [final] ).

cnf(i_0_4730,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2574]),
    [final] ).

cnf(i_0_4731,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2575]),
    [final] ).

cnf(i_0_4732,plain,
    hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),top_to178429151t_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2576]),
    [final] ).

cnf(i_0_4733,plain,
    hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),top_top_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2577]),
    [final] ).

cnf(i_0_4734,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),X1))
    | X1 != top_top_fun_nat_bool ),
    inference(split_conjunct,[status(thm)],[i_0_2484]),
    [final] ).

cnf(i_0_4735,plain,
    ( X1 = zero_zero_nat
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2578]),
    [final] ).

cnf(i_0_4736,plain,
    ( X1 = zero_zero_nat
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2482]),
    [final] ).

cnf(i_0_4737,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2579]),
    [final] ).

cnf(i_0_4738,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2580]),
    [final] ).

cnf(i_0_4739,plain,
    ( hAPP_nat_nat(times_times_nat(X1),X2) = hAPP_nat_nat(suc,zero_zero_nat)
    | X1 != hAPP_nat_nat(suc,zero_zero_nat)
    | X2 != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2581]),
    [final] ).

cnf(i_0_4740,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = hAPP_nat_nat(suc,zero_zero_nat)
    | X1 != zero_zero_nat
    | X2 != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2499]),
    [final] ).

cnf(i_0_4741,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = hAPP_nat_nat(suc,zero_zero_nat)
    | X1 != hAPP_nat_nat(suc,zero_zero_nat)
    | X2 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2499]),
    [final] ).

cnf(i_0_4742,plain,
    ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)
    | X1 != zero_zero_nat
    | X2 != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_4743,plain,
    ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)
    | X1 != hAPP_nat_nat(suc,zero_zero_nat)
    | X2 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_4744,plain,
    ( X1 = X3
    | X2 = zero_zero_nat
    | hAPP_nat_nat(times_times_nat(X1),X2) != hAPP_nat_nat(times_times_nat(X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2582]),
    [final] ).

cnf(i_0_4745,plain,
    ( X1 = zero_zero_nat
    | X2 = X3
    | hAPP_nat_nat(times_times_nat(X1),X2) != hAPP_nat_nat(times_times_nat(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2583]),
    [final] ).

cnf(i_0_4746,plain,
    ( X2 = X3
    | X1 = zero_zero_nat
    | hAPP_nat_nat(times_times_nat(X1),X2) != hAPP_nat_nat(times_times_nat(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2584]),
    [final] ).

cnf(i_0_4747,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk483_0),arrow_1681063817le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_2585]),
    [final] ).

cnf(i_0_4748,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk20_0),arrow_1681063817le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_1991]),
    [final] ).

cnf(i_0_4749,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,esk19_0),arrow_1681063817le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_1992]),
    [final] ).

cnf(i_0_4750,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lba),arrow_1681063817le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_75__096Lba_A_058_ALin_096]),
    [final] ).

cnf(i_0_4751,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lab),arrow_1681063817le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_74__096Lab_A_058_ALin_096]),
    [final] ).

cnf(i_0_4752,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,p),arrow_1721807329e_Prof)),
    inference(split_conjunct,[status(thm)],[fact_3__096P_A_058_AProf_096]),
    [final] ).

cnf(i_0_4753,plain,
    hAPP_n1699378549t_bool(ord_at4362885an_nat(X1),hAPP_nat_nat(suc,X2)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_2586]),
    [final] ).

cnf(i_0_4754,plain,
    ( X2 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2587]),
    [final] ).

cnf(i_0_4755,plain,
    ( X1 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(times_times_nat(X1),X2) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2581]),
    [final] ).

cnf(i_0_4756,plain,
    ( X1 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(times_times_nat(X2),X1) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2581]),
    [final] ).

cnf(i_0_4757,plain,
    ( X1 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2588]),
    [final] ).

cnf(i_0_4758,plain,
    ( X1 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2588]),
    [final] ).

cnf(i_0_4759,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),top_top_fun_nat_bool))
    | esk76_1(X1) != esk77_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2517]),
    [final] ).

cnf(i_0_4760,plain,
    ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),top_to1576102282i_bool))
    | esk74_1(X1) != esk75_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2518]),
    [final] ).

cnf(i_0_4761,plain,
    hAPP_f2026336507t_bool(image_579431497di_nat(esk506_0),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2589]),
    [final] ).

cnf(i_0_4762,plain,
    hAPP_f2026336507t_bool(image_579431497di_nat(h),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[fact_1127_surjh]),
    [final] ).

cnf(i_0_4763,plain,
    ( is_Arr43961803e_indi(esk75_1(X1))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),top_to1576102282i_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2518]),
    [final] ).

cnf(i_0_4764,plain,
    ( is_Arr43961803e_indi(esk74_1(X1))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X1),top_to1576102282i_bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2518]),
    [final] ).

cnf(i_0_4765,plain,
    is_fun1568535512t_bool(undefi312741927t_bool(fun(product_unit,bool))),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J]),
    [final] ).

cnf(i_0_4766,plain,
    is_fun1236654035i_bool(undefi1547870882i_bool(fun(arrow_1271263838e_indi,bool))),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___001]),
    [final] ).

cnf(i_0_4767,plain,
    hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,X1)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,X1),
    inference(split_conjunct,[status(thm)],[i_0_2590]),
    [final] ).

cnf(i_0_4768,plain,
    hAPP_nat_nat(suc,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),one_one_nat),
    inference(split_conjunct,[status(thm)],[i_0_2591]),
    [final] ).

cnf(i_0_4769,plain,
    hAPP_n1699378549t_bool(ord_less_nat,X1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2592]),
    [final] ).

cnf(i_0_4770,plain,
    ( is_Arr1861959080le_alt(esk22_2(X1,X2))
    | X2 = X1
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1704]),
    [final] ).

cnf(i_0_4771,plain,
    ( is_Arr1861959080le_alt(esk21_2(X1,X2))
    | X2 = X1
    | ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1704]),
    [final] ).

cnf(i_0_4772,plain,
    ( is_fun961089132t_bool(esk26_2(X1,X2))
    | X1 = X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1928]),
    [final] ).

cnf(i_0_4773,plain,
    hAPP_nat_nat(suc,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X1),
    inference(split_conjunct,[status(thm)],[i_0_2593]),
    [final] ).

cnf(i_0_4774,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2594]),
    [final] ).

cnf(i_0_4775,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2595]),
    [final] ).

cnf(i_0_4776,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2596]),
    [final] ).

cnf(i_0_4777,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2597]),
    [final] ).

cnf(i_0_4778,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2598]),
    [final] ).

cnf(i_0_4779,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2599]),
    [final] ).

cnf(i_0_4780,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2600]),
    [final] ).

cnf(i_0_4781,plain,
    ( hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,X1),X2) = X1
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2601]),
    [final] ).

cnf(i_0_4782,plain,
    ( hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,X1),X2) = X1
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2602]),
    [final] ).

cnf(i_0_4783,plain,
    ( hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_alt,X1),X2) = X1
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2603]),
    [final] ).

cnf(i_0_4784,plain,
    ( hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,X1),X2) = X1
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2604]),
    [final] ).

cnf(i_0_4785,plain,
    ( hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,X1),X2) = X1
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2605]),
    [final] ).

cnf(i_0_4786,plain,
    ( hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,X1),X2) = X1
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2606]),
    [final] ).

cnf(i_0_4787,plain,
    ( hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,X1),X2) = X1
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2607]),
    [final] ).

cnf(i_0_4788,plain,
    ( hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,X1),X2) = X1
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2608]),
    [final] ).

cnf(i_0_4789,plain,
    ( hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_bool,X1),X2) = X1
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2609]),
    [final] ).

cnf(i_0_4790,plain,
    ( hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,X1),X2) = X1
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2610]),
    [final] ).

cnf(i_0_4791,plain,
    ( hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,X1),X2) = X1
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2611]),
    [final] ).

cnf(i_0_4792,plain,
    ( hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,X1),X2) = X1
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2612]),
    [final] ).

cnf(i_0_4793,plain,
    ( hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_bool,X1),X2) = X1
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2613]),
    [final] ).

cnf(i_0_4794,plain,
    ( hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,X1),X2) = X1
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2614]),
    [final] ).

cnf(i_0_4795,plain,
    ( hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,X1),X2) = X1
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2615]),
    [final] ).

cnf(i_0_4796,plain,
    ( hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,X1),X2) = X1
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2616]),
    [final] ).

cnf(i_0_4797,plain,
    ( hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,X1),X2) = X1
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2617]),
    [final] ).

cnf(i_0_4798,plain,
    ( hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,X1),X2) = X1
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2618]),
    [final] ).

cnf(i_0_4799,plain,
    ( hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,X1),X2) = X1
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2619]),
    [final] ).

cnf(i_0_4800,plain,
    ( hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,X1),X2) = X1
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2620]),
    [final] ).

cnf(i_0_4801,plain,
    ( hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,X1),X2) = X1
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2621]),
    [final] ).

cnf(i_0_4802,plain,
    ( hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,X1),X2) = X1
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2622]),
    [final] ).

cnf(i_0_4803,plain,
    ( hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,X1),X2) = X1
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2623]),
    [final] ).

cnf(i_0_4804,plain,
    ( hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,X1),X2) = X1
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2624]),
    [final] ).

cnf(i_0_4805,plain,
    ( hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,X1),X2) = X1
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2625]),
    [final] ).

cnf(i_0_4806,plain,
    ( hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,X1),X2) = X1
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2626]),
    [final] ).

cnf(i_0_4807,plain,
    ( hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,X1),X2) = X1
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2627]),
    [final] ).

cnf(i_0_4808,plain,
    ( hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,X1),X2) = X1
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2628]),
    [final] ).

cnf(i_0_4809,plain,
    ( hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,X1),X2) = X1
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2629]),
    [final] ).

cnf(i_0_4810,plain,
    ( hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,X1),X2) = X1
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2630]),
    [final] ).

cnf(i_0_4811,hypothesis,
    ( is_bool(hAPP_f592646513l_bool(X1,X2))
    | ~ is_fun279392540l_bool(X1)
    | ~ is_fun961089132t_bool(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2631]),
    [final] ).

cnf(i_0_4812,plain,
    ( is_bool(hAPP_A1785763630i_bool(X1,X2))
    | ~ is_fun1236654035i_bool(X1)
    | ~ is_Arr43961803e_indi(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2632]),
    [final] ).

cnf(i_0_4813,plain,
    ( hAPP_nat_nat(times_times_nat(X1),X2) = hAPP_nat_nat(times_times_nat(X1),X3)
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2583]),
    [final] ).

cnf(i_0_4814,plain,
    ( hAPP_nat_nat(times_times_nat(X1),X2) = hAPP_nat_nat(times_times_nat(X1),X3)
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2584]),
    [final] ).

cnf(i_0_4815,plain,
    ( hAPP_nat_nat(times_times_nat(X2),X1) = hAPP_nat_nat(times_times_nat(X3),X1)
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2582]),
    [final] ).

cnf(i_0_4816,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = zero_zero_nat
    | X1 != zero_zero_nat
    | X2 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2588]),
    [final] ).

cnf(i_0_4817,plain,
    ( X1 = X2
    | hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2633]),
    [final] ).

cnf(i_0_4818,plain,
    ( X1 = X2
    | hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2634]),
    [final] ).

cnf(i_0_4819,plain,
    ( is_Arr1861959080le_alt(esk8_1(X1))
    | hBOOL(hAPP_P606313927t_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1935]),
    [final] ).

cnf(i_0_4820,plain,
    ( is_Arr1861959080le_alt(esk7_1(X1))
    | hBOOL(hAPP_P606313927t_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1935]),
    [final] ).

cnf(i_0_4821,plain,
    hAPP_nat_nat(times_times_nat(X1),X2) = hAPP_nat_nat(times_times_nat(X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_2635]),
    [final] ).

cnf(i_0_4822,plain,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2636]),
    [final] ).

cnf(i_0_4823,plain,
    ( is_Arr1861959080le_alt(esk17_1(X1))
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1701]),
    [final] ).

cnf(i_0_4824,plain,
    ( is_Arr1861959080le_alt(esk16_1(X1))
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1701]),
    [final] ).

cnf(i_0_4825,plain,
    ( is_Arr1861959080le_alt(esk13_1(X1))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_4826,plain,
    ( is_Arr1861959080le_alt(esk12_1(X1))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]),
    [final] ).

cnf(i_0_4827,plain,
    hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,X1),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2637]),
    [final] ).

cnf(i_0_4828,plain,
    hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,X1),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2638]),
    [final] ).

cnf(i_0_4829,plain,
    hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,X1),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2639]),
    [final] ).

cnf(i_0_4830,plain,
    hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,X1),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2640]),
    [final] ).

cnf(i_0_4831,plain,
    hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,X1),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2641]),
    [final] ).

cnf(i_0_4832,plain,
    hAPP_A2046586321t_bool(hAPP_f1491725936t_bool(cOMBK_847149194e_indi,X1),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2642]),
    [final] ).

cnf(i_0_4833,plain,
    hAPP_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_alt,X1),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2643]),
    [final] ).

cnf(i_0_4834,plain,
    hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,X1),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2644]),
    [final] ).

cnf(i_0_4835,plain,
    ( is_fun1217980910e_indi(hilber693666498di_nat(X1,X2))
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2645]),
    [final] ).

cnf(i_0_4836,plain,
    ( is_fun1568535512t_bool(hAPP_f1710744577t_bool(X2,X1))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2646]),
    [final] ).

cnf(i_0_4837,plain,
    ( is_fun1568535512t_bool(hAPP_f427533077t_bool(X2,X1))
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2647]),
    [final] ).

cnf(i_0_4838,plain,
    ( is_fun1568535512t_bool(hAPP_b1096750261t_bool(X2,X1))
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2648]),
    [final] ).

cnf(i_0_4839,plain,
    ( is_fun2093718614t_bool(hAPP_f1617919085t_bool(X2,X1))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2649]),
    [final] ).

cnf(i_0_4840,plain,
    ( is_bool(hAPP_P606313927t_bool(X1,X2))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2650]),
    [final] ).

cnf(i_0_4841,plain,
    ( is_bool(hAPP_f1749234559l_bool(X2,X1))
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2651]),
    [final] ).

cnf(i_0_4842,plain,
    ( is_bool(hAPP_f250445784l_bool(X2,X1))
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2652]),
    [final] ).

cnf(i_0_4843,plain,
    ( is_bool(hAPP_f312250286l_bool(X1,X2))
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2653]),
    [final] ).

cnf(i_0_4844,plain,
    ( is_bool(hAPP_f777333846l_bool(X2,X1))
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2654]),
    [final] ).

cnf(i_0_4845,plain,
    ( is_bool(hAPP_f2028818269l_bool(X2,X1))
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2655]),
    [final] ).

cnf(i_0_4846,plain,
    ( is_bool(hAPP_f965095724l_bool(X1,X2))
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2656]),
    [final] ).

cnf(i_0_4847,plain,
    ( is_bool(hAPP_f1599966040l_bool(X2,X1))
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2657]),
    [final] ).

cnf(i_0_4848,plain,
    ( is_bool(hAPP_f324780729l_bool(X2,X1))
    | ~ is_fun2093718614t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2658]),
    [final] ).

cnf(i_0_4849,plain,
    ( is_bool(hAPP_P1676879539t_bool(X1,X2))
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2659]),
    [final] ).

cnf(i_0_4850,plain,
    ( is_bool(hAPP_bool_bool(X2,X1))
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2660]),
    [final] ).

cnf(i_0_4851,plain,
    ( is_bool(hAPP_A862370221t_bool(X2,X1))
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2661]),
    [final] ).

cnf(i_0_4852,plain,
    ( is_Arr43961803e_indi(hAPP_f1582908258e_indi(X2,X1))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2662]),
    [final] ).

cnf(i_0_4853,plain,
    ( is_Arr43961803e_indi(hAPP_n1951273283e_indi(X1,X2))
    | ~ is_fun1217980910e_indi(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2663]),
    [final] ).

cnf(i_0_4854,plain,
    ( is_fun1236654035i_bool(hAPP_f244157820i_bool(X2,X1))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2664]),
    [final] ).

cnf(i_0_4855,plain,
    ( is_fun1236654035i_bool(hAPP_f580451669i_bool(X2,X1))
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2665]),
    [final] ).

cnf(i_0_4856,plain,
    ( is_fun1236654035i_bool(hAPP_b1337486384i_bool(X2,X1))
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2666]),
    [final] ).

cnf(i_0_4857,plain,
    ( is_fun961089132t_bool(hAPP_f515126293t_bool(X2,X1))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2667]),
    [final] ).

cnf(i_0_4858,plain,
    ( is_fun961089132t_bool(hAPP_b1703662281t_bool(X2,X1))
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2668]),
    [final] ).

cnf(i_0_4859,plain,
    ( is_fun961089132t_bool(hAPP_A1677245848t_bool(X2,X1))
    | ~ is_Arr43961803e_indi(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2669]),
    [final] ).

cnf(i_0_4860,plain,
    ( is_fun961089132t_bool(hAPP_A568203993t_bool(X2,X1))
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2670]),
    [final] ).

cnf(i_0_4861,plain,
    ( is_fun288122577l_bool(hAPP_f146009813l_bool(X2,X1))
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2671]),
    [final] ).

cnf(i_0_4862,plain,
    ( is_fun288122577l_bool(hAPP_b1048178734l_bool(X2,X1))
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2672]),
    [final] ).

cnf(i_0_4863,plain,
    ( is_fun288122577l_bool(hAPP_A1952883197l_bool(X2,X1))
    | ~ is_Arr43961803e_indi(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2673]),
    [final] ).

cnf(i_0_4864,plain,
    ( is_fun288122577l_bool(pi_Arr990697634t_bool(X1,X2))
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2674]),
    [final] ).

cnf(i_0_4865,plain,
    ( is_fun279392540l_bool(hAPP_f863359027l_bool(X2,X1))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2675]),
    [final] ).

cnf(i_0_4866,plain,
    ( is_fun279392540l_bool(hAPP_f111185985l_bool(X2,X1))
    | ~ is_fun279392540l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2676]),
    [final] ).

cnf(i_0_4867,plain,
    ( is_fun279392540l_bool(hAPP_b1812770943l_bool(X2,X1))
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2677]),
    [final] ).

cnf(i_0_4868,plain,
    ( is_fun279392540l_bool(hAPP_A60074736l_bool(X2,X1))
    | ~ is_Arr43961803e_indi(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2678]),
    [final] ).

cnf(i_0_4869,plain,
    ( is_fun279392540l_bool(hAPP_A187815023l_bool(X2,X1))
    | ~ is_Arr1861959080le_alt(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2679]),
    [final] ).

cnf(i_0_4870,plain,
    ( is_fun279392540l_bool(pi_Pro666468413t_bool(X1,X2))
    | ~ is_fun961089132t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2680]),
    [final] ).

cnf(i_0_4871,plain,
    ( is_fun158382675l_bool(hAPP_f1765205l_bool(X2,X1))
    | ~ is_fun158382675l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2681]),
    [final] ).

cnf(i_0_4872,plain,
    ( is_fun158382675l_bool(hAPP_b517355696l_bool(X2,X1))
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2682]),
    [final] ).

cnf(i_0_4873,plain,
    ( is_fun158382675l_bool(hAPP_A1112981887l_bool(X2,X1))
    | ~ is_Arr43961803e_indi(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2683]),
    [final] ).

cnf(i_0_4874,plain,
    ( is_fun158382675l_bool(pi_fun150026276t_bool(X1,X2))
    | ~ is_fun288122577l_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2684]),
    [final] ).

cnf(i_0_4875,plain,
    ( X2 = one_one_nat
    | X1 = zero_zero_nat
    | X1 != hAPP_nat_nat(times_times_nat(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2685]),
    [final] ).

cnf(i_0_4876,plain,
    hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2686]),
    [final] ).

cnf(i_0_4877,plain,
    hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2687]),
    [final] ).

cnf(i_0_4878,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),zero_zero_nat) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2688]),
    [final] ).

cnf(i_0_4879,plain,
    ( X1 = zero_zero_nat
    | X2 = zero_zero_nat
    | hAPP_nat_nat(times_times_nat(X1),X2) != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2689]),
    [final] ).

cnf(i_0_4880,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2690]),
    [final] ).

cnf(i_0_4881,plain,
    pi_Pro666468413t_bool(X1,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool)) = top_to1853035173l_bool,
    inference(split_conjunct,[status(thm)],[i_0_2691]),
    [final] ).

cnf(i_0_4882,plain,
    pi_fun150026276t_bool(X1,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool,
    inference(split_conjunct,[status(thm)],[i_0_2692]),
    [final] ).

cnf(i_0_4883,plain,
    pi_Arr990697634t_bool(X1,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool,
    inference(split_conjunct,[status(thm)],[i_0_2693]),
    [final] ).

cnf(i_0_4884,plain,
    ( X1 = one_one_nat
    | hAPP_nat_nat(times_times_nat(X1),X2) != one_one_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2694]),
    [final] ).

cnf(i_0_4885,plain,
    ( X1 = one_one_nat
    | hAPP_nat_nat(times_times_nat(X2),X1) != one_one_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2694]),
    [final] ).

cnf(i_0_4886,plain,
    ( X1 = one_one_nat
    | one_one_nat != hAPP_nat_nat(times_times_nat(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2695]),
    [final] ).

cnf(i_0_4887,plain,
    ( X1 = one_one_nat
    | one_one_nat != hAPP_nat_nat(times_times_nat(X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2695]),
    [final] ).

cnf(i_0_4888,plain,
    hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(esk506_0),top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[i_0_2589]),
    [final] ).

cnf(i_0_4889,plain,
    hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(h),top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[fact_20_injh]),
    [final] ).

cnf(i_0_4890,plain,
    top_top_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)),
    inference(split_conjunct,[status(thm)],[fact_179_UNIV__def]),
    [final] ).

cnf(i_0_4891,plain,
    top_to565915683t_bool = hAPP_f515126293t_bool(collec2096990994le_alt,hAPP_b1703662281t_bool(cOMBK_306730240le_alt,fTrue)),
    inference(split_conjunct,[status(thm)],[fact_176_UNIV__def]),
    [final] ).

cnf(i_0_4892,plain,
    top_to1853035173l_bool = hAPP_f111185985l_bool(collec1553055422t_bool,hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,fTrue)),
    inference(split_conjunct,[status(thm)],[fact_173_UNIV__def]),
    [final] ).

cnf(i_0_4893,plain,
    top_to1714702858l_bool = hAPP_f1765205l_bool(collec418781817t_bool,hAPP_b517355696l_bool(cOMBK_1626390631t_bool,fTrue)),
    inference(split_conjunct,[status(thm)],[fact_175_UNIV__def]),
    [final] ).

cnf(i_0_4894,plain,
    top_to522745736l_bool = hAPP_f146009813l_bool(collec1063742455t_bool,hAPP_b1048178734l_bool(cOMBK_272667621t_bool,fTrue)),
    inference(split_conjunct,[status(thm)],[fact_174_UNIV__def]),
    [final] ).

cnf(i_0_4895,plain,
    top_to1257323279t_bool = hAPP_f427533077t_bool(collect_Product_unit,hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)),
    inference(split_conjunct,[status(thm)],[fact_178_UNIV__def]),
    [final] ).

cnf(i_0_4896,plain,
    top_to1576102282i_bool = hAPP_f580451669i_bool(collec1611109369e_indi,hAPP_b1337486384i_bool(cOMBK_575487463e_indi,fTrue)),
    inference(split_conjunct,[status(thm)],[fact_177_UNIV__def]),
    [final] ).

cnf(i_0_4897,plain,
    arrow_1721807329e_Prof = pi_Arr990697634t_bool(top_to1576102282i_bool,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,arrow_1681063817le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_579_Prof__def]),
    [final] ).

cnf(i_0_4898,plain,
    ( hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X1))
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2594]),
    [final] ).

cnf(i_0_4899,plain,
    ( hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X1))
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2595]),
    [final] ).

cnf(i_0_4900,plain,
    ( hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X1))
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2596]),
    [final] ).

cnf(i_0_4901,plain,
    ( hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X1))
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2597]),
    [final] ).

cnf(i_0_4902,plain,
    ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X1))
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2598]),
    [final] ).

cnf(i_0_4903,plain,
    ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X1))
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2599]),
    [final] ).

cnf(i_0_4904,plain,
    ( hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X1))
    | ~ hBOOL(top_top_bool) ),
    inference(split_conjunct,[status(thm)],[i_0_2600]),
    [final] ).

cnf(i_0_4905,plain,
    is_fun1568535512t_bool(hAPP_P332578347t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2696]),
    [final] ).

cnf(i_0_4906,plain,
    is_fun1568535512t_bool(hAPP_f1866147972t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2697]),
    [final] ).

cnf(i_0_4907,plain,
    is_fun1568535512t_bool(hAPP_f1061584978t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2698]),
    [final] ).

cnf(i_0_4908,plain,
    is_fun1568535512t_bool(hAPP_f1891021702t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2699]),
    [final] ).

cnf(i_0_4909,plain,
    is_fun1568535512t_bool(hAPP_n454528608t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2700]),
    [final] ).

cnf(i_0_4910,plain,
    is_fun2093718614t_bool(hAPP_f861874780t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2701]),
    [final] ).

cnf(i_0_4911,plain,
    is_fun2093718614t_bool(hAPP_n539120590t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2702]),
    [final] ).

cnf(i_0_4912,plain,
    is_bool(hAPP_f22590837l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2703]),
    [final] ).

cnf(i_0_4913,plain,
    is_bool(hAPP_f1306865520l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2704]),
    [final] ).

cnf(i_0_4914,plain,
    is_bool(hAPP_f866275871l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2705]),
    [final] ).

cnf(i_0_4915,plain,
    is_bool(hAPP_f167218729l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2706]),
    [final] ).

cnf(i_0_4916,plain,
    is_bool(hAPP_f560831258l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2707]),
    [final] ).

cnf(i_0_4917,plain,
    is_bool(hAPP_f1644647260l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2708]),
    [final] ).

cnf(i_0_4918,plain,
    is_bool(hAPP_f859154022l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2709]),
    [final] ).

cnf(i_0_4919,plain,
    is_bool(hAPP_f10461143l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2710]),
    [final] ).

cnf(i_0_4920,plain,
    is_bool(hAPP_f770608346l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2711]),
    [final] ).

cnf(i_0_4921,plain,
    is_bool(hAPP_f597137892l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2712]),
    [final] ).

cnf(i_0_4922,plain,
    is_bool(hAPP_f1725204053l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2713]),
    [final] ).

cnf(i_0_4923,plain,
    is_bool(hAPP_f415146997l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2714]),
    [final] ).

cnf(i_0_4924,plain,
    is_bool(hAPP_f1846209297l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2715]),
    [final] ).

cnf(i_0_4925,plain,
    is_bool(hAPP_f1508442332l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2716]),
    [final] ).

cnf(i_0_4926,plain,
    is_bool(hAPP_f844512602l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2717]),
    [final] ).

cnf(i_0_4927,plain,
    is_bool(hAPP_f339859954l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2718]),
    [final] ).

cnf(i_0_4928,plain,
    is_bool(hAPP_f537623936l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2719]),
    [final] ).

cnf(i_0_4929,plain,
    is_bool(hAPP_f1637334154l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2720]),
    [final] ).

cnf(i_0_4930,plain,
    is_bool(hAPP_f795156475l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2721]),
    [final] ).

cnf(i_0_4931,plain,
    is_bool(hAPP_f1351174655l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2722]),
    [final] ).

cnf(i_0_4932,plain,
    is_bool(hAPP_f817604743l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2723]),
    [final] ).

cnf(i_0_4933,plain,
    is_bool(hAPP_f651410150l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2724]),
    [final] ).

cnf(i_0_4934,plain,
    is_bool(hAPP_f599145828l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2725]),
    [final] ).

cnf(i_0_4935,plain,
    is_bool(hAPP_f67777128l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2726]),
    [final] ).

cnf(i_0_4936,plain,
    is_bool(hAPP_f1837019376l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2727]),
    [final] ).

cnf(i_0_4937,plain,
    is_bool(hAPP_f785974231l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2728]),
    [final] ).

cnf(i_0_4938,plain,
    is_bool(hAPP_f1252760917l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2729]),
    [final] ).

cnf(i_0_4939,plain,
    is_bool(hAPP_f1632652727l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2730]),
    [final] ).

cnf(i_0_4940,plain,
    is_bool(hAPP_f54304608l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2731]),
    [final] ).

cnf(i_0_4941,plain,
    is_bool(hAPP_f387058535l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2732]),
    [final] ).

cnf(i_0_4942,plain,
    is_bool(hAPP_f2013399995l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2733]),
    [final] ).

cnf(i_0_4943,plain,
    is_bool(hAPP_nat_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2734]),
    [final] ).

cnf(i_0_4944,plain,
    is_Arr43961803e_indi(hAPP_P710098616e_indi(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2735]),
    [final] ).

cnf(i_0_4945,plain,
    is_Arr43961803e_indi(hAPP_f1693298207e_indi(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2736]),
    [final] ).

cnf(i_0_4946,plain,
    is_Arr43961803e_indi(hAPP_f836059805e_indi(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2737]),
    [final] ).

cnf(i_0_4947,plain,
    is_fun1236654035i_bool(hAPP_P1875867302i_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2738]),
    [final] ).

cnf(i_0_4948,plain,
    is_fun1236654035i_bool(hAPP_f1552576127i_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2739]),
    [final] ).

cnf(i_0_4949,plain,
    is_fun1236654035i_bool(hAPP_f632777549i_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2740]),
    [final] ).

cnf(i_0_4950,plain,
    is_fun1236654035i_bool(hAPP_f1948454017i_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2741]),
    [final] ).

cnf(i_0_4951,plain,
    is_fun1236654035i_bool(hAPP_n821919323i_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2742]),
    [final] ).

cnf(i_0_4952,plain,
    is_fun961089132t_bool(hAPP_f899613158t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2743]),
    [final] ).

cnf(i_0_4953,hypothesis,
    is_fun961089132t_bool(hAPP_f412050202t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2744]),
    [final] ).

cnf(i_0_4954,plain,
    is_fun961089132t_bool(hAPP_P1341894483t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2745]),
    [final] ).

cnf(i_0_4955,plain,
    is_fun961089132t_bool(hAPP_n588788980t_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2746]),
    [final] ).

cnf(i_0_4956,plain,
    is_fun288122577l_bool(hAPP_f226010187l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2747]),
    [final] ).

cnf(i_0_4957,plain,
    is_fun288122577l_bool(hAPP_P254387896l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2748]),
    [final] ).

cnf(i_0_4958,plain,
    is_fun288122577l_bool(hAPP_n2095207769l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2749]),
    [final] ).

cnf(i_0_4959,hypothesis,
    is_fun279392540l_bool(hAPP_P229966473l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2750]),
    [final] ).

cnf(i_0_4960,plain,
    is_fun279392540l_bool(hAPP_f769545506l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2751]),
    [final] ).

cnf(i_0_4961,plain,
    is_fun279392540l_bool(hAPP_f1277514478l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2752]),
    [final] ).

cnf(i_0_4962,plain,
    is_fun279392540l_bool(hAPP_P1294997365l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2753]),
    [final] ).

cnf(i_0_4963,plain,
    is_fun279392540l_bool(hAPP_n1674354836l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2754]),
    [final] ).

cnf(i_0_4964,plain,
    is_fun158382675l_bool(hAPP_f1449238989l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2755]),
    [final] ).

cnf(i_0_4965,plain,
    is_fun158382675l_bool(hAPP_P1171466554l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2756]),
    [final] ).

cnf(i_0_4966,plain,
    is_fun158382675l_bool(hAPP_n295497947l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2757]),
    [final] ).

cnf(i_0_4967,plain,
    hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2758]),
    [final] ).

cnf(i_0_4968,plain,
    hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2759]),
    [final] ).

cnf(i_0_4969,plain,
    hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2760]),
    [final] ).

cnf(i_0_4970,plain,
    hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2761]),
    [final] ).

cnf(i_0_4971,plain,
    hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2762]),
    [final] ).

cnf(i_0_4972,plain,
    hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2763]),
    [final] ).

cnf(i_0_4973,plain,
    hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2764]),
    [final] ).

cnf(i_0_4974,plain,
    hAPP_n1699378549t_bool(ord_greaterThan_nat,zero_zero_nat) = hAPP_f800510211t_bool(image_nat_nat(suc),top_top_fun_nat_bool),
    inference(split_conjunct,[status(thm)],[fact_1135_greaterThan__0]),
    [final] ).

cnf(i_0_4975,plain,
    ( hAPP_nat_nat(times_times_nat(X1),X2) = one_one_nat
    | X1 != one_one_nat
    | X2 != one_one_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2694]),
    [final] ).

cnf(i_0_4976,plain,
    ( one_one_nat = hAPP_nat_nat(times_times_nat(X1),X2)
    | X1 != one_one_nat
    | X2 != one_one_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2695]),
    [final] ).

cnf(i_0_4977,plain,
    hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,f)),
    inference(split_conjunct,[status(thm)],[fact_1_u]),
    [final] ).

cnf(i_0_4978,plain,
    hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,f)),
    inference(split_conjunct,[status(thm)],[fact_0_assms_I3_J]),
    [final] ).

cnf(i_0_4979,plain,
    hBOOL(hAPP_f1599966040l_bool(finite106199483e_indi,top_to1576102282i_bool)),
    inference(split_conjunct,[status(thm)],[fact_1031_finite__indi]),
    [final] ).

cnf(i_0_4980,plain,
    ( hAPP_nat_nat(times_times_nat(X1),X2) = zero_zero_nat
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2689]),
    [final] ).

cnf(i_0_4981,plain,
    ( hAPP_nat_nat(times_times_nat(X2),X1) = zero_zero_nat
    | X1 != zero_zero_nat ),
    inference(split_conjunct,[status(thm)],[i_0_2689]),
    [final] ).

cnf(i_0_4982,plain,
    hAPP_nat_nat(suc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_2765]),
    [final] ).

cnf(i_0_4983,plain,
    X1 != hAPP_nat_nat(suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2766]),
    [final] ).

cnf(i_0_4984,plain,
    ( X1 = zero_zero_nat
    | X1 = hAPP_nat_nat(suc,esk503_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2767]),
    [final] ).

cnf(i_0_4985,plain,
    ( X1 = zero_zero_nat
    | X1 = hAPP_nat_nat(suc,esk502_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2768]),
    [final] ).

cnf(i_0_4986,plain,
    ( hAPP_f427533077t_bool(collect_Product_unit,X1) = X1
    | ~ is_fun1568535512t_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2769]),
    [final] ).

cnf(i_0_4987,plain,
    ( hAPP_f580451669i_bool(collec1611109369e_indi,X1) = X1
    | ~ is_fun1236654035i_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2770]),
    [final] ).

cnf(i_0_4988,plain,
    hAPP_nat_nat(suc,X1) != zero_zero_nat,
    inference(split_conjunct,[status(thm)],[i_0_2771]),
    [final] ).

cnf(i_0_4989,plain,
    hAPP_nat_nat(suc,X1) != zero_zero_nat,
    inference(split_conjunct,[status(thm)],[i_0_2772]),
    [final] ).

cnf(i_0_4990,plain,
    hAPP_nat_nat(suc,X1) != zero_zero_nat,
    inference(split_conjunct,[status(thm)],[i_0_2773]),
    [final] ).

cnf(i_0_4991,plain,
    zero_zero_nat != hAPP_nat_nat(suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2774]),
    [final] ).

cnf(i_0_4992,plain,
    zero_zero_nat != hAPP_nat_nat(suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2775]),
    [final] ).

cnf(i_0_4993,plain,
    zero_zero_nat != hAPP_nat_nat(suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2776]),
    [final] ).

cnf(i_0_4994,plain,
    hAPP_nat_nat(times_times_nat(X1),one_one_nat) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2777]),
    [final] ).

cnf(i_0_4995,plain,
    hAPP_nat_nat(times_times_nat(X1),zero_zero_nat) = zero_zero_nat,
    inference(split_conjunct,[status(thm)],[i_0_2778]),
    [final] ).

cnf(i_0_4996,plain,
    hAPP_nat_nat(times_times_nat(one_one_nat),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2779]),
    [final] ).

cnf(i_0_4997,plain,
    hAPP_nat_nat(times_times_nat(zero_zero_nat),X1) = zero_zero_nat,
    inference(split_conjunct,[status(thm)],[i_0_2780]),
    [final] ).

cnf(i_0_4998,plain,
    hAPP_nat_nat(size_size_nat,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2781]),
    [final] ).

cnf(i_0_4999,plain,
    hAPP_nat_nat(cOMBI_nat,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2782]),
    [final] ).

cnf(i_0_5000,plain,
    hAPP_f800510211t_bool(collect_nat,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2783]),
    [final] ).

cnf(i_0_5001,plain,
    hAPP_f2030293770ol_nat(finite1949902593t_unit,top_to1257323279t_bool) = one_one_nat,
    inference(split_conjunct,[status(thm)],[fact_1035_card__UNIV__unit]),
    [final] ).

cnf(i_0_5002,plain,
    hAPP_bool_nat(bool_size,fTrue) = zero_zero_nat,
    inference(split_conjunct,[status(thm)],[fact_1187_bool_Osize_I1_J]),
    [final] ).

cnf(i_0_5003,plain,
    hAPP_bool_nat(bool_size,fFalse) = zero_zero_nat,
    inference(split_conjunct,[status(thm)],[fact_1188_bool_Osize_I2_J]),
    [final] ).

cnf(i_0_5004,plain,
    hAPP_nat_nat(size_size_nat,zero_zero_nat) = zero_zero_nat,
    inference(split_conjunct,[status(thm)],[fact_1185_nat_Osize_I3_J]),
    [final] ).

cnf(i_0_5005,plain,
    hAPP_nat_nat(nat_size,zero_zero_nat) = zero_zero_nat,
    inference(split_conjunct,[status(thm)],[fact_1182_nat_Osize_I1_J]),
    [final] ).

cnf(i_0_5006,plain,
    hAPP_n1699378549t_bool(ord_atLeast_nat,zero_zero_nat) = top_top_fun_nat_bool,
    inference(split_conjunct,[status(thm)],[fact_1197_atLeast__0]),
    [final] ).

cnf(i_0_5007,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(split_conjunct,[status(thm)],[fact_1109_One__nat__def]),
    [final] ).

cnf(i_0_5008,plain,
    ( X1 = fTrue
    | X1 = fFalse
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2784]),
    [final] ).

cnf(i_0_5009,plain,
    ( X1 = fTrue
    | X1 = fFalse
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2785]),
    [final] ).

cnf(i_0_5010,plain,
    ( X1 = fTrue
    | X1 = fFalse
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2786]),
    [final] ).

cnf(i_0_5011,plain,
    is_bool(undefined_bool(bool)),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__HOL__Obool]),
    [final] ).

cnf(i_0_5012,plain,
    is_Arr43961803e_indi(undefi237088188e_indi(arrow_1271263838e_indi)),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi]),
    [final] ).

cnf(i_0_5013,plain,
    is_Arr1861959080le_alt(undefi462180727le_alt(arrow_107136085le_alt)),
    inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt]),
    [final] ).

cnf(i_0_5014,plain,
    ~ hBOOL(fFalse),
    inference(split_conjunct,[status(thm)],[i_0_2787]),
    [final] ).

cnf(i_0_5015,plain,
    hBOOL(fTrue),
    inference(split_conjunct,[status(thm)],[help_fTrue_1_1_U]),
    [final] ).

cnf(i_0_5016,plain,
    is_fun1568535512t_bool(top_to1257323279t_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL]),
    [final] ).

cnf(i_0_5017,plain,
    is_fun2093718614t_bool(top_to178429151t_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____]),
    [final] ).

cnf(i_0_5018,plain,
    is_bool(fTrue),
    inference(split_conjunct,[status(thm)],[gsy_c_fTrue]),
    [final] ).

cnf(i_0_5019,plain,
    is_bool(fFalse),
    inference(split_conjunct,[status(thm)],[gsy_c_fFalse]),
    [final] ).

cnf(i_0_5020,plain,
    is_bool(top_top_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool]),
    [final] ).

cnf(i_0_5021,plain,
    is_fun1236654035i_bool(top_to1576102282i_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____002]),
    [final] ).

cnf(i_0_5022,plain,
    is_Arr1861959080le_alt(e),
    inference(split_conjunct,[status(thm)],[gsy_v_e____]),
    [final] ).

cnf(i_0_5023,hypothesis,
    is_Arr1861959080le_alt(d),
    inference(split_conjunct,[status(thm)],[gsy_v_d____]),
    [final] ).

cnf(i_0_5024,hypothesis,
    is_Arr1861959080le_alt(c),
    inference(split_conjunct,[status(thm)],[gsy_v_c____]),
    [final] ).

cnf(i_0_5025,plain,
    is_Arr1861959080le_alt(b),
    inference(split_conjunct,[status(thm)],[gsy_v_b____]),
    [final] ).

cnf(i_0_5026,plain,
    is_Arr1861959080le_alt(a),
    inference(split_conjunct,[status(thm)],[gsy_v_a____]),
    [final] ).

cnf(i_0_5027,plain,
    is_fun961089132t_bool(esk483_0),
    inference(split_conjunct,[status(thm)],[i_0_2585]),
    [final] ).

cnf(i_0_5028,plain,
    is_fun961089132t_bool(esk20_0),
    inference(split_conjunct,[status(thm)],[i_0_1991]),
    [final] ).

cnf(i_0_5029,plain,
    is_fun961089132t_bool(esk19_0),
    inference(split_conjunct,[status(thm)],[i_0_1992]),
    [final] ).

cnf(i_0_5030,plain,
    is_fun961089132t_bool(lba),
    inference(split_conjunct,[status(thm)],[gsy_v_Lba____]),
    [final] ).

cnf(i_0_5031,plain,
    is_fun961089132t_bool(lab),
    inference(split_conjunct,[status(thm)],[gsy_v_Lab____]),
    [final] ).

cnf(i_0_5032,plain,
    is_fun961089132t_bool(top_to565915683t_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir]),
    [final] ).

cnf(i_0_5033,plain,
    is_fun288122577l_bool(top_to522745736l_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira]),
    [final] ).

cnf(i_0_5034,plain,
    is_fun288122577l_bool(arrow_1721807329e_Prof),
    inference(split_conjunct,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OProf]),
    [final] ).

cnf(i_0_5035,plain,
    is_fun279392540l_bool(top_to1853035173l_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord]),
    [final] ).

cnf(i_0_5036,plain,
    is_fun279392540l_bool(arrow_1681063817le_Lin),
    inference(split_conjunct,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OLin]),
    [final] ).

cnf(i_0_5037,plain,
    is_fun158382675l_bool(top_to1714702858l_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde]),
    [final] ).

cnf(i_0_5038,plain,
    is_fun158382675l_bool(arrow_1587283740nimity),
    inference(split_conjunct,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Ounanimity]),
    [final] ).

cnf(i_0_5039,plain,
    is_fun158382675l_bool(arrow_1654180089le_IIA),
    inference(split_conjunct,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OIIA]),
    [final] ).

cnf(i_0_5040,plain,
    c != d,
    inference(split_conjunct,[status(thm)],[fact_2__096c_A_126_061_Ad_096]),
    [final] ).

cnf(i_0_5041,plain,
    a != b,
    inference(split_conjunct,[status(thm)],[fact_76__096a_A_126_061_Ab_096]),
    [final] ).

cnf(i_0_5042,axiom,
    X1 = X1 ).

cnf(i_0_5043,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_5044,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_5045,axiom,
    ( X1 != X2
    | hAPP_f592646513l_bool(X1,X3) = hAPP_f592646513l_bool(X2,X3) ) ).

cnf(i_0_5046,axiom,
    ( X1 != X2
    | hAPP_f592646513l_bool(X3,X1) = hAPP_f592646513l_bool(X3,X2) ) ).

cnf(i_0_5047,axiom,
    ( X1 != X2
    | hAPP_n454528608t_bool(X1,X3) = hAPP_n454528608t_bool(X2,X3) ) ).

cnf(i_0_5048,axiom,
    ( X1 != X2
    | hAPP_n454528608t_bool(X3,X1) = hAPP_n454528608t_bool(X3,X2) ) ).

cnf(i_0_5049,axiom,
    ( X1 != X2
    | hAPP_n821919323i_bool(X1,X3) = hAPP_n821919323i_bool(X2,X3) ) ).

cnf(i_0_5050,axiom,
    ( X1 != X2
    | hAPP_n821919323i_bool(X3,X1) = hAPP_n821919323i_bool(X3,X2) ) ).

cnf(i_0_5051,axiom,
    ( X1 != X2
    | hAPP_f2026336507t_bool(X1,X3) = hAPP_f2026336507t_bool(X2,X3) ) ).

cnf(i_0_5052,axiom,
    ( X1 != X2
    | hAPP_f2026336507t_bool(X3,X1) = hAPP_f2026336507t_bool(X3,X2) ) ).

cnf(i_0_5053,axiom,
    ( X1 != X2
    | hAPP_nat_nat(X1,X3) = hAPP_nat_nat(X2,X3) ) ).

cnf(i_0_5054,axiom,
    ( X1 != X2
    | hAPP_nat_nat(X3,X1) = hAPP_nat_nat(X3,X2) ) ).

cnf(i_0_5055,axiom,
    ( X1 != X2
    | hAPP_b1013836512t_bool(X1,X3) = hAPP_b1013836512t_bool(X2,X3) ) ).

cnf(i_0_5056,axiom,
    ( X1 != X2
    | hAPP_b1013836512t_bool(X3,X1) = hAPP_b1013836512t_bool(X3,X2) ) ).

cnf(i_0_5057,axiom,
    ( X1 != X2
    | hAPP_bool_bool(X1,X3) = hAPP_bool_bool(X2,X3) ) ).

cnf(i_0_5058,axiom,
    ( X1 != X2
    | hAPP_bool_bool(X3,X1) = hAPP_bool_bool(X3,X2) ) ).

cnf(i_0_5059,axiom,
    ( X1 != X2
    | hAPP_b589554111l_bool(X1,X3) = hAPP_b589554111l_bool(X2,X3) ) ).

cnf(i_0_5060,axiom,
    ( X1 != X2
    | hAPP_b589554111l_bool(X3,X1) = hAPP_b589554111l_bool(X3,X2) ) ).

cnf(i_0_5061,axiom,
    ( X1 != X2
    | hAPP_f800510211t_bool(X1,X3) = hAPP_f800510211t_bool(X2,X3) ) ).

cnf(i_0_5062,axiom,
    ( X1 != X2
    | hAPP_f800510211t_bool(X3,X1) = hAPP_f800510211t_bool(X3,X2) ) ).

cnf(i_0_5063,axiom,
    ( X1 != X2
    | hAPP_P229966473l_bool(X1,X3) = hAPP_P229966473l_bool(X2,X3) ) ).

cnf(i_0_5064,axiom,
    ( X1 != X2
    | hAPP_P229966473l_bool(X3,X1) = hAPP_P229966473l_bool(X3,X2) ) ).

cnf(i_0_5065,axiom,
    ( X1 != X2
    | hAPP_f2030293770ol_nat(X1,X3) = hAPP_f2030293770ol_nat(X2,X3) ) ).

cnf(i_0_5066,axiom,
    ( X1 != X2
    | hAPP_f2030293770ol_nat(X3,X1) = hAPP_f2030293770ol_nat(X3,X2) ) ).

cnf(i_0_5067,axiom,
    ( X1 != X2
    | hAPP_f22106695ol_nat(X1,X3) = hAPP_f22106695ol_nat(X2,X3) ) ).

cnf(i_0_5068,axiom,
    ( X1 != X2
    | hAPP_f22106695ol_nat(X3,X1) = hAPP_f22106695ol_nat(X3,X2) ) ).

cnf(i_0_5069,axiom,
    ( X1 != X2
    | hAPP_bool_nat(X1,X3) = hAPP_bool_nat(X2,X3) ) ).

cnf(i_0_5070,axiom,
    ( X1 != X2
    | hAPP_bool_nat(X3,X1) = hAPP_bool_nat(X3,X2) ) ).

cnf(i_0_5071,axiom,
    ( X1 != X2
    | hAPP_A702847159le_alt(X1,X3) = hAPP_A702847159le_alt(X2,X3) ) ).

cnf(i_0_5072,axiom,
    ( X1 != X2
    | hAPP_A702847159le_alt(X3,X1) = hAPP_A702847159le_alt(X3,X2) ) ).

cnf(i_0_5073,axiom,
    ( X1 != X2
    | hAPP_A1677245848t_bool(X1,X3) = hAPP_A1677245848t_bool(X2,X3) ) ).

cnf(i_0_5074,axiom,
    ( X1 != X2
    | hAPP_A1677245848t_bool(X3,X1) = hAPP_A1677245848t_bool(X3,X2) ) ).

cnf(i_0_5075,axiom,
    ( X1 != X2
    | hAPP_f777333846l_bool(X1,X3) = hAPP_f777333846l_bool(X2,X3) ) ).

cnf(i_0_5076,axiom,
    ( X1 != X2
    | hAPP_f777333846l_bool(X3,X1) = hAPP_f777333846l_bool(X3,X2) ) ).

cnf(i_0_5077,axiom,
    ( X1 != X2
    | hAPP_f312250286l_bool(X1,X3) = hAPP_f312250286l_bool(X2,X3) ) ).

cnf(i_0_5078,axiom,
    ( X1 != X2
    | hAPP_f312250286l_bool(X3,X1) = hAPP_f312250286l_bool(X3,X2) ) ).

cnf(i_0_5079,axiom,
    ( X1 != X2
    | hAPP_nat_bool(X1,X3) = hAPP_nat_bool(X2,X3) ) ).

cnf(i_0_5080,axiom,
    ( X1 != X2
    | hAPP_nat_bool(X3,X1) = hAPP_nat_bool(X3,X2) ) ).

cnf(i_0_5081,axiom,
    ( X1 != X2
    | hAPP_n1699378549t_bool(X1,X3) = hAPP_n1699378549t_bool(X2,X3) ) ).

cnf(i_0_5082,axiom,
    ( X1 != X2
    | hAPP_n1699378549t_bool(X3,X1) = hAPP_n1699378549t_bool(X3,X2) ) ).

cnf(i_0_5083,axiom,
    ( X1 != X2
    | hAPP_f54304608l_bool(X1,X3) = hAPP_f54304608l_bool(X2,X3) ) ).

cnf(i_0_5084,axiom,
    ( X1 != X2
    | hAPP_f54304608l_bool(X3,X1) = hAPP_f54304608l_bool(X3,X2) ) ).

cnf(i_0_5085,axiom,
    ( X1 != X2
    | hAPP_n215258509l_bool(X1,X3) = hAPP_n215258509l_bool(X2,X3) ) ).

cnf(i_0_5086,axiom,
    ( X1 != X2
    | hAPP_n215258509l_bool(X3,X1) = hAPP_n215258509l_bool(X3,X2) ) ).

cnf(i_0_5087,axiom,
    ( X1 != X2
    | hAPP_A1637648121di_nat(X1,X3) = hAPP_A1637648121di_nat(X2,X3) ) ).

cnf(i_0_5088,axiom,
    ( X1 != X2
    | hAPP_A1637648121di_nat(X3,X1) = hAPP_A1637648121di_nat(X3,X2) ) ).

cnf(i_0_5089,axiom,
    ( X1 != X2
    | hAPP_A568203993t_bool(X1,X3) = hAPP_A568203993t_bool(X2,X3) ) ).

cnf(i_0_5090,axiom,
    ( X1 != X2
    | hAPP_A568203993t_bool(X3,X1) = hAPP_A568203993t_bool(X3,X2) ) ).

cnf(i_0_5091,axiom,
    ( X1 != X2
    | hAPP_f393984045t_bool(X1,X3) = hAPP_f393984045t_bool(X2,X3) ) ).

cnf(i_0_5092,axiom,
    ( X1 != X2
    | hAPP_f393984045t_bool(X3,X1) = hAPP_f393984045t_bool(X3,X2) ) ).

cnf(i_0_5093,axiom,
    ( X1 != X2
    | hAPP_A1941004017t_bool(X1,X3) = hAPP_A1941004017t_bool(X2,X3) ) ).

cnf(i_0_5094,axiom,
    ( X1 != X2
    | hAPP_A1941004017t_bool(X3,X1) = hAPP_A1941004017t_bool(X3,X2) ) ).

cnf(i_0_5095,axiom,
    ( X1 != X2
    | hAPP_f412050202t_bool(X1,X3) = hAPP_f412050202t_bool(X2,X3) ) ).

cnf(i_0_5096,axiom,
    ( X1 != X2
    | hAPP_f412050202t_bool(X3,X1) = hAPP_f412050202t_bool(X3,X2) ) ).

cnf(i_0_5097,axiom,
    ( X1 != X2
    | hAPP_f344580165t_bool(X1,X3) = hAPP_f344580165t_bool(X2,X3) ) ).

cnf(i_0_5098,axiom,
    ( X1 != X2
    | hAPP_f344580165t_bool(X3,X1) = hAPP_f344580165t_bool(X3,X2) ) ).

cnf(i_0_5099,axiom,
    ( X1 != X2
    | hAPP_P332578347t_bool(X1,X3) = hAPP_P332578347t_bool(X2,X3) ) ).

cnf(i_0_5100,axiom,
    ( X1 != X2
    | hAPP_P332578347t_bool(X3,X1) = hAPP_P332578347t_bool(X3,X2) ) ).

cnf(i_0_5101,axiom,
    ( X1 != X2
    | pi_Pro666468413t_bool(X1,X3) = pi_Pro666468413t_bool(X2,X3) ) ).

cnf(i_0_5102,axiom,
    ( X1 != X2
    | pi_Pro666468413t_bool(X3,X1) = pi_Pro666468413t_bool(X3,X2) ) ).

cnf(i_0_5103,axiom,
    ( X1 != X2
    | hAPP_P606313927t_bool(X1,X3) = hAPP_P606313927t_bool(X2,X3) ) ).

cnf(i_0_5104,axiom,
    ( X1 != X2
    | hAPP_P606313927t_bool(X3,X1) = hAPP_P606313927t_bool(X3,X2) ) ).

cnf(i_0_5105,axiom,
    ( X1 != X2
    | hAPP_P324742453l_bool(X1,X3) = hAPP_P324742453l_bool(X2,X3) ) ).

cnf(i_0_5106,axiom,
    ( X1 != X2
    | hAPP_P324742453l_bool(X3,X1) = hAPP_P324742453l_bool(X3,X2) ) ).

cnf(i_0_5107,axiom,
    ( X1 != X2
    | hAPP_P1875867302i_bool(X1,X3) = hAPP_P1875867302i_bool(X2,X3) ) ).

cnf(i_0_5108,axiom,
    ( X1 != X2
    | hAPP_P1875867302i_bool(X3,X1) = hAPP_P1875867302i_bool(X3,X2) ) ).

cnf(i_0_5109,axiom,
    ( X1 != X2
    | hAPP_f1710744577t_bool(X1,X3) = hAPP_f1710744577t_bool(X2,X3) ) ).

cnf(i_0_5110,axiom,
    ( X1 != X2
    | hAPP_f1710744577t_bool(X3,X1) = hAPP_f1710744577t_bool(X3,X2) ) ).

cnf(i_0_5111,axiom,
    ( X1 != X2
    | hAPP_f210572555l_bool(X1,X3) = hAPP_f210572555l_bool(X2,X3) ) ).

cnf(i_0_5112,axiom,
    ( X1 != X2
    | hAPP_f210572555l_bool(X3,X1) = hAPP_f210572555l_bool(X3,X2) ) ).

cnf(i_0_5113,axiom,
    ( X1 != X2
    | hAPP_f244157820i_bool(X1,X3) = hAPP_f244157820i_bool(X2,X3) ) ).

cnf(i_0_5114,axiom,
    ( X1 != X2
    | hAPP_f244157820i_bool(X3,X1) = hAPP_f244157820i_bool(X3,X2) ) ).

cnf(i_0_5115,axiom,
    ( X1 != X2
    | hAPP_f1866147972t_bool(X1,X3) = hAPP_f1866147972t_bool(X2,X3) ) ).

cnf(i_0_5116,axiom,
    ( X1 != X2
    | hAPP_f1866147972t_bool(X3,X1) = hAPP_f1866147972t_bool(X3,X2) ) ).

cnf(i_0_5117,axiom,
    ( X1 != X2
    | hAPP_f1624277646l_bool(X1,X3) = hAPP_f1624277646l_bool(X2,X3) ) ).

cnf(i_0_5118,axiom,
    ( X1 != X2
    | hAPP_f1624277646l_bool(X3,X1) = hAPP_f1624277646l_bool(X3,X2) ) ).

cnf(i_0_5119,axiom,
    ( X1 != X2
    | hAPP_f1552576127i_bool(X1,X3) = hAPP_f1552576127i_bool(X2,X3) ) ).

cnf(i_0_5120,axiom,
    ( X1 != X2
    | hAPP_f1552576127i_bool(X3,X1) = hAPP_f1552576127i_bool(X3,X2) ) ).

cnf(i_0_5121,axiom,
    ( X1 != X2
    | pi_fun150026276t_bool(X1,X3) = pi_fun150026276t_bool(X2,X3) ) ).

cnf(i_0_5122,axiom,
    ( X1 != X2
    | pi_fun150026276t_bool(X3,X1) = pi_fun150026276t_bool(X3,X2) ) ).

cnf(i_0_5123,axiom,
    ( X1 != X2
    | hAPP_f1277514478l_bool(X1,X3) = hAPP_f1277514478l_bool(X2,X3) ) ).

cnf(i_0_5124,axiom,
    ( X1 != X2
    | hAPP_f1277514478l_bool(X3,X1) = hAPP_f1277514478l_bool(X3,X2) ) ).

cnf(i_0_5125,axiom,
    ( X1 != X2
    | hAPP_f1891021702t_bool(X1,X3) = hAPP_f1891021702t_bool(X2,X3) ) ).

cnf(i_0_5126,axiom,
    ( X1 != X2
    | hAPP_f1891021702t_bool(X3,X1) = hAPP_f1891021702t_bool(X3,X2) ) ).

cnf(i_0_5127,axiom,
    ( X1 != X2
    | hAPP_f965095724l_bool(X1,X3) = hAPP_f965095724l_bool(X2,X3) ) ).

cnf(i_0_5128,axiom,
    ( X1 != X2
    | hAPP_f965095724l_bool(X3,X1) = hAPP_f965095724l_bool(X3,X2) ) ).

cnf(i_0_5129,axiom,
    ( X1 != X2
    | hAPP_f839832464l_bool(X1,X3) = hAPP_f839832464l_bool(X2,X3) ) ).

cnf(i_0_5130,axiom,
    ( X1 != X2
    | hAPP_f839832464l_bool(X3,X1) = hAPP_f839832464l_bool(X3,X2) ) ).

cnf(i_0_5131,axiom,
    ( X1 != X2
    | hAPP_f1749234559l_bool(X1,X3) = hAPP_f1749234559l_bool(X2,X3) ) ).

cnf(i_0_5132,axiom,
    ( X1 != X2
    | hAPP_f1749234559l_bool(X3,X1) = hAPP_f1749234559l_bool(X3,X2) ) ).

cnf(i_0_5133,axiom,
    ( X1 != X2
    | hAPP_f1948454017i_bool(X1,X3) = hAPP_f1948454017i_bool(X2,X3) ) ).

cnf(i_0_5134,axiom,
    ( X1 != X2
    | hAPP_f1948454017i_bool(X3,X1) = hAPP_f1948454017i_bool(X3,X2) ) ).

cnf(i_0_5135,axiom,
    ( X1 != X2
    | hAPP_P1341894483t_bool(X1,X3) = hAPP_P1341894483t_bool(X2,X3) ) ).

cnf(i_0_5136,axiom,
    ( X1 != X2
    | hAPP_P1341894483t_bool(X3,X1) = hAPP_P1341894483t_bool(X3,X2) ) ).

cnf(i_0_5137,axiom,
    ( X1 != X2
    | hAPP_P1294997365l_bool(X1,X3) = hAPP_P1294997365l_bool(X2,X3) ) ).

cnf(i_0_5138,axiom,
    ( X1 != X2
    | hAPP_P1294997365l_bool(X3,X1) = hAPP_P1294997365l_bool(X3,X2) ) ).

cnf(i_0_5139,axiom,
    ( X1 != X2
    | hAPP_P1171466554l_bool(X1,X3) = hAPP_P1171466554l_bool(X2,X3) ) ).

cnf(i_0_5140,axiom,
    ( X1 != X2
    | hAPP_P1171466554l_bool(X3,X1) = hAPP_P1171466554l_bool(X3,X2) ) ).

cnf(i_0_5141,axiom,
    ( X1 != X2
    | hAPP_P254387896l_bool(X1,X3) = hAPP_P254387896l_bool(X2,X3) ) ).

cnf(i_0_5142,axiom,
    ( X1 != X2
    | hAPP_P254387896l_bool(X3,X1) = hAPP_P254387896l_bool(X3,X2) ) ).

cnf(i_0_5143,axiom,
    ( X1 != X2
    | hAPP_P32877782t_bool(X1,X3) = hAPP_P32877782t_bool(X2,X3) ) ).

cnf(i_0_5144,axiom,
    ( X1 != X2
    | hAPP_P32877782t_bool(X3,X1) = hAPP_P32877782t_bool(X3,X2) ) ).

cnf(i_0_5145,axiom,
    ( X1 != X2
    | hAPP_n1006566506l_bool(X1,X3) = hAPP_n1006566506l_bool(X2,X3) ) ).

cnf(i_0_5146,axiom,
    ( X1 != X2
    | hAPP_n1006566506l_bool(X3,X1) = hAPP_n1006566506l_bool(X3,X2) ) ).

cnf(i_0_5147,axiom,
    ( X1 != X2
    | hAPP_n1951273283e_indi(X1,X3) = hAPP_n1951273283e_indi(X2,X3) ) ).

cnf(i_0_5148,axiom,
    ( X1 != X2
    | hAPP_n1951273283e_indi(X3,X1) = hAPP_n1951273283e_indi(X3,X2) ) ).

cnf(i_0_5149,axiom,
    ( X1 != X2
    | hAPP_b1703662281t_bool(X1,X3) = hAPP_b1703662281t_bool(X2,X3) ) ).

cnf(i_0_5150,axiom,
    ( X1 != X2
    | hAPP_b1703662281t_bool(X3,X1) = hAPP_b1703662281t_bool(X3,X2) ) ).

cnf(i_0_5151,axiom,
    ( X1 != X2
    | hAPP_b1812770943l_bool(X1,X3) = hAPP_b1812770943l_bool(X2,X3) ) ).

cnf(i_0_5152,axiom,
    ( X1 != X2
    | hAPP_b1812770943l_bool(X3,X1) = hAPP_b1812770943l_bool(X3,X2) ) ).

cnf(i_0_5153,axiom,
    ( X1 != X2
    | hAPP_b517355696l_bool(X1,X3) = hAPP_b517355696l_bool(X2,X3) ) ).

cnf(i_0_5154,axiom,
    ( X1 != X2
    | hAPP_b517355696l_bool(X3,X1) = hAPP_b517355696l_bool(X3,X2) ) ).

cnf(i_0_5155,axiom,
    ( X1 != X2
    | hAPP_b1048178734l_bool(X1,X3) = hAPP_b1048178734l_bool(X2,X3) ) ).

cnf(i_0_5156,axiom,
    ( X1 != X2
    | hAPP_b1048178734l_bool(X3,X1) = hAPP_b1048178734l_bool(X3,X2) ) ).

cnf(i_0_5157,axiom,
    ( X1 != X2
    | pi_Arr990697634t_bool(X1,X3) = pi_Arr990697634t_bool(X2,X3) ) ).

cnf(i_0_5158,axiom,
    ( X1 != X2
    | pi_Arr990697634t_bool(X3,X1) = pi_Arr990697634t_bool(X3,X2) ) ).

cnf(i_0_5159,axiom,
    ( X1 != X2
    | hAPP_A60074736l_bool(X1,X3) = hAPP_A60074736l_bool(X2,X3) ) ).

cnf(i_0_5160,axiom,
    ( X1 != X2
    | hAPP_A60074736l_bool(X3,X1) = hAPP_A60074736l_bool(X3,X2) ) ).

cnf(i_0_5161,axiom,
    ( X1 != X2
    | hAPP_A1112981887l_bool(X1,X3) = hAPP_A1112981887l_bool(X2,X3) ) ).

cnf(i_0_5162,axiom,
    ( X1 != X2
    | hAPP_A1112981887l_bool(X3,X1) = hAPP_A1112981887l_bool(X3,X2) ) ).

cnf(i_0_5163,axiom,
    ( X1 != X2
    | hAPP_A1952883197l_bool(X1,X3) = hAPP_A1952883197l_bool(X2,X3) ) ).

cnf(i_0_5164,axiom,
    ( X1 != X2
    | hAPP_A1952883197l_bool(X3,X1) = hAPP_A1952883197l_bool(X3,X2) ) ).

cnf(i_0_5165,axiom,
    ( X1 != X2
    | hAPP_A2046586321t_bool(X1,X3) = hAPP_A2046586321t_bool(X2,X3) ) ).

cnf(i_0_5166,axiom,
    ( X1 != X2
    | hAPP_A2046586321t_bool(X3,X1) = hAPP_A2046586321t_bool(X3,X2) ) ).

cnf(i_0_5167,axiom,
    ( X1 != X2
    | hAPP_A1785763630i_bool(X1,X3) = hAPP_A1785763630i_bool(X2,X3) ) ).

cnf(i_0_5168,axiom,
    ( X1 != X2
    | hAPP_A1785763630i_bool(X3,X1) = hAPP_A1785763630i_bool(X3,X2) ) ).

cnf(i_0_5169,axiom,
    ( X1 != X2
    | esk24_2(X1,X3) = esk24_2(X2,X3) ) ).

cnf(i_0_5170,axiom,
    ( X1 != X2
    | esk24_2(X3,X1) = esk24_2(X3,X2) ) ).

cnf(i_0_5171,axiom,
    ( X1 != X2
    | esk25_2(X1,X3) = esk25_2(X2,X3) ) ).

cnf(i_0_5172,axiom,
    ( X1 != X2
    | esk25_2(X3,X1) = esk25_2(X3,X2) ) ).

cnf(i_0_5173,axiom,
    ( X1 != X2
    | hAPP_P1676879539t_bool(X1,X3) = hAPP_P1676879539t_bool(X2,X3) ) ).

cnf(i_0_5174,axiom,
    ( X1 != X2
    | hAPP_P1676879539t_bool(X3,X1) = hAPP_P1676879539t_bool(X3,X2) ) ).

cnf(i_0_5175,axiom,
    ( X1 != X2
    | hAPP_A1664620203t_bool(X1,X3) = hAPP_A1664620203t_bool(X2,X3) ) ).

cnf(i_0_5176,axiom,
    ( X1 != X2
    | hAPP_A1664620203t_bool(X3,X1) = hAPP_A1664620203t_bool(X3,X2) ) ).

cnf(i_0_5177,axiom,
    ( X1 != X2
    | hAPP_f515126293t_bool(X1,X3) = hAPP_f515126293t_bool(X2,X3) ) ).

cnf(i_0_5178,axiom,
    ( X1 != X2
    | hAPP_f515126293t_bool(X3,X1) = hAPP_f515126293t_bool(X3,X2) ) ).

cnf(i_0_5179,axiom,
    ( X1 != X2
    | hAPP_f111185985l_bool(X1,X3) = hAPP_f111185985l_bool(X2,X3) ) ).

cnf(i_0_5180,axiom,
    ( X1 != X2
    | hAPP_f111185985l_bool(X3,X1) = hAPP_f111185985l_bool(X3,X2) ) ).

cnf(i_0_5181,axiom,
    ( X1 != X2
    | hAPP_f1765205l_bool(X1,X3) = hAPP_f1765205l_bool(X2,X3) ) ).

cnf(i_0_5182,axiom,
    ( X1 != X2
    | hAPP_f1765205l_bool(X3,X1) = hAPP_f1765205l_bool(X3,X2) ) ).

cnf(i_0_5183,axiom,
    ( X1 != X2
    | hAPP_f146009813l_bool(X1,X3) = hAPP_f146009813l_bool(X2,X3) ) ).

cnf(i_0_5184,axiom,
    ( X1 != X2
    | hAPP_f146009813l_bool(X3,X1) = hAPP_f146009813l_bool(X3,X2) ) ).

cnf(i_0_5185,axiom,
    ( X1 != X2
    | hAPP_f250445784l_bool(X1,X3) = hAPP_f250445784l_bool(X2,X3) ) ).

cnf(i_0_5186,axiom,
    ( X1 != X2
    | hAPP_f250445784l_bool(X3,X1) = hAPP_f250445784l_bool(X3,X2) ) ).

cnf(i_0_5187,axiom,
    ( X1 != X2
    | hilber693666498di_nat(X1,X3) = hilber693666498di_nat(X2,X3) ) ).

cnf(i_0_5188,axiom,
    ( X1 != X2
    | hilber693666498di_nat(X3,X1) = hilber693666498di_nat(X3,X2) ) ).

cnf(i_0_5189,axiom,
    ( X1 != X2
    | hilber195283148at_nat(X1,X3) = hilber195283148at_nat(X2,X3) ) ).

cnf(i_0_5190,axiom,
    ( X1 != X2
    | hilber195283148at_nat(X3,X1) = hilber195283148at_nat(X3,X2) ) ).

cnf(i_0_5191,axiom,
    ( X1 != X2
    | esk72_2(X1,X3) = esk72_2(X2,X3) ) ).

cnf(i_0_5192,axiom,
    ( X1 != X2
    | esk72_2(X3,X1) = esk72_2(X3,X2) ) ).

cnf(i_0_5193,axiom,
    ( X1 != X2
    | esk73_2(X1,X3) = esk73_2(X2,X3) ) ).

cnf(i_0_5194,axiom,
    ( X1 != X2
    | esk73_2(X3,X1) = esk73_2(X3,X2) ) ).

cnf(i_0_5195,axiom,
    ( X1 != X2
    | esk40_2(X1,X3) = esk40_2(X2,X3) ) ).

cnf(i_0_5196,axiom,
    ( X1 != X2
    | esk40_2(X3,X1) = esk40_2(X3,X2) ) ).

cnf(i_0_5197,axiom,
    ( X1 != X2
    | esk39_2(X1,X3) = esk39_2(X2,X3) ) ).

cnf(i_0_5198,axiom,
    ( X1 != X2
    | esk39_2(X3,X1) = esk39_2(X3,X2) ) ).

cnf(i_0_5199,axiom,
    ( X1 != X2
    | esk38_2(X1,X3) = esk38_2(X2,X3) ) ).

cnf(i_0_5200,axiom,
    ( X1 != X2
    | esk38_2(X3,X1) = esk38_2(X3,X2) ) ).

cnf(i_0_5201,axiom,
    ( X1 != X2
    | esk37_2(X1,X3) = esk37_2(X2,X3) ) ).

cnf(i_0_5202,axiom,
    ( X1 != X2
    | esk37_2(X3,X1) = esk37_2(X3,X2) ) ).

cnf(i_0_5203,axiom,
    ( X1 != X2
    | hAPP_A1102281708t_bool(X1,X3) = hAPP_A1102281708t_bool(X2,X3) ) ).

cnf(i_0_5204,axiom,
    ( X1 != X2
    | hAPP_A1102281708t_bool(X3,X1) = hAPP_A1102281708t_bool(X3,X2) ) ).

cnf(i_0_5205,axiom,
    ( X1 != X2
    | hAPP_f427493225t_bool(X1,X3) = hAPP_f427493225t_bool(X2,X3) ) ).

cnf(i_0_5206,axiom,
    ( X1 != X2
    | hAPP_f427493225t_bool(X3,X1) = hAPP_f427493225t_bool(X3,X2) ) ).

cnf(i_0_5207,axiom,
    ( X1 != X2
    | hAPP_A1455239488t_bool(X1,X3) = hAPP_A1455239488t_bool(X2,X3) ) ).

cnf(i_0_5208,axiom,
    ( X1 != X2
    | hAPP_A1455239488t_bool(X3,X1) = hAPP_A1455239488t_bool(X3,X2) ) ).

cnf(i_0_5209,axiom,
    ( X1 != X2
    | hAPP_A1625428400t_bool(X1,X3) = hAPP_A1625428400t_bool(X2,X3) ) ).

cnf(i_0_5210,axiom,
    ( X1 != X2
    | hAPP_A1625428400t_bool(X3,X1) = hAPP_A1625428400t_bool(X3,X2) ) ).

cnf(i_0_5211,axiom,
    ( X1 != X2
    | hAPP_A621939144t_bool(X1,X3) = hAPP_A621939144t_bool(X2,X3) ) ).

cnf(i_0_5212,axiom,
    ( X1 != X2
    | hAPP_A621939144t_bool(X3,X1) = hAPP_A621939144t_bool(X3,X2) ) ).

cnf(i_0_5213,axiom,
    ( X1 != X2
    | hAPP_f1663053423t_bool(X1,X3) = hAPP_f1663053423t_bool(X2,X3) ) ).

cnf(i_0_5214,axiom,
    ( X1 != X2
    | hAPP_f1663053423t_bool(X3,X1) = hAPP_f1663053423t_bool(X3,X2) ) ).

cnf(i_0_5215,axiom,
    ( X1 != X2
    | hAPP_A572596845t_bool(X1,X3) = hAPP_A572596845t_bool(X2,X3) ) ).

cnf(i_0_5216,axiom,
    ( X1 != X2
    | hAPP_A572596845t_bool(X3,X1) = hAPP_A572596845t_bool(X3,X2) ) ).

cnf(i_0_5217,axiom,
    ( X1 != X2
    | hAPP_A862370221t_bool(X1,X3) = hAPP_A862370221t_bool(X2,X3) ) ).

cnf(i_0_5218,axiom,
    ( X1 != X2
    | hAPP_A862370221t_bool(X3,X1) = hAPP_A862370221t_bool(X3,X2) ) ).

cnf(i_0_5219,axiom,
    ( X1 != X2
    | hAPP_f653880381t_bool(X1,X3) = hAPP_f653880381t_bool(X2,X3) ) ).

cnf(i_0_5220,axiom,
    ( X1 != X2
    | hAPP_f653880381t_bool(X3,X1) = hAPP_f653880381t_bool(X3,X2) ) ).

cnf(i_0_5221,axiom,
    ( X1 != X2
    | hAPP_A187815023l_bool(X1,X3) = hAPP_A187815023l_bool(X2,X3) ) ).

cnf(i_0_5222,axiom,
    ( X1 != X2
    | hAPP_A187815023l_bool(X3,X1) = hAPP_A187815023l_bool(X3,X2) ) ).

cnf(i_0_5223,axiom,
    ( X1 != X2
    | hAPP_b1588041841t_bool(X1,X3) = hAPP_b1588041841t_bool(X2,X3) ) ).

cnf(i_0_5224,axiom,
    ( X1 != X2
    | hAPP_b1588041841t_bool(X3,X1) = hAPP_b1588041841t_bool(X3,X2) ) ).

cnf(i_0_5225,axiom,
    ( X1 != X2
    | hAPP_A1553574765l_bool(X1,X3) = hAPP_A1553574765l_bool(X2,X3) ) ).

cnf(i_0_5226,axiom,
    ( X1 != X2
    | hAPP_A1553574765l_bool(X3,X1) = hAPP_A1553574765l_bool(X3,X2) ) ).

cnf(i_0_5227,axiom,
    ( X1 != X2
    | hAPP_f1539445765l_bool(X1,X3) = hAPP_f1539445765l_bool(X2,X3) ) ).

cnf(i_0_5228,axiom,
    ( X1 != X2
    | hAPP_f1539445765l_bool(X3,X1) = hAPP_f1539445765l_bool(X3,X2) ) ).

cnf(i_0_5229,axiom,
    ( X1 != X2
    | esk76_1(X1) = esk76_1(X2) ) ).

cnf(i_0_5230,axiom,
    ( X1 != X2
    | esk77_1(X1) = esk77_1(X2) ) ).

cnf(i_0_5231,axiom,
    ( X1 != X2
    | esk74_1(X1) = esk74_1(X2) ) ).

cnf(i_0_5232,axiom,
    ( X1 != X2
    | esk75_1(X1) = esk75_1(X2) ) ).

cnf(i_0_5233,axiom,
    ( X1 != X2
    | hAPP_f427533077t_bool(X1,X3) = hAPP_f427533077t_bool(X2,X3) ) ).

cnf(i_0_5234,axiom,
    ( X1 != X2
    | hAPP_f427533077t_bool(X3,X1) = hAPP_f427533077t_bool(X3,X2) ) ).

cnf(i_0_5235,axiom,
    ( X1 != X2
    | hAPP_f580451669i_bool(X1,X3) = hAPP_f580451669i_bool(X2,X3) ) ).

cnf(i_0_5236,axiom,
    ( X1 != X2
    | hAPP_f580451669i_bool(X3,X1) = hAPP_f580451669i_bool(X3,X2) ) ).

cnf(i_0_5237,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_5238,axiom,
    ( X1 != X2
    | ~ is_fun288122577l_bool(X1)
    | is_fun288122577l_bool(X2) ) ).

cnf(i_0_5239,axiom,
    ( X1 != X2
    | ~ is_fun279392540l_bool(X1)
    | is_fun279392540l_bool(X2) ) ).

cnf(i_0_5240,axiom,
    ( X1 != X2
    | ~ is_fun1217980910e_indi(X1)
    | is_fun1217980910e_indi(X2) ) ).

cnf(i_0_5241,axiom,
    ( X1 != X2
    | ~ is_Arr1861959080le_alt(X1)
    | is_Arr1861959080le_alt(X2) ) ).

cnf(i_0_5242,axiom,
    ( X1 != X2
    | ~ is_Arr43961803e_indi(X1)
    | is_Arr43961803e_indi(X2) ) ).

cnf(i_0_5243,axiom,
    ( X1 != X2
    | ~ is_fun961089132t_bool(X1)
    | is_fun961089132t_bool(X2) ) ).

cnf(i_0_5244,axiom,
    ( X1 != X2
    | ~ is_fun158382675l_bool(X1)
    | is_fun158382675l_bool(X2) ) ).

cnf(i_0_5245,axiom,
    ( X1 != X2
    | ~ is_fun1568535512t_bool(X1)
    | is_fun1568535512t_bool(X2) ) ).

cnf(i_0_5246,axiom,
    ( X1 != X2
    | ~ is_fun2093718614t_bool(X1)
    | is_fun2093718614t_bool(X2) ) ).

cnf(i_0_5247,axiom,
    ( X1 != X2
    | ~ is_bool(X1)
    | is_bool(X2) ) ).

cnf(i_0_5248,axiom,
    ( X1 != X2
    | ~ is_fun1236654035i_bool(X1)
    | is_fun1236654035i_bool(X2) ) ).

cnf(i_0_5042_001,axiom,
    X1 = X1 ).

cnf(i_0_5043_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_5044_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_5045_004,axiom,
    ( X1 != X2
    | hAPP_f592646513l_bool(X1,X3) = hAPP_f592646513l_bool(X2,X3) ) ).

cnf(i_0_5046_005,axiom,
    ( X1 != X2
    | hAPP_f592646513l_bool(X3,X1) = hAPP_f592646513l_bool(X3,X2) ) ).

cnf(i_0_5047_006,axiom,
    ( X1 != X2
    | hAPP_n454528608t_bool(X1,X3) = hAPP_n454528608t_bool(X2,X3) ) ).

cnf(i_0_5048_007,axiom,
    ( X1 != X2
    | hAPP_n454528608t_bool(X3,X1) = hAPP_n454528608t_bool(X3,X2) ) ).

cnf(i_0_5049_008,axiom,
    ( X1 != X2
    | hAPP_n821919323i_bool(X1,X3) = hAPP_n821919323i_bool(X2,X3) ) ).

cnf(i_0_5050_009,axiom,
    ( X1 != X2
    | hAPP_n821919323i_bool(X3,X1) = hAPP_n821919323i_bool(X3,X2) ) ).

cnf(i_0_5051_010,axiom,
    ( X1 != X2
    | hAPP_f2026336507t_bool(X1,X3) = hAPP_f2026336507t_bool(X2,X3) ) ).

cnf(i_0_5052_011,axiom,
    ( X1 != X2
    | hAPP_f2026336507t_bool(X3,X1) = hAPP_f2026336507t_bool(X3,X2) ) ).

cnf(i_0_5053_012,axiom,
    ( X1 != X2
    | hAPP_nat_nat(X1,X3) = hAPP_nat_nat(X2,X3) ) ).

cnf(i_0_5054_013,axiom,
    ( X1 != X2
    | hAPP_nat_nat(X3,X1) = hAPP_nat_nat(X3,X2) ) ).

cnf(i_0_5055_014,axiom,
    ( X1 != X2
    | hAPP_b1013836512t_bool(X1,X3) = hAPP_b1013836512t_bool(X2,X3) ) ).

cnf(i_0_5056_015,axiom,
    ( X1 != X2
    | hAPP_b1013836512t_bool(X3,X1) = hAPP_b1013836512t_bool(X3,X2) ) ).

cnf(i_0_5057_016,axiom,
    ( X1 != X2
    | hAPP_bool_bool(X1,X3) = hAPP_bool_bool(X2,X3) ) ).

cnf(i_0_5058_017,axiom,
    ( X1 != X2
    | hAPP_bool_bool(X3,X1) = hAPP_bool_bool(X3,X2) ) ).

cnf(i_0_5059_018,axiom,
    ( X1 != X2
    | hAPP_b589554111l_bool(X1,X3) = hAPP_b589554111l_bool(X2,X3) ) ).

cnf(i_0_5060_019,axiom,
    ( X1 != X2
    | hAPP_b589554111l_bool(X3,X1) = hAPP_b589554111l_bool(X3,X2) ) ).

cnf(i_0_5061_020,axiom,
    ( X1 != X2
    | hAPP_f800510211t_bool(X1,X3) = hAPP_f800510211t_bool(X2,X3) ) ).

cnf(i_0_5062_021,axiom,
    ( X1 != X2
    | hAPP_f800510211t_bool(X3,X1) = hAPP_f800510211t_bool(X3,X2) ) ).

cnf(i_0_5063_022,axiom,
    ( X1 != X2
    | hAPP_P229966473l_bool(X1,X3) = hAPP_P229966473l_bool(X2,X3) ) ).

cnf(i_0_5064_023,axiom,
    ( X1 != X2
    | hAPP_P229966473l_bool(X3,X1) = hAPP_P229966473l_bool(X3,X2) ) ).

cnf(i_0_5065_024,axiom,
    ( X1 != X2
    | hAPP_f2030293770ol_nat(X1,X3) = hAPP_f2030293770ol_nat(X2,X3) ) ).

cnf(i_0_5066_025,axiom,
    ( X1 != X2
    | hAPP_f2030293770ol_nat(X3,X1) = hAPP_f2030293770ol_nat(X3,X2) ) ).

cnf(i_0_5067_026,axiom,
    ( X1 != X2
    | hAPP_f22106695ol_nat(X1,X3) = hAPP_f22106695ol_nat(X2,X3) ) ).

cnf(i_0_5068_027,axiom,
    ( X1 != X2
    | hAPP_f22106695ol_nat(X3,X1) = hAPP_f22106695ol_nat(X3,X2) ) ).

cnf(i_0_5069_028,axiom,
    ( X1 != X2
    | hAPP_bool_nat(X1,X3) = hAPP_bool_nat(X2,X3) ) ).

cnf(i_0_5070_029,axiom,
    ( X1 != X2
    | hAPP_bool_nat(X3,X1) = hAPP_bool_nat(X3,X2) ) ).

cnf(i_0_5071_030,axiom,
    ( X1 != X2
    | hAPP_A702847159le_alt(X1,X3) = hAPP_A702847159le_alt(X2,X3) ) ).

cnf(i_0_5072_031,axiom,
    ( X1 != X2
    | hAPP_A702847159le_alt(X3,X1) = hAPP_A702847159le_alt(X3,X2) ) ).

cnf(i_0_5073_032,axiom,
    ( X1 != X2
    | hAPP_A1677245848t_bool(X1,X3) = hAPP_A1677245848t_bool(X2,X3) ) ).

cnf(i_0_5074_033,axiom,
    ( X1 != X2
    | hAPP_A1677245848t_bool(X3,X1) = hAPP_A1677245848t_bool(X3,X2) ) ).

cnf(i_0_5075_034,axiom,
    ( X1 != X2
    | hAPP_f777333846l_bool(X1,X3) = hAPP_f777333846l_bool(X2,X3) ) ).

cnf(i_0_5076_035,axiom,
    ( X1 != X2
    | hAPP_f777333846l_bool(X3,X1) = hAPP_f777333846l_bool(X3,X2) ) ).

cnf(i_0_5077_036,axiom,
    ( X1 != X2
    | hAPP_f312250286l_bool(X1,X3) = hAPP_f312250286l_bool(X2,X3) ) ).

cnf(i_0_5078_037,axiom,
    ( X1 != X2
    | hAPP_f312250286l_bool(X3,X1) = hAPP_f312250286l_bool(X3,X2) ) ).

cnf(i_0_5079_038,axiom,
    ( X1 != X2
    | hAPP_nat_bool(X1,X3) = hAPP_nat_bool(X2,X3) ) ).

cnf(i_0_5080_039,axiom,
    ( X1 != X2
    | hAPP_nat_bool(X3,X1) = hAPP_nat_bool(X3,X2) ) ).

cnf(i_0_5081_040,axiom,
    ( X1 != X2
    | hAPP_n1699378549t_bool(X1,X3) = hAPP_n1699378549t_bool(X2,X3) ) ).

cnf(i_0_5082_041,axiom,
    ( X1 != X2
    | hAPP_n1699378549t_bool(X3,X1) = hAPP_n1699378549t_bool(X3,X2) ) ).

cnf(i_0_5083_042,axiom,
    ( X1 != X2
    | hAPP_f54304608l_bool(X1,X3) = hAPP_f54304608l_bool(X2,X3) ) ).

cnf(i_0_5084_043,axiom,
    ( X1 != X2
    | hAPP_f54304608l_bool(X3,X1) = hAPP_f54304608l_bool(X3,X2) ) ).

cnf(i_0_5085_044,axiom,
    ( X1 != X2
    | hAPP_n215258509l_bool(X1,X3) = hAPP_n215258509l_bool(X2,X3) ) ).

cnf(i_0_5086_045,axiom,
    ( X1 != X2
    | hAPP_n215258509l_bool(X3,X1) = hAPP_n215258509l_bool(X3,X2) ) ).

cnf(i_0_5087_046,axiom,
    ( X1 != X2
    | hAPP_A1637648121di_nat(X1,X3) = hAPP_A1637648121di_nat(X2,X3) ) ).

cnf(i_0_5088_047,axiom,
    ( X1 != X2
    | hAPP_A1637648121di_nat(X3,X1) = hAPP_A1637648121di_nat(X3,X2) ) ).

cnf(i_0_5089_048,axiom,
    ( X1 != X2
    | hAPP_A568203993t_bool(X1,X3) = hAPP_A568203993t_bool(X2,X3) ) ).

cnf(i_0_5090_049,axiom,
    ( X1 != X2
    | hAPP_A568203993t_bool(X3,X1) = hAPP_A568203993t_bool(X3,X2) ) ).

cnf(i_0_5091_050,axiom,
    ( X1 != X2
    | hAPP_f393984045t_bool(X1,X3) = hAPP_f393984045t_bool(X2,X3) ) ).

cnf(i_0_5092_051,axiom,
    ( X1 != X2
    | hAPP_f393984045t_bool(X3,X1) = hAPP_f393984045t_bool(X3,X2) ) ).

cnf(i_0_5093_052,axiom,
    ( X1 != X2
    | hAPP_A1941004017t_bool(X1,X3) = hAPP_A1941004017t_bool(X2,X3) ) ).

cnf(i_0_5094_053,axiom,
    ( X1 != X2
    | hAPP_A1941004017t_bool(X3,X1) = hAPP_A1941004017t_bool(X3,X2) ) ).

cnf(i_0_5095_054,axiom,
    ( X1 != X2
    | hAPP_f412050202t_bool(X1,X3) = hAPP_f412050202t_bool(X2,X3) ) ).

cnf(i_0_5096_055,axiom,
    ( X1 != X2
    | hAPP_f412050202t_bool(X3,X1) = hAPP_f412050202t_bool(X3,X2) ) ).

cnf(i_0_5097_056,axiom,
    ( X1 != X2
    | hAPP_f344580165t_bool(X1,X3) = hAPP_f344580165t_bool(X2,X3) ) ).

cnf(i_0_5098_057,axiom,
    ( X1 != X2
    | hAPP_f344580165t_bool(X3,X1) = hAPP_f344580165t_bool(X3,X2) ) ).

cnf(i_0_5099_058,axiom,
    ( X1 != X2
    | hAPP_P332578347t_bool(X1,X3) = hAPP_P332578347t_bool(X2,X3) ) ).

cnf(i_0_5100_059,axiom,
    ( X1 != X2
    | hAPP_P332578347t_bool(X3,X1) = hAPP_P332578347t_bool(X3,X2) ) ).

cnf(i_0_5101_060,axiom,
    ( X1 != X2
    | pi_Pro666468413t_bool(X1,X3) = pi_Pro666468413t_bool(X2,X3) ) ).

cnf(i_0_5102_061,axiom,
    ( X1 != X2
    | pi_Pro666468413t_bool(X3,X1) = pi_Pro666468413t_bool(X3,X2) ) ).

cnf(i_0_5103_062,axiom,
    ( X1 != X2
    | hAPP_P606313927t_bool(X1,X3) = hAPP_P606313927t_bool(X2,X3) ) ).

cnf(i_0_5104_063,axiom,
    ( X1 != X2
    | hAPP_P606313927t_bool(X3,X1) = hAPP_P606313927t_bool(X3,X2) ) ).

cnf(i_0_5105_064,axiom,
    ( X1 != X2
    | hAPP_P324742453l_bool(X1,X3) = hAPP_P324742453l_bool(X2,X3) ) ).

cnf(i_0_5106_065,axiom,
    ( X1 != X2
    | hAPP_P324742453l_bool(X3,X1) = hAPP_P324742453l_bool(X3,X2) ) ).

cnf(i_0_5107_066,axiom,
    ( X1 != X2
    | hAPP_P1875867302i_bool(X1,X3) = hAPP_P1875867302i_bool(X2,X3) ) ).

cnf(i_0_5108_067,axiom,
    ( X1 != X2
    | hAPP_P1875867302i_bool(X3,X1) = hAPP_P1875867302i_bool(X3,X2) ) ).

cnf(i_0_5109_068,axiom,
    ( X1 != X2
    | hAPP_f1710744577t_bool(X1,X3) = hAPP_f1710744577t_bool(X2,X3) ) ).

cnf(i_0_5110_069,axiom,
    ( X1 != X2
    | hAPP_f1710744577t_bool(X3,X1) = hAPP_f1710744577t_bool(X3,X2) ) ).

cnf(i_0_5111_070,axiom,
    ( X1 != X2
    | hAPP_f210572555l_bool(X1,X3) = hAPP_f210572555l_bool(X2,X3) ) ).

cnf(i_0_5112_071,axiom,
    ( X1 != X2
    | hAPP_f210572555l_bool(X3,X1) = hAPP_f210572555l_bool(X3,X2) ) ).

cnf(i_0_5113_072,axiom,
    ( X1 != X2
    | hAPP_f244157820i_bool(X1,X3) = hAPP_f244157820i_bool(X2,X3) ) ).

cnf(i_0_5114_073,axiom,
    ( X1 != X2
    | hAPP_f244157820i_bool(X3,X1) = hAPP_f244157820i_bool(X3,X2) ) ).

cnf(i_0_5115_074,axiom,
    ( X1 != X2
    | hAPP_f1866147972t_bool(X1,X3) = hAPP_f1866147972t_bool(X2,X3) ) ).

cnf(i_0_5116_075,axiom,
    ( X1 != X2
    | hAPP_f1866147972t_bool(X3,X1) = hAPP_f1866147972t_bool(X3,X2) ) ).

cnf(i_0_5117_076,axiom,
    ( X1 != X2
    | hAPP_f1624277646l_bool(X1,X3) = hAPP_f1624277646l_bool(X2,X3) ) ).

cnf(i_0_5118_077,axiom,
    ( X1 != X2
    | hAPP_f1624277646l_bool(X3,X1) = hAPP_f1624277646l_bool(X3,X2) ) ).

cnf(i_0_5119_078,axiom,
    ( X1 != X2
    | hAPP_f1552576127i_bool(X1,X3) = hAPP_f1552576127i_bool(X2,X3) ) ).

cnf(i_0_5120_079,axiom,
    ( X1 != X2
    | hAPP_f1552576127i_bool(X3,X1) = hAPP_f1552576127i_bool(X3,X2) ) ).

cnf(i_0_5121_080,axiom,
    ( X1 != X2
    | pi_fun150026276t_bool(X1,X3) = pi_fun150026276t_bool(X2,X3) ) ).

cnf(i_0_5122_081,axiom,
    ( X1 != X2
    | pi_fun150026276t_bool(X3,X1) = pi_fun150026276t_bool(X3,X2) ) ).

cnf(i_0_5123_082,axiom,
    ( X1 != X2
    | hAPP_f1277514478l_bool(X1,X3) = hAPP_f1277514478l_bool(X2,X3) ) ).

cnf(i_0_5124_083,axiom,
    ( X1 != X2
    | hAPP_f1277514478l_bool(X3,X1) = hAPP_f1277514478l_bool(X3,X2) ) ).

cnf(i_0_5125_084,axiom,
    ( X1 != X2
    | hAPP_f1891021702t_bool(X1,X3) = hAPP_f1891021702t_bool(X2,X3) ) ).

cnf(i_0_5126_085,axiom,
    ( X1 != X2
    | hAPP_f1891021702t_bool(X3,X1) = hAPP_f1891021702t_bool(X3,X2) ) ).

cnf(i_0_5127_086,axiom,
    ( X1 != X2
    | hAPP_f965095724l_bool(X1,X3) = hAPP_f965095724l_bool(X2,X3) ) ).

cnf(i_0_5128_087,axiom,
    ( X1 != X2
    | hAPP_f965095724l_bool(X3,X1) = hAPP_f965095724l_bool(X3,X2) ) ).

cnf(i_0_5129_088,axiom,
    ( X1 != X2
    | hAPP_f839832464l_bool(X1,X3) = hAPP_f839832464l_bool(X2,X3) ) ).

cnf(i_0_5130_089,axiom,
    ( X1 != X2
    | hAPP_f839832464l_bool(X3,X1) = hAPP_f839832464l_bool(X3,X2) ) ).

cnf(i_0_5131_090,axiom,
    ( X1 != X2
    | hAPP_f1749234559l_bool(X1,X3) = hAPP_f1749234559l_bool(X2,X3) ) ).

cnf(i_0_5132_091,axiom,
    ( X1 != X2
    | hAPP_f1749234559l_bool(X3,X1) = hAPP_f1749234559l_bool(X3,X2) ) ).

cnf(i_0_5133_092,axiom,
    ( X1 != X2
    | hAPP_f1948454017i_bool(X1,X3) = hAPP_f1948454017i_bool(X2,X3) ) ).

cnf(i_0_5134_093,axiom,
    ( X1 != X2
    | hAPP_f1948454017i_bool(X3,X1) = hAPP_f1948454017i_bool(X3,X2) ) ).

cnf(i_0_5135_094,axiom,
    ( X1 != X2
    | hAPP_P1341894483t_bool(X1,X3) = hAPP_P1341894483t_bool(X2,X3) ) ).

cnf(i_0_5136_095,axiom,
    ( X1 != X2
    | hAPP_P1341894483t_bool(X3,X1) = hAPP_P1341894483t_bool(X3,X2) ) ).

cnf(i_0_5137_096,axiom,
    ( X1 != X2
    | hAPP_P1294997365l_bool(X1,X3) = hAPP_P1294997365l_bool(X2,X3) ) ).

cnf(i_0_5138_097,axiom,
    ( X1 != X2
    | hAPP_P1294997365l_bool(X3,X1) = hAPP_P1294997365l_bool(X3,X2) ) ).

cnf(i_0_5139_098,axiom,
    ( X1 != X2
    | hAPP_P1171466554l_bool(X1,X3) = hAPP_P1171466554l_bool(X2,X3) ) ).

cnf(i_0_5140_099,axiom,
    ( X1 != X2
    | hAPP_P1171466554l_bool(X3,X1) = hAPP_P1171466554l_bool(X3,X2) ) ).

cnf(i_0_5141_100,axiom,
    ( X1 != X2
    | hAPP_P254387896l_bool(X1,X3) = hAPP_P254387896l_bool(X2,X3) ) ).

cnf(i_0_5142_101,axiom,
    ( X1 != X2
    | hAPP_P254387896l_bool(X3,X1) = hAPP_P254387896l_bool(X3,X2) ) ).

cnf(i_0_5143_102,axiom,
    ( X1 != X2
    | hAPP_P32877782t_bool(X1,X3) = hAPP_P32877782t_bool(X2,X3) ) ).

cnf(i_0_5144_103,axiom,
    ( X1 != X2
    | hAPP_P32877782t_bool(X3,X1) = hAPP_P32877782t_bool(X3,X2) ) ).

cnf(i_0_5145_104,axiom,
    ( X1 != X2
    | hAPP_n1006566506l_bool(X1,X3) = hAPP_n1006566506l_bool(X2,X3) ) ).

cnf(i_0_5146_105,axiom,
    ( X1 != X2
    | hAPP_n1006566506l_bool(X3,X1) = hAPP_n1006566506l_bool(X3,X2) ) ).

cnf(i_0_5147_106,axiom,
    ( X1 != X2
    | hAPP_n1951273283e_indi(X1,X3) = hAPP_n1951273283e_indi(X2,X3) ) ).

cnf(i_0_5148_107,axiom,
    ( X1 != X2
    | hAPP_n1951273283e_indi(X3,X1) = hAPP_n1951273283e_indi(X3,X2) ) ).

cnf(i_0_5149_108,axiom,
    ( X1 != X2
    | hAPP_b1703662281t_bool(X1,X3) = hAPP_b1703662281t_bool(X2,X3) ) ).

cnf(i_0_5150_109,axiom,
    ( X1 != X2
    | hAPP_b1703662281t_bool(X3,X1) = hAPP_b1703662281t_bool(X3,X2) ) ).

cnf(i_0_5151_110,axiom,
    ( X1 != X2
    | hAPP_b1812770943l_bool(X1,X3) = hAPP_b1812770943l_bool(X2,X3) ) ).

cnf(i_0_5152_111,axiom,
    ( X1 != X2
    | hAPP_b1812770943l_bool(X3,X1) = hAPP_b1812770943l_bool(X3,X2) ) ).

cnf(i_0_5153_112,axiom,
    ( X1 != X2
    | hAPP_b517355696l_bool(X1,X3) = hAPP_b517355696l_bool(X2,X3) ) ).

cnf(i_0_5154_113,axiom,
    ( X1 != X2
    | hAPP_b517355696l_bool(X3,X1) = hAPP_b517355696l_bool(X3,X2) ) ).

cnf(i_0_5155_114,axiom,
    ( X1 != X2
    | hAPP_b1048178734l_bool(X1,X3) = hAPP_b1048178734l_bool(X2,X3) ) ).

cnf(i_0_5156_115,axiom,
    ( X1 != X2
    | hAPP_b1048178734l_bool(X3,X1) = hAPP_b1048178734l_bool(X3,X2) ) ).

cnf(i_0_5157_116,axiom,
    ( X1 != X2
    | pi_Arr990697634t_bool(X1,X3) = pi_Arr990697634t_bool(X2,X3) ) ).

cnf(i_0_5158_117,axiom,
    ( X1 != X2
    | pi_Arr990697634t_bool(X3,X1) = pi_Arr990697634t_bool(X3,X2) ) ).

cnf(i_0_5159_118,axiom,
    ( X1 != X2
    | hAPP_A60074736l_bool(X1,X3) = hAPP_A60074736l_bool(X2,X3) ) ).

cnf(i_0_5160_119,axiom,
    ( X1 != X2
    | hAPP_A60074736l_bool(X3,X1) = hAPP_A60074736l_bool(X3,X2) ) ).

cnf(i_0_5161_120,axiom,
    ( X1 != X2
    | hAPP_A1112981887l_bool(X1,X3) = hAPP_A1112981887l_bool(X2,X3) ) ).

cnf(i_0_5162_121,axiom,
    ( X1 != X2
    | hAPP_A1112981887l_bool(X3,X1) = hAPP_A1112981887l_bool(X3,X2) ) ).

cnf(i_0_5163_122,axiom,
    ( X1 != X2
    | hAPP_A1952883197l_bool(X1,X3) = hAPP_A1952883197l_bool(X2,X3) ) ).

cnf(i_0_5164_123,axiom,
    ( X1 != X2
    | hAPP_A1952883197l_bool(X3,X1) = hAPP_A1952883197l_bool(X3,X2) ) ).

cnf(i_0_5165_124,axiom,
    ( X1 != X2
    | hAPP_A2046586321t_bool(X1,X3) = hAPP_A2046586321t_bool(X2,X3) ) ).

cnf(i_0_5166_125,axiom,
    ( X1 != X2
    | hAPP_A2046586321t_bool(X3,X1) = hAPP_A2046586321t_bool(X3,X2) ) ).

cnf(i_0_5167_126,axiom,
    ( X1 != X2
    | hAPP_A1785763630i_bool(X1,X3) = hAPP_A1785763630i_bool(X2,X3) ) ).

cnf(i_0_5168_127,axiom,
    ( X1 != X2
    | hAPP_A1785763630i_bool(X3,X1) = hAPP_A1785763630i_bool(X3,X2) ) ).

cnf(i_0_5169_128,axiom,
    ( X1 != X2
    | esk24_2(X1,X3) = esk24_2(X2,X3) ) ).

cnf(i_0_5170_129,axiom,
    ( X1 != X2
    | esk24_2(X3,X1) = esk24_2(X3,X2) ) ).

cnf(i_0_5171_130,axiom,
    ( X1 != X2
    | esk25_2(X1,X3) = esk25_2(X2,X3) ) ).

cnf(i_0_5172_131,axiom,
    ( X1 != X2
    | esk25_2(X3,X1) = esk25_2(X3,X2) ) ).

cnf(i_0_5173_132,axiom,
    ( X1 != X2
    | hAPP_P1676879539t_bool(X1,X3) = hAPP_P1676879539t_bool(X2,X3) ) ).

cnf(i_0_5174_133,axiom,
    ( X1 != X2
    | hAPP_P1676879539t_bool(X3,X1) = hAPP_P1676879539t_bool(X3,X2) ) ).

cnf(i_0_5175_134,axiom,
    ( X1 != X2
    | hAPP_A1664620203t_bool(X1,X3) = hAPP_A1664620203t_bool(X2,X3) ) ).

cnf(i_0_5176_135,axiom,
    ( X1 != X2
    | hAPP_A1664620203t_bool(X3,X1) = hAPP_A1664620203t_bool(X3,X2) ) ).

cnf(i_0_5177_136,axiom,
    ( X1 != X2
    | hAPP_f515126293t_bool(X1,X3) = hAPP_f515126293t_bool(X2,X3) ) ).

cnf(i_0_5178_137,axiom,
    ( X1 != X2
    | hAPP_f515126293t_bool(X3,X1) = hAPP_f515126293t_bool(X3,X2) ) ).

cnf(i_0_5179_138,axiom,
    ( X1 != X2
    | hAPP_f111185985l_bool(X1,X3) = hAPP_f111185985l_bool(X2,X3) ) ).

cnf(i_0_5180_139,axiom,
    ( X1 != X2
    | hAPP_f111185985l_bool(X3,X1) = hAPP_f111185985l_bool(X3,X2) ) ).

cnf(i_0_5181_140,axiom,
    ( X1 != X2
    | hAPP_f1765205l_bool(X1,X3) = hAPP_f1765205l_bool(X2,X3) ) ).

cnf(i_0_5182_141,axiom,
    ( X1 != X2
    | hAPP_f1765205l_bool(X3,X1) = hAPP_f1765205l_bool(X3,X2) ) ).

cnf(i_0_5183_142,axiom,
    ( X1 != X2
    | hAPP_f146009813l_bool(X1,X3) = hAPP_f146009813l_bool(X2,X3) ) ).

cnf(i_0_5184_143,axiom,
    ( X1 != X2
    | hAPP_f146009813l_bool(X3,X1) = hAPP_f146009813l_bool(X3,X2) ) ).

cnf(i_0_5185_144,axiom,
    ( X1 != X2
    | hAPP_f250445784l_bool(X1,X3) = hAPP_f250445784l_bool(X2,X3) ) ).

cnf(i_0_5186_145,axiom,
    ( X1 != X2
    | hAPP_f250445784l_bool(X3,X1) = hAPP_f250445784l_bool(X3,X2) ) ).

cnf(i_0_5187_146,axiom,
    ( X1 != X2
    | hilber693666498di_nat(X1,X3) = hilber693666498di_nat(X2,X3) ) ).

cnf(i_0_5188_147,axiom,
    ( X1 != X2
    | hilber693666498di_nat(X3,X1) = hilber693666498di_nat(X3,X2) ) ).

cnf(i_0_5189_148,axiom,
    ( X1 != X2
    | hilber195283148at_nat(X1,X3) = hilber195283148at_nat(X2,X3) ) ).

cnf(i_0_5190_149,axiom,
    ( X1 != X2
    | hilber195283148at_nat(X3,X1) = hilber195283148at_nat(X3,X2) ) ).

cnf(i_0_5191_150,axiom,
    ( X1 != X2
    | esk72_2(X1,X3) = esk72_2(X2,X3) ) ).

cnf(i_0_5192_151,axiom,
    ( X1 != X2
    | esk72_2(X3,X1) = esk72_2(X3,X2) ) ).

cnf(i_0_5193_152,axiom,
    ( X1 != X2
    | esk73_2(X1,X3) = esk73_2(X2,X3) ) ).

cnf(i_0_5194_153,axiom,
    ( X1 != X2
    | esk73_2(X3,X1) = esk73_2(X3,X2) ) ).

cnf(i_0_5195_154,axiom,
    ( X1 != X2
    | esk40_2(X1,X3) = esk40_2(X2,X3) ) ).

cnf(i_0_5196_155,axiom,
    ( X1 != X2
    | esk40_2(X3,X1) = esk40_2(X3,X2) ) ).

cnf(i_0_5197_156,axiom,
    ( X1 != X2
    | esk39_2(X1,X3) = esk39_2(X2,X3) ) ).

cnf(i_0_5198_157,axiom,
    ( X1 != X2
    | esk39_2(X3,X1) = esk39_2(X3,X2) ) ).

cnf(i_0_5199_158,axiom,
    ( X1 != X2
    | esk38_2(X1,X3) = esk38_2(X2,X3) ) ).

cnf(i_0_5200_159,axiom,
    ( X1 != X2
    | esk38_2(X3,X1) = esk38_2(X3,X2) ) ).

cnf(i_0_5201_160,axiom,
    ( X1 != X2
    | esk37_2(X1,X3) = esk37_2(X2,X3) ) ).

cnf(i_0_5202_161,axiom,
    ( X1 != X2
    | esk37_2(X3,X1) = esk37_2(X3,X2) ) ).

cnf(i_0_5203_162,axiom,
    ( X1 != X2
    | hAPP_A1102281708t_bool(X1,X3) = hAPP_A1102281708t_bool(X2,X3) ) ).

cnf(i_0_5204_163,axiom,
    ( X1 != X2
    | hAPP_A1102281708t_bool(X3,X1) = hAPP_A1102281708t_bool(X3,X2) ) ).

cnf(i_0_5205_164,axiom,
    ( X1 != X2
    | hAPP_f427493225t_bool(X1,X3) = hAPP_f427493225t_bool(X2,X3) ) ).

cnf(i_0_5206_165,axiom,
    ( X1 != X2
    | hAPP_f427493225t_bool(X3,X1) = hAPP_f427493225t_bool(X3,X2) ) ).

cnf(i_0_5207_166,axiom,
    ( X1 != X2
    | hAPP_A1455239488t_bool(X1,X3) = hAPP_A1455239488t_bool(X2,X3) ) ).

cnf(i_0_5208_167,axiom,
    ( X1 != X2
    | hAPP_A1455239488t_bool(X3,X1) = hAPP_A1455239488t_bool(X3,X2) ) ).

cnf(i_0_5209_168,axiom,
    ( X1 != X2
    | hAPP_A1625428400t_bool(X1,X3) = hAPP_A1625428400t_bool(X2,X3) ) ).

cnf(i_0_5210_169,axiom,
    ( X1 != X2
    | hAPP_A1625428400t_bool(X3,X1) = hAPP_A1625428400t_bool(X3,X2) ) ).

cnf(i_0_5211_170,axiom,
    ( X1 != X2
    | hAPP_A621939144t_bool(X1,X3) = hAPP_A621939144t_bool(X2,X3) ) ).

cnf(i_0_5212_171,axiom,
    ( X1 != X2
    | hAPP_A621939144t_bool(X3,X1) = hAPP_A621939144t_bool(X3,X2) ) ).

cnf(i_0_5213_172,axiom,
    ( X1 != X2
    | hAPP_f1663053423t_bool(X1,X3) = hAPP_f1663053423t_bool(X2,X3) ) ).

cnf(i_0_5214_173,axiom,
    ( X1 != X2
    | hAPP_f1663053423t_bool(X3,X1) = hAPP_f1663053423t_bool(X3,X2) ) ).

cnf(i_0_5215_174,axiom,
    ( X1 != X2
    | hAPP_A572596845t_bool(X1,X3) = hAPP_A572596845t_bool(X2,X3) ) ).

cnf(i_0_5216_175,axiom,
    ( X1 != X2
    | hAPP_A572596845t_bool(X3,X1) = hAPP_A572596845t_bool(X3,X2) ) ).

cnf(i_0_5217_176,axiom,
    ( X1 != X2
    | hAPP_A862370221t_bool(X1,X3) = hAPP_A862370221t_bool(X2,X3) ) ).

cnf(i_0_5218_177,axiom,
    ( X1 != X2
    | hAPP_A862370221t_bool(X3,X1) = hAPP_A862370221t_bool(X3,X2) ) ).

cnf(i_0_5219_178,axiom,
    ( X1 != X2
    | hAPP_f653880381t_bool(X1,X3) = hAPP_f653880381t_bool(X2,X3) ) ).

cnf(i_0_5220_179,axiom,
    ( X1 != X2
    | hAPP_f653880381t_bool(X3,X1) = hAPP_f653880381t_bool(X3,X2) ) ).

cnf(i_0_5221_180,axiom,
    ( X1 != X2
    | hAPP_A187815023l_bool(X1,X3) = hAPP_A187815023l_bool(X2,X3) ) ).

cnf(i_0_5222_181,axiom,
    ( X1 != X2
    | hAPP_A187815023l_bool(X3,X1) = hAPP_A187815023l_bool(X3,X2) ) ).

cnf(i_0_5223_182,axiom,
    ( X1 != X2
    | hAPP_b1588041841t_bool(X1,X3) = hAPP_b1588041841t_bool(X2,X3) ) ).

cnf(i_0_5224_183,axiom,
    ( X1 != X2
    | hAPP_b1588041841t_bool(X3,X1) = hAPP_b1588041841t_bool(X3,X2) ) ).

cnf(i_0_5225_184,axiom,
    ( X1 != X2
    | hAPP_A1553574765l_bool(X1,X3) = hAPP_A1553574765l_bool(X2,X3) ) ).

cnf(i_0_5226_185,axiom,
    ( X1 != X2
    | hAPP_A1553574765l_bool(X3,X1) = hAPP_A1553574765l_bool(X3,X2) ) ).

cnf(i_0_5227_186,axiom,
    ( X1 != X2
    | hAPP_f1539445765l_bool(X1,X3) = hAPP_f1539445765l_bool(X2,X3) ) ).

cnf(i_0_5228_187,axiom,
    ( X1 != X2
    | hAPP_f1539445765l_bool(X3,X1) = hAPP_f1539445765l_bool(X3,X2) ) ).

cnf(i_0_5229_188,axiom,
    ( X1 != X2
    | esk76_1(X1) = esk76_1(X2) ) ).

cnf(i_0_5230_189,axiom,
    ( X1 != X2
    | esk77_1(X1) = esk77_1(X2) ) ).

cnf(i_0_5231_190,axiom,
    ( X1 != X2
    | esk74_1(X1) = esk74_1(X2) ) ).

cnf(i_0_5232_191,axiom,
    ( X1 != X2
    | esk75_1(X1) = esk75_1(X2) ) ).

cnf(i_0_5233_192,axiom,
    ( X1 != X2
    | hAPP_f427533077t_bool(X1,X3) = hAPP_f427533077t_bool(X2,X3) ) ).

cnf(i_0_5234_193,axiom,
    ( X1 != X2
    | hAPP_f427533077t_bool(X3,X1) = hAPP_f427533077t_bool(X3,X2) ) ).

cnf(i_0_5235_194,axiom,
    ( X1 != X2
    | hAPP_f580451669i_bool(X1,X3) = hAPP_f580451669i_bool(X2,X3) ) ).

cnf(i_0_5236_195,axiom,
    ( X1 != X2
    | hAPP_f580451669i_bool(X3,X1) = hAPP_f580451669i_bool(X3,X2) ) ).

cnf(i_0_5237_196,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_5238_197,axiom,
    ( X1 != X2
    | ~ is_fun288122577l_bool(X1)
    | is_fun288122577l_bool(X2) ) ).

cnf(i_0_5239_198,axiom,
    ( X1 != X2
    | ~ is_fun279392540l_bool(X1)
    | is_fun279392540l_bool(X2) ) ).

cnf(i_0_5240_199,axiom,
    ( X1 != X2
    | ~ is_fun1217980910e_indi(X1)
    | is_fun1217980910e_indi(X2) ) ).

cnf(i_0_5241_200,axiom,
    ( X1 != X2
    | ~ is_Arr1861959080le_alt(X1)
    | is_Arr1861959080le_alt(X2) ) ).

cnf(i_0_5242_201,axiom,
    ( X1 != X2
    | ~ is_Arr43961803e_indi(X1)
    | is_Arr43961803e_indi(X2) ) ).

cnf(i_0_5243_202,axiom,
    ( X1 != X2
    | ~ is_fun961089132t_bool(X1)
    | is_fun961089132t_bool(X2) ) ).

cnf(i_0_5244_203,axiom,
    ( X1 != X2
    | ~ is_fun158382675l_bool(X1)
    | is_fun158382675l_bool(X2) ) ).

cnf(i_0_5245_204,axiom,
    ( X1 != X2
    | ~ is_fun1568535512t_bool(X1)
    | is_fun1568535512t_bool(X2) ) ).

cnf(i_0_5246_205,axiom,
    ( X1 != X2
    | ~ is_fun2093718614t_bool(X1)
    | is_fun2093718614t_bool(X2) ) ).

cnf(i_0_5247_206,axiom,
    ( X1 != X2
    | ~ is_bool(X1)
    | is_bool(X2) ) ).

cnf(i_0_5248_207,axiom,
    ( X1 != X2
    | ~ is_fun1236654035i_bool(X1)
    | is_fun1236654035i_bool(X2) ) ).

cnf(i_0_5249,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X3 = X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X4))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X1),X2))) ),
    inference(equality_inference,[],[3299]) ).

cnf(i_0_5250,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X1 = X3
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),X4))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X1),X2))) ),
    inference(equality_inference,[],[3300]) ).

cnf(i_0_5251,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X1 = X3
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),arrow_1539419881_below(X4,X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X3)),X4)) ),
    inference(equality_inference,[],[3309]) ).

cnf(i_0_5252,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X3 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),arrow_1539419881_below(X4,X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),X4)) ),
    inference(equality_inference,[],[3310]) ).

cnf(i_0_5253,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X3 = X1
    | X3 = X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X1),X2))) ),
    inference(equality_inference,[],[3327]) ).

cnf(i_0_5254,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | X3 = X1
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),X4))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X3),X1))) ),
    inference(equality_inference,[],[3329]) ).

cnf(i_0_5255,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X3 = X2
    | X3 = X2
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),X4))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X1),X2))) ),
    inference(equality_inference,[],[3338]) ).

cnf(i_0_5256,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X1 = X2
    | X1 = X3
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),X4))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X1),X2))) ),
    inference(equality_inference,[],[3339]) ).

cnf(i_0_5257,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X2 = X3
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),X4))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X3)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X1),X2))) ),
    inference(equality_inference,[],[3341]) ).

cnf(i_0_5258,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X3 = X2
    | X3 = X1
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),arrow_1539419881_below(X4,X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X3)),X4)) ),
    inference(equality_inference,[],[3342]) ).

cnf(i_0_5259,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3)
    | X2 = X3
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),arrow_1539419881_below(X4,X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),X4)) ),
    inference(equality_inference,[],[3344]) ).

cnf(i_0_5260,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X3 = X1
    | X1 = X3
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X3)),arrow_1539419881_below(X4,X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X2),X3)),X4)) ),
    inference(equality_inference,[],[3352]) ).

cnf(i_0_5261,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X2 = X1
    | X3 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),arrow_1539419881_below(X4,X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),X4)) ),
    inference(equality_inference,[],[3353]) ).

cnf(i_0_5262,plain,
    ( X1 = X2
    | ~ is_Arr1861959080le_alt(X3)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X3 = X1
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X1)),arrow_1539419881_below(X4,X1,X2)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X3),X2)),X4)) ),
    inference(equality_inference,[],[3355]) ).

cnf(i_0_5263,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3)
    | X2 = X3
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X1)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,X4),X2),X3))) ),
    inference(equality_inference,[],[3359]) ).

cnf(i_0_5264,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X3)
    | X2 = X3
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X1)),arrow_1539419881_below(X4,X2,X3)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X4),arrow_1681063817le_Lin)) ),
    inference(equality_inference,[],[3450]) ).

cnf(i_0_5265,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X3),X1))) ),
    inference(equality_inference,[],[3567]) ).

cnf(i_0_5266,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X3),X2))) ),
    inference(equality_inference,[],[3568]) ).

cnf(i_0_5267,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | X1 = X2
    | X2 = X1
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,X3),X1))) ),
    inference(equality_inference,[],[3751]) ).

cnf(i_0_5268,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X2)
    | X1 = X2
    | X1 = X2
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X1),X2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,X3),X2))) ),
    inference(equality_inference,[],[3752]) ).

cnf(i_0_5269,plain,
    ( ~ is_Arr43961803e_indi(X1)
    | ~ is_Arr43961803e_indi(X1)
    | X1 = X1
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X2),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),X3))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),X3)) ),
    inference(equality_inference,[],[3805]) ).

cnf(i_0_5270,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X2),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
    inference(equality_inference,[],[3814]) ).

cnf(i_0_5271,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
    inference(equality_inference,[],[4021]) ).

cnf(i_0_5272,plain,
    ( ~ is_Arr43961803e_indi(X1)
    | hAPP_n1951273283e_indi(hilber693666498di_nat(X2,X3),hAPP_A1637648121di_nat(X3,X1)) = X1
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X3),X2))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X1),X2)) ),
    inference(equality_inference,[],[4025]) ).

cnf(i_0_5273,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(X1,X2),hAPP_nat_nat(X2,X3)) = X3
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X2),X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1)) ),
    inference(equality_inference,[],[4067]) ).

cnf(i_0_5274,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))),
    inference(equality_inference,[],[4267]) ).

cnf(i_0_5275,plain,
    X1 = X1,
    inference(equality_inference,[],[4269]) ).

cnf(i_0_5276,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
    inference(equality_inference,[],[4372]) ).

cnf(i_0_5277,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X1 = X1 ),
    inference(equality_inference,[],[4407]) ).

cnf(i_0_5278,plain,
    ( ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | ~ is_Arr1861959080le_alt(X1)
    | ~ is_Arr1861959080le_alt(X2)
    | X2 = X2 ),
    inference(equality_inference,[],[4409]) ).

cnf(i_0_5279,plain,
    ( ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X1)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X1),X1)) ),
    inference(equality_inference,[],[4421]) ).

cnf(i_0_5280,plain,
    ( ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X1)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X1),X1)) ),
    inference(equality_inference,[],[4425]) ).

cnf(i_0_5281,plain,
    ( ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X1)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X1),X1)) ),
    inference(equality_inference,[],[4427]) ).

cnf(i_0_5282,plain,
    ( ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X1)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X1),X1)) ),
    inference(equality_inference,[],[4429]) ).

cnf(i_0_5283,plain,
    ( ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X1)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X1),X1)) ),
    inference(equality_inference,[],[4431]) ).

cnf(i_0_5284,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),
    inference(equality_inference,[],[4432]) ).

cnf(i_0_5285,plain,
    ( ~ is_Arr43961803e_indi(X1)
    | hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,X2),hAPP_A1637648121di_nat(X2,X1)) = X1
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X2),top_to1576102282i_bool)) ),
    inference(equality_inference,[],[4438]) ).

cnf(i_0_5286,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
    inference(equality_inference,[],[4458]) ).

cnf(i_0_5287,plain,
    ( ~ is_fun961089132t_bool(top_to565915683t_bool)
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),top_to565915683t_bool)) ),
    inference(equality_inference,[],[4462]) ).

cnf(i_0_5288,plain,
    ( ~ is_fun279392540l_bool(top_to1853035173l_bool)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),top_to1853035173l_bool)) ),
    inference(equality_inference,[],[4463]) ).

cnf(i_0_5289,plain,
    ( ~ is_fun158382675l_bool(top_to1714702858l_bool)
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),top_to1714702858l_bool)) ),
    inference(equality_inference,[],[4464]) ).

cnf(i_0_5290,plain,
    ( ~ is_fun288122577l_bool(top_to522745736l_bool)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),top_to522745736l_bool)) ),
    inference(equality_inference,[],[4465]) ).

cnf(i_0_5291,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,X1),hAPP_nat_nat(X1,X2)) = X2
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X1),top_top_fun_nat_bool)) ),
    inference(equality_inference,[],[4468]) ).

cnf(i_0_5292,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X1))),
    inference(equality_inference,[],[4469]) ).

cnf(i_0_5293,plain,
    ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X1)),
    inference(equality_inference,[],[4481]) ).

cnf(i_0_5294,plain,
    ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X1),X1)),
    inference(equality_inference,[],[4482]) ).

cnf(i_0_5295,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X1)),
    inference(equality_inference,[],[4486]) ).

cnf(i_0_5296,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X1)),
    inference(equality_inference,[],[4487]) ).

cnf(i_0_5297,plain,
    ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X1)),
    inference(equality_inference,[],[4489]) ).

cnf(i_0_5298,plain,
    ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X1),X1)),
    inference(equality_inference,[],[4490]) ).

cnf(i_0_5299,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
    inference(equality_inference,[],[4501]) ).

cnf(i_0_5300,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
    inference(equality_inference,[],[4502]) ).

cnf(i_0_5301,plain,
    ( ~ is_Arr43961803e_indi(X1)
    | ~ is_Arr43961803e_indi(X1)
    | X1 = X1
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(X2),top_to1576102282i_bool)) ),
    inference(equality_inference,[],[4504]) ).

cnf(i_0_5302,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
    inference(equality_inference,[],[4508]) ).

cnf(i_0_5303,plain,
    X1 = X1,
    inference(equality_inference,[],[4537]) ).

cnf(i_0_5304,plain,
    X1 = X1,
    inference(equality_inference,[],[4541]) ).

cnf(i_0_5305,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(X2),top_top_fun_nat_bool)) ),
    inference(equality_inference,[],[4568]) ).

cnf(i_0_5306,plain,
    ( ~ is_fun961089132t_bool(X1)
    | ~ is_fun961089132t_bool(X1)
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X1)) ),
    inference(equality_inference,[],[4584]) ).

cnf(i_0_5307,plain,
    ( ~ is_fun279392540l_bool(X1)
    | ~ is_fun279392540l_bool(X1)
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X1)) ),
    inference(equality_inference,[],[4588]) ).

cnf(i_0_5308,plain,
    ( ~ is_fun158382675l_bool(X1)
    | ~ is_fun158382675l_bool(X1)
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X1)) ),
    inference(equality_inference,[],[4592]) ).

cnf(i_0_5309,plain,
    ( ~ is_fun288122577l_bool(X1)
    | ~ is_fun288122577l_bool(X1)
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X1)) ),
    inference(equality_inference,[],[4596]) ).

cnf(i_0_5310,plain,
    ( ~ is_fun1568535512t_bool(X1)
    | ~ is_fun1568535512t_bool(X1)
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X1)) ),
    inference(equality_inference,[],[4600]) ).

cnf(i_0_5311,plain,
    ( ~ is_fun1236654035i_bool(X1)
    | ~ is_fun1236654035i_bool(X1)
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X1)) ),
    inference(equality_inference,[],[4604]) ).

cnf(i_0_5312,plain,
    ( ~ is_fun2093718614t_bool(X1)
    | ~ is_fun2093718614t_bool(X1)
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X1)) ),
    inference(equality_inference,[],[4607]) ).

cnf(i_0_5313,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X1))),
    inference(equality_inference,[],[4618]) ).

cnf(i_0_5314,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X1),X1)),
    inference(equality_inference,[],[4649]) ).

cnf(i_0_5315,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X1),X1)),
    inference(equality_inference,[],[4650]) ).

cnf(i_0_5316,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X1),X1)),
    inference(equality_inference,[],[4651]) ).

cnf(i_0_5317,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X1),X1)),
    inference(equality_inference,[],[4652]) ).

cnf(i_0_5318,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X1),X1)),
    inference(equality_inference,[],[4653]) ).

cnf(i_0_5319,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
    inference(equality_inference,[],[4663]) ).

cnf(i_0_5320,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
    inference(equality_inference,[],[4664]) ).

cnf(i_0_5321,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X1),X1)),
    inference(equality_inference,[],[4665]) ).

cnf(i_0_5322,plain,
    hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X1),X1)),
    inference(equality_inference,[],[4666]) ).

cnf(i_0_5323,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
    inference(equality_inference,[],[4672]) ).

cnf(i_0_5324,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
    inference(equality_inference,[],[4673]) ).

cnf(i_0_5325,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)),
    inference(equality_inference,[],[4674]) ).

cnf(i_0_5326,plain,
    ( ~ is_fun961089132t_bool(top_to565915683t_bool)
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),top_to565915683t_bool)) ),
    inference(equality_inference,[],[4675]) ).

cnf(i_0_5327,plain,
    ( ~ is_fun279392540l_bool(top_to1853035173l_bool)
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),top_to1853035173l_bool)) ),
    inference(equality_inference,[],[4676]) ).

cnf(i_0_5328,plain,
    ( ~ is_fun158382675l_bool(top_to1714702858l_bool)
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),top_to1714702858l_bool)) ),
    inference(equality_inference,[],[4677]) ).

cnf(i_0_5329,plain,
    ( ~ is_fun288122577l_bool(top_to522745736l_bool)
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),top_to522745736l_bool)) ),
    inference(equality_inference,[],[4678]) ).

cnf(i_0_5330,plain,
    ( ~ is_fun1568535512t_bool(top_to1257323279t_bool)
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),top_to1257323279t_bool)) ),
    inference(equality_inference,[],[4679]) ).

cnf(i_0_5331,plain,
    ( ~ is_fun1236654035i_bool(top_to1576102282i_bool)
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),top_to1576102282i_bool)) ),
    inference(equality_inference,[],[4680]) ).

cnf(i_0_5332,plain,
    ( ~ is_fun2093718614t_bool(top_to178429151t_bool)
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),top_to178429151t_bool)) ),
    inference(equality_inference,[],[4681]) ).

cnf(i_0_5333,plain,
    ( X1 = X1
    | X2 = zero_zero_nat ),
    inference(equality_inference,[],[4744]) ).

cnf(i_0_5334,plain,
    ( X1 = X1
    | X2 = zero_zero_nat ),
    inference(equality_inference,[],[4746]) ).

cnf(i_0_5335,plain,
    hAPP_nat_nat(times_times_nat(zero_zero_nat),X1) = hAPP_nat_nat(times_times_nat(zero_zero_nat),X2),
    inference(equality_inference,[],[4814]) ).

cnf(i_0_5336,plain,
    hAPP_nat_nat(times_times_nat(X1),zero_zero_nat) = hAPP_nat_nat(times_times_nat(X2),zero_zero_nat),
    inference(equality_inference,[],[4815]) ).

cnf(i_0_5337,plain,
    X1 = X1,
    inference(equality_inference,[],[4818]) ).

cnf(i_0_5338,plain,
    hAPP_nat_nat(times_times_nat(zero_zero_nat),X1) = zero_zero_nat,
    inference(equality_inference,[],[4980]) ).

cnf(i_0_5339,plain,
    hAPP_nat_nat(times_times_nat(X1),zero_zero_nat) = zero_zero_nat,
    inference(equality_inference,[],[4981]) ).

cnf(i_0_5340,plain,
    $false,
    inference(scs_inference,[],[i_0_3680,i_0_2801,i_0_2790]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SCT171+3 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32  % Computer : n021.cluster.edu
% 0.14/0.32  % Model    : x86_64 x86_64
% 0.14/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32  % Memory   : 8042.1875MB
% 0.14/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32  % CPULimit   : 300
% 0.14/0.32  % WCLimit    : 300
% 0.14/0.32  % DateTime   : Tue May  5 02:01:55 EDT 2026
% 0.14/0.32  % CPUTime    : 
% 0.14/0.33  % start to proof: theBenchmark
% 3.47/2.88  % Version  : CSE_E---1.7
% 3.47/2.88  % Problem  : theBenchmark.p
% 3.47/2.88  % SZS status Theorem for theBenchmark.p
% 3.47/2.88  % SZS output start CNFRefutation
% See solution above
% 3.65/3.04  % Total time : 2.544s
%------------------------------------------------------------------------------